10342_10423_10432_13042_13402_14023_14032_14302_31042_31402
Counting sequence:
1, 1, 2, 6, 24, 110, 542, 2799, 14975, 82426, 464439, 2668696, 15590947, 92387771, 554235797, 3360762215, 20572588024, 126994846167, 789843392407, 4945658400827, 31156847757346, 197372223749307, 1256639062895178, 8037899799839392, 51632123130113648, 332965680525489034, 2155032578334932181, 13994894183898326706, 91168577061355394739, 595647225999722818853, 3902285001349867314168, 25630676832602563200385, 168750297979027894412233, 1113552222620902815451600, 7363795447342770870024276, 48793973634981118848915115, 323933962268822275888080745, 2154412502267235584948639896, 14353009161052489617924532103, 95777054162532446361403123733, 640102958508432656579046888088, 4284261365582167429146407847753, 28715078846673643499581690646374, 192718858783377721118101392937498, 1295068202645806611822956329651290, 8713468485540653143192296684504060, 58694420454229649372904880591543694, 395811726652054941050534770747536186, 2672062675665504824067039994096571372, 18057267603795247049931889484242273044, 122148238577919318716662105283316738887, 827057219727443444863448375601195077799, 5605074856739946516319493725612049643318, 38019815052131568635628660407639944657501, 258111483792289314425130855364215285957490, 1753719671290416779479029082883022861639723, 11924934735502828139909917291176034514903801, 81148960920091763857381517069590213176187314, 552624023546942652401954534373071463918007564, 3766046677816087120567618720131602804469166364, 25682695426159398909229009068642334473387952776, 175260799257911026754772274406653653225948156508, 1196765440172003507802343061067218904234097758571, 8177199072063818235684798263031163513730786235798, 55906590100800096396033159634229849469903758308017, 382451478558112449607443689242669583357556020762879, 2617802959461458610243838053798885638182839625775330, 17928235001873062554664163196386412791060560526154930, 122848854181301746449421717990470286539250636794686782, 842230561444098915670473597279564549275383404691506668, 5777112147380986241337901635888587105989713683738549709, 39646457394441807477873656632871028120952784413368709915, 272211134884128787304334480810005388321656383429893185888, 1869862441638004994404884934435273169704718157405144489567, 12850211997269417933745588148033679722782664580583958967031, 88349193983529008182495936566177811191059217645537867800774, 607689261997218036768384253367139857602866992222924280630213, 4181599192087826677379738436560396191265317334902834866935983, 28785945319349210705128578223283092603983703568698773989669095, 198240049081480795157939375328673931255523617269742477216075235, 1365748792410113994631968371878767020714886161154675226062859316, 9412709589380091908036824874779771447633322631328833813752491557, 64896149108256453585961343839094715411796073489092245565854565671, 447589403535730801698019731559311588223662970900983679048137170921, 3088115767352736758617042238454470609707425060019358200557421270608, 21313594096370391975776184356826106074048294776494185880293333028665, 147151843517741731222042393367553306776211298763329824576384470719011, 1016289170785944208362952060146987555942706288054201337716403180416525, 7021149977601823827836332281033947734453284600260193693227945886520750, 48521638573011094030632834168251344172010713603640000916271740218082845, 335425380429882318002757863229369045100390740218661738299424116569515690, 2319459176441127863572362218314004358300983734634202391480981345766770395, 16043720392250620181684596838197600243593291798907704109158165069207525645, 111006460408586289415140933584312027435739213199885393797659074886092663170, 768269530730929266186120189016485955981974425353342797110630337612113396450, 5318615526745731165834217716204976308635514450311788795471084626263005067015, 36829917381384255334078351836511195385419857510762388078216122175188628640995, 255104227365235512684235493636522768141420607478862889328428654336431867962606, 1767449465767854097140213683956728290256956052325665562724565522096901673928611, 12248602494588707135493684422323898939368249964933074166434845090652120774755813, 84905157903463687171942611079592657677519517657909166358172690175300967526342552
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24547/
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[39,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[39,x]*F[8,x]
F[8,x] = F[337,x]+F[9,x]
F[9,x] = F[10,x]+F[336,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[39,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[11,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[39,x]
F[21,x,k[0]] = F[22,x,k[0]]+F[329,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[28,x]
F[23,x,k[0]] = F[0,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[27,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x] = F[0,x]+F[29,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[39,x]
F[32,x] = F[304,x]+F[33,x]
F[33,x] = F[34,x]+F[40,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[2,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[39,x]
F[38,x] = F[1,x]+F[36,x]
F[39,x] = x
F[40,x] = F[41,x]
F[41,x] = F[39,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[40,x]+F[5,x]
F[44,x] = F[45,x]
F[45,x] = F[39,x]*F[46,x]
F[46,x] = F[47,x,1]
F[48,x,k[0]] = F[39,x]*F[47,x,k[0]]*F[52,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[327,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[39,x]*F[52,x,k[0]]*F[55,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[27,x,k[0]]*F[52,x,k[0]]
F[55,x,k[0]] = F[324,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[203,x,k[0]]+F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[0,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[39,x]*F[61,x]
F[61,x] = F[44,x]+F[57,x]
F[62,x] = F[2,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[39,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[62,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[39,x]*F[69,x]
F[69,x] = F[44,x]+F[70,x]
F[70,x] = F[62,x]
F[71,x] = F[72,x]
F[72,x] = F[39,x]*F[73,x]
F[73,x] = F[74,x]+F[91,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[4,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[27,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[88,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]*F[87,x]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[0,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[39,x]*F[79,x,k[0]]
F[87,x] = F[1,x]+F[39,x]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[39,x]*F[52,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[58,x]+F[83,x,k[0]]
F[91,x] = F[92,x]
F[92,x] = F[39,x]*F[4,x]*F[93,x]
F[93,x] = F[94,x,1]
F[95,x,k[0]] = F[317,x]*F[39,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[323,x,k[0]]+F[96,x,k[0]]
F[97,x,k[0]] = F[319,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[123,x,k[0]]+F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[0,x]*F[4,x]
F[101,x] = F[102,x]
F[102,x] = F[0,x]*F[103,x]*F[39,x]
F[103,x] = 1/F[39,x]*F[104,x]
F[104,x] = F[105,x]
F[105,x] = -F[108,x]+F[106,x]
F[106,x] = 1/F[39,x]*F[107,x]
F[107,x] = F[63,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[2,x]+F[63,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[2,x]^2
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[39,x]
F[114,x] = F[115,x]+F[121,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[39,x]
F[118,x] = F[105,x]+F[119,x]
F[119,x] = F[110,x]+F[120,x]
F[120,x] = F[116,x]+F[2,x]
F[121,x] = F[122,x]
F[122,x] = F[103,x]*F[120,x]*F[39,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[311,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]+F[310,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[141,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]*F[134,x]*F[39,x]*F[52,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[134,x]*F[39,x]*F[52,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[4,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[27,x,k[0]]
F[133,x,k[0]] = F[132,x,k[0]]*F[39,x]
F[133,x,k[0]] = F[19,x,k[0]]
F[134,x] = F[135,x]+F[39,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]+F[2,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[39,x]
F[140,x] = F[2,x]+F[59,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[39,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[303,x,k[0]]
F[145,x,k[0]] = F[144,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[39,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[165,x,k[0]]
F[149,x,k[0]] = F[0,x]*F[148,x,k[0]]
F[150,x,k[0]] = F[149,x,k[0]]+F[163,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[39,x]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[160,x]
F[154,x,k[0]] = F[0,x]*F[155,x,k[0]]
F[155,x,k[0]] = F[156,x]+F[55,x,k[0]]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[2,x]+F[6,x]
F[158,x] = F[159,x]
F[159,x] = F[157,x]*F[38,x]*F[39,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[38,x]*F[4,x]
F[162,x] = F[138,x]+F[39,x]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[162,x]*F[38,x]*F[4,x]*F[52,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]*F[24,x,k[0]]
F[167,x,k[0]] = F[0,x]*F[166,x,k[0]]*F[39,x]
F[167,x,k[0]] = F[168,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]+F[295,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[39,x]
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[39,x]
F[172,x,k[0]] = F[173,x,k[0]]+F[294,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[39,x]
F[175,x,k[0]] = F[176,x,k[0]]+F[274,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[39,x]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[222,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]*F[2,x]
F[180,x,k[0]] = F[181,x,k[0]]+F[188,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[183,x,k[0]]
F[182,x,k[0]] = F[23,x,k[0]]*F[52,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[186,x,k[0]] = F[185,x,k[0]]*F[39,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[129,x,k[0]] = F[187,x,k[0]]+F[23,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[217,x,k[0]]
F[190,x,k[0]] = F[189,x,k[0]]*F[27,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[192,x,k[0]] = F[191,x,k[0]]+F[29,x]
F[192,x,k[0]] = F[193,x,k[0]]+F[194,x,k[0]]
F[193,x,k[0]] = F[2,x]*F[52,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[205,x,k[0]]
F[197,x,k[0]] = F[198,x]+F[201,x,k[0]]
F[198,x] = F[199,x]+F[29,x]
F[199,x] = F[200,x]
F[200,x] = F[39,x]*F[62,x]
F[201,x,k[0]] = F[202,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]*F[39,x]
F[126,x,k[0]] = F[203,x,k[0]]+F[204,x]
F[204,x] = F[0,x]+F[62,x]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]*F[39,x]
F[207,x,k[0]] = (F[208,x,k[0]]*k[0]-F[208,x,1])/(-1+k[0])
F[208,x,k[0]] = F[209,x,k[0]]+F[214,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[212,x,k[0]]
F[210,x,k[0]] = F[205,x,k[0]]+F[211,x,k[0]]
F[211,x,k[0]] = F[126,x,k[0]]+F[197,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[39,x]*F[55,x,k[0]]
F[215,x,k[0]] = F[212,x,k[0]]+F[214,x,k[0]]
F[216,x,k[0]] = F[215,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[216,x,k[0]] = F[171,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]*F[39,x]
F[166,x,k[0]] = F[219,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]+F[26,x,k[0]]
F[166,x,k[0]] = F[181,x,k[0]]+F[221,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]*F[39,x]
F[224,x,k[0]] = F[225,x,k[0]]+F[226,x,k[0]]
F[225,x,k[0]] = F[118,x]*F[180,x,k[0]]
F[226,x,k[0]] = F[166,x,k[0]]*F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[229,x]*F[39,x]
F[229,x] = F[230,x]+F[231,x]
F[230,x] = F[120,x]*F[58,x]
F[231,x] = F[232,x]
F[232,x] = F[120,x]*F[233,x]*F[39,x]
F[233,x] = 1/F[0,x]/F[39,x]*F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[236,x]+F[62,x]
F[236,x] = -F[273,x]+F[237,x]
F[237,x] = F[238,x]
F[238,x] = F[239,x]*F[39,x]
F[239,x] = 1/F[250,x]/F[39,x]*F[240,x]
F[240,x] = -F[254,x]+F[241,x]
F[241,x] = 1/F[39,x]*F[242,x]
F[242,x] = F[243,x]
F[243,x] = -F[246,x]+F[244,x]
F[244,x] = 1/F[39,x]*F[245,x]
F[245,x] = F[63,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[248,x]
F[248,x] = F[249,x]*F[39,x]
F[249,x] = F[250,x]+F[251,x]
F[250,x] = F[1,x]+F[247,x]
F[251,x] = F[252,x]+F[39,x]
F[252,x] = F[253,x]
F[253,x] = F[247,x]*F[39,x]
F[254,x] = F[255,x,1]
F[255,x,k[0]] = F[256,x,k[0]]+F[73,x]
F[256,x,k[0]] = F[257,x,k[0]]
F[257,x,k[0]] = F[258,x,k[0]]*F[27,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[261,x]
F[259,x,k[0]] = F[255,x,k[0]]*F[260,x,k[0]]
F[260,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[261,x] = F[262,x]
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]
F[264,x] = F[265,x]*F[39,x]
F[265,x] = F[266,x]+F[267,x]
F[266,x] = F[38,x]*F[4,x]
F[267,x] = F[268,x]
F[268,x] = F[269,x]*F[38,x]*F[39,x]
F[269,x] = F[239,x]+F[270,x]
F[270,x] = F[271,x]*F[4,x]
F[271,x] = F[272,x]
F[272,x] = F[265,x]*F[39,x]
F[273,x] = F[0,x]*F[2,x]
F[274,x,k[0]] = F[275,x,k[0]]
F[275,x,k[0]] = F[166,x,k[0]]*F[276,x]
F[276,x] = F[263,x]+F[277,x]
F[277,x] = -F[288,x]+F[278,x]
F[278,x] = 1/F[39,x]*F[279,x]
F[279,x] = F[280,x]
F[280,x] = -F[287,x]+F[281,x]
F[281,x] = F[282,x]+F[283,x]
F[282,x] = F[116,x]+F[2,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]*F[39,x]
F[285,x] = F[286,x]
F[286,x] = F[233,x]*F[39,x]
F[287,x] = F[2,x]*F[87,x]
F[288,x] = F[289,x]*F[87,x]
F[289,x] = F[281,x]+F[290,x]
F[290,x] = -F[293,x]+F[291,x]
F[291,x] = 1/F[39,x]*F[292,x]
F[292,x] = F[6,x]
F[293,x] = F[157,x]+F[283,x]
F[294,x,k[0]] = F[49,x,k[0]]
F[295,x,k[0]] = F[178,x,k[0]]+F[296,x,k[0]]
F[296,x,k[0]] = F[297,x,k[0]]
F[297,x,k[0]] = F[166,x,k[0]]*F[298,x]
F[298,x] = F[138,x]+F[299,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[39,x]
F[301,x] = F[277,x]+F[302,x]
F[302,x] = F[289,x]*F[39,x]
F[303,x,k[0]] = F[304,x]
F[304,x] = F[305,x]+F[307,x]
F[305,x] = F[15,x]+F[306,x]
F[306,x] = F[194,x,1]
F[307,x] = F[308,x]
F[308,x] = F[309,x]*F[39,x]
F[309,x] = F[173,x,1]
F[310,x] = F[4,x]+F[66,x]
F[311,x,k[0]] = F[312,x,k[0]]
F[312,x,k[0]] = F[313,x,k[0]]*F[39,x]
F[313,x,k[0]] = -k[0]*(F[314,x,1]-F[314,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[314,x,k[0]]+F[315,x]
F[315,x] = F[316,x]+F[318,x]
F[316,x] = F[317,x]*F[4,x]
F[317,x] = F[0,x]+F[282,x]
F[318,x] = F[101,x]+F[121,x]
F[319,x,k[0]] = F[320,x,k[0]]+F[321,x,k[0]]
F[320,x,k[0]] = F[120,x]*F[76,x,k[0]]
F[321,x,k[0]] = F[322,x,k[0]]
F[322,x,k[0]] = F[120,x]*F[39,x]*F[94,x,k[0]]
F[323,x,k[0]] = F[317,x]*F[76,x,k[0]]
F[324,x,k[0]] = F[325,x,k[0]]
F[325,x,k[0]] = F[326,x,k[0]]*F[39,x]
F[326,x,k[0]] = (F[47,x,k[0]]*k[0]-F[47,x,1])/(-1+k[0])
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[120,x]*F[166,x,k[0]]*F[39,x]
F[329,x,k[0]] = F[330,x,k[0]]
F[330,x,k[0]] = F[23,x,k[0]]*F[331,x,k[0]]*F[39,x]
F[332,x,k[0]] = F[331,x,k[0]]*F[39,x]
F[332,x,k[0]] = F[333,x,k[0]]
F[333,x,k[0]] = F[334,x,k[0]]*F[39,x]
F[335,x,k[0]] = F[27,x,k[0]]*F[334,x,k[0]]
F[335,x,k[0]] = F[123,x,k[0]]
F[336,x] = F[191,x,1]
F[337,x] = F[307,x]+F[43,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_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{337}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{336}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{39}\! \left(x \right)
F_{32}\! \left(x \right) = F_{304}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{40}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = x
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{47}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{327}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{39}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{39}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{39}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{44}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{62}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{39}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{91}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{52}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{95}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{39}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{319}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{0}\! \left(x \right) F_{103}\! \left(x \right) F_{39}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{63}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{39}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{121}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{39}\! \left(x \right)
F_{118}\! \left(x \right) = F_{105}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{110}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{103}\! \left(x \right) F_{120}\! \left(x \right) F_{39}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{310}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{134}\! \left(x \right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{134}\! \left(x \right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{39}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{39}\! \left(x \right)
F_{140}\! \left(x \right) = F_{2}\! \left(x \right)+F_{59}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{160}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{157}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{138}\! \left(x \right)+F_{39}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{162}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{166}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{295}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x \right)+F_{201}\! \left(x , y\right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{29}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{39}\! \left(x \right) F_{62}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{0}\! \left(x \right)+F_{62}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{207}\! \left(x , y\right) = -\frac{-F_{208}\! \left(x , y\right) y +F_{208}\! \left(x , 1\right)}{-1+y}
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{215}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{118}\! \left(x \right) F_{180}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{39}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{231}\! \left(x \right)
F_{230}\! \left(x \right) = F_{120}\! \left(x \right) F_{58}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{120}\! \left(x \right) F_{233}\! \left(x \right) F_{39}\! \left(x \right)
F_{233}\! \left(x \right) = \frac{F_{234}\! \left(x \right)}{F_{0}\! \left(x \right) F_{39}\! \left(x \right)}
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{62}\! \left(x \right)
F_{236}\! \left(x \right) = -F_{273}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right) F_{39}\! \left(x \right)
F_{239}\! \left(x \right) = \frac{F_{240}\! \left(x \right)}{F_{250}\! \left(x \right) F_{39}\! \left(x \right)}
F_{240}\! \left(x \right) = -F_{254}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = \frac{F_{242}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = -F_{246}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{245}\! \left(x \right) = F_{63}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right) F_{39}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{251}\! \left(x \right)
F_{250}\! \left(x \right) = F_{1}\! \left(x \right)+F_{247}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{39}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{247}\! \left(x \right) F_{39}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x , 1\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{261}\! \left(x \right)
F_{259}\! \left(x , y\right) = F_{255}\! \left(x , y\right) F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right) F_{39}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)+F_{267}\! \left(x \right)
F_{266}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{269}\! \left(x \right) = F_{239}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right) F_{4}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{265}\! \left(x \right) F_{39}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{263}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = \frac{F_{279}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{283}\! \left(x \right)
F_{282}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right) F_{39}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = F_{233}\! \left(x \right) F_{39}\! \left(x \right)
F_{287}\! \left(x \right) = F_{2}\! \left(x \right) F_{87}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right) F_{87}\! \left(x \right)
F_{289}\! \left(x \right) = F_{281}\! \left(x \right)+F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = \frac{F_{292}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{292}\! \left(x \right) = F_{6}\! \left(x \right)
F_{293}\! \left(x \right) = F_{157}\! \left(x \right)+F_{283}\! \left(x \right)
F_{294}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{138}\! \left(x \right)+F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{39}\! \left(x \right)
F_{301}\! \left(x \right) = F_{277}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{289}\! \left(x \right) F_{39}\! \left(x \right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{307}\! \left(x \right)
F_{305}\! \left(x \right) = F_{15}\! \left(x \right)+F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right) F_{39}\! \left(x \right)
F_{309}\! \left(x \right) = F_{173}\! \left(x , 1\right)
F_{310}\! \left(x \right) = F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{311}\! \left(x , y\right) = F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{313}\! \left(x , y\right) = -\frac{y \left(F_{314}\! \left(x , 1\right)-F_{314}\! \left(x , y\right)\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{314}\! \left(x , y\right)+F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)+F_{318}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{4}\! \left(x \right)
F_{317}\! \left(x \right) = F_{0}\! \left(x \right)+F_{282}\! \left(x \right)
F_{318}\! \left(x \right) = F_{101}\! \left(x \right)+F_{121}\! \left(x \right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{321}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{39}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{326}\! \left(x , y\right) = -\frac{-y F_{47}\! \left(x , y\right)+F_{47}\! \left(x , 1\right)}{-1+y}
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{166}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{331}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{331}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{335}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{334}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{336}\! \left(x \right) = F_{191}\! \left(x , 1\right)
F_{337}\! \left(x \right) = F_{307}\! \left(x \right)+F_{43}\! \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_39(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_39(x)*F_8(x))
Eq(F_8(x), F_337(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_336(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_39(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_11(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_39(x))
Eq(F_21(x, k_0), F_22(x, k_0) + F_329(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_28(x))
Eq(F_23(x, k_0), F_0(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_27(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x), F_0(x) + F_29(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_39(x))
Eq(F_32(x), F_304(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_40(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_2(x)*F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_39(x))
Eq(F_38(x), F_1(x) + F_36(x))
Eq(F_39(x), x)
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_39(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_40(x) + F_5(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_39(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_48(x, k_0), F_39(x)*F_47(x, k_0)*F_52(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_327(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_39(x)*F_52(x, k_0)*F_55(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_27(x, k_0)*F_52(x, k_0))
Eq(F_55(x, k_0), F_324(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_203(x, k_0) + F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_0(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_39(x)*F_61(x))
Eq(F_61(x), F_44(x) + F_57(x))
Eq(F_62(x), F_2(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_39(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_62(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_39(x)*F_69(x))
Eq(F_69(x), F_44(x) + F_70(x))
Eq(F_70(x), F_62(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_39(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_91(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_4(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_27(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_88(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0)*F_87(x))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_0(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_39(x)*F_79(x, k_0))
Eq(F_87(x), F_1(x) + F_39(x))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_39(x)*F_52(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_58(x) + F_83(x, k_0))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_39(x)*F_4(x)*F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_95(x, k_0), F_317(x)*F_39(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_323(x, k_0) + F_96(x, k_0))
Eq(F_97(x, k_0), F_319(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_123(x, k_0) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_0(x)*F_4(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_0(x)*F_103(x)*F_39(x))
Eq(F_103(x), F_104(x)/F_39(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_108(x))
Eq(F_106(x), F_107(x)/F_39(x))
Eq(F_107(x), F_63(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_2(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_2(x)**2)
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_39(x))
Eq(F_114(x), F_115(x) + F_121(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_39(x))
Eq(F_118(x), F_105(x) + F_119(x))
Eq(F_119(x), F_110(x) + F_120(x))
Eq(F_120(x), F_116(x) + F_2(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_103(x)*F_120(x)*F_39(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_311(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0) + F_310(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_141(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0)*F_134(x)*F_39(x)*F_52(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_134(x)*F_39(x)*F_52(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_4(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_27(x, k_0))
Eq(F_133(x, k_0), F_132(x, k_0)*F_39(x))
Eq(F_133(x, k_0), F_19(x, k_0))
Eq(F_134(x), F_135(x) + F_39(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x) + F_2(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_39(x))
Eq(F_140(x), F_2(x) + F_59(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_39(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_303(x, k_0))
Eq(F_145(x, k_0), F_144(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_39(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_165(x, k_0))
Eq(F_149(x, k_0), F_0(x)*F_148(x, k_0))
Eq(F_150(x, k_0), F_149(x, k_0) + F_163(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_39(x))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_160(x))
Eq(F_154(x, k_0), F_0(x)*F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x) + F_55(x, k_0))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_2(x) + F_6(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_157(x)*F_38(x)*F_39(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_38(x)*F_4(x))
Eq(F_162(x), F_138(x) + F_39(x))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_162(x)*F_38(x)*F_4(x)*F_52(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0)*F_24(x, k_0))
Eq(F_167(x, k_0), F_0(x)*F_166(x, k_0)*F_39(x))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0) + F_295(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_39(x))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_39(x))
Eq(F_172(x, k_0), F_173(x, k_0) + F_294(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_39(x))
Eq(F_175(x, k_0), F_176(x, k_0) + F_274(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_39(x))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_222(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0)*F_2(x))
Eq(F_180(x, k_0), F_181(x, k_0) + F_188(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_183(x, k_0))
Eq(F_182(x, k_0), F_23(x, k_0)*F_52(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_186(x, k_0), F_185(x, k_0)*F_39(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_129(x, k_0), F_187(x, k_0) + F_23(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_217(x, k_0))
Eq(F_190(x, k_0), F_189(x, k_0)*F_27(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_192(x, k_0), F_191(x, k_0) + F_29(x))
Eq(F_192(x, k_0), F_193(x, k_0) + F_194(x, k_0))
Eq(F_193(x, k_0), F_2(x)*F_52(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_205(x, k_0))
Eq(F_197(x, k_0), F_198(x) + F_201(x, k_0))
Eq(F_198(x), F_199(x) + F_29(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_39(x)*F_62(x))
Eq(F_201(x, k_0), F_202(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0)*F_39(x))
Eq(F_126(x, k_0), F_203(x, k_0) + F_204(x))
Eq(F_204(x), F_0(x) + F_62(x))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0)*F_39(x))
Eq(F_207(x, k_0), (-k_0*F_208(x, k_0) + F_208(x, 1))/(1 - k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_214(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_212(x, k_0))
Eq(F_210(x, k_0), F_205(x, k_0) + F_211(x, k_0))
Eq(F_211(x, k_0), F_126(x, k_0) + F_197(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_39(x)*F_55(x, k_0))
Eq(F_215(x, k_0), F_212(x, k_0) + F_214(x, k_0))
Eq(F_216(x, k_0), F_215(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_216(x, k_0), F_171(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0)*F_39(x))
Eq(F_166(x, k_0), F_219(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0) + F_26(x, k_0))
Eq(F_166(x, k_0), F_181(x, k_0) + F_221(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0)*F_39(x))
Eq(F_224(x, k_0), F_225(x, k_0) + F_226(x, k_0))
Eq(F_225(x, k_0), F_118(x)*F_180(x, k_0))
Eq(F_226(x, k_0), F_166(x, k_0)*F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_229(x)*F_39(x))
Eq(F_229(x), F_230(x) + F_231(x))
Eq(F_230(x), F_120(x)*F_58(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_120(x)*F_233(x)*F_39(x))
Eq(F_233(x), F_234(x)/(F_0(x)*F_39(x)))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_236(x) + F_62(x))
Eq(F_236(x), F_237(x) - F_273(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_239(x)*F_39(x))
Eq(F_239(x), F_240(x)/(F_250(x)*F_39(x)))
Eq(F_240(x), F_241(x) - F_254(x))
Eq(F_241(x), F_242(x)/F_39(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_244(x) - F_246(x))
Eq(F_244(x), F_245(x)/F_39(x))
Eq(F_245(x), F_63(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_249(x)*F_39(x))
Eq(F_249(x), F_250(x) + F_251(x))
Eq(F_250(x), F_1(x) + F_247(x))
Eq(F_251(x), F_252(x) + F_39(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_247(x)*F_39(x))
Eq(F_254(x), F_255(x, 1))
Eq(F_255(x, k_0), F_256(x, k_0) + F_73(x))
Eq(F_256(x, k_0), F_257(x, k_0))
Eq(F_257(x, k_0), F_258(x, k_0)*F_27(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_261(x))
Eq(F_259(x, k_0), F_255(x, k_0)*F_260(x, k_0))
Eq(F_260(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_261(x), F_262(x))
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_265(x)*F_39(x))
Eq(F_265(x), F_266(x) + F_267(x))
Eq(F_266(x), F_38(x)*F_4(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_269(x)*F_38(x)*F_39(x))
Eq(F_269(x), F_239(x) + F_270(x))
Eq(F_270(x), F_271(x)*F_4(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_265(x)*F_39(x))
Eq(F_273(x), F_0(x)*F_2(x))
Eq(F_274(x, k_0), F_275(x, k_0))
Eq(F_275(x, k_0), F_166(x, k_0)*F_276(x))
Eq(F_276(x), F_263(x) + F_277(x))
Eq(F_277(x), F_278(x) - F_288(x))
Eq(F_278(x), F_279(x)/F_39(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_281(x) - F_287(x))
Eq(F_281(x), F_282(x) + F_283(x))
Eq(F_282(x), F_116(x) + F_2(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x)*F_39(x))
Eq(F_285(x), F_286(x))
Eq(F_286(x), F_233(x)*F_39(x))
Eq(F_287(x), F_2(x)*F_87(x))
Eq(F_288(x), F_289(x)*F_87(x))
Eq(F_289(x), F_281(x) + F_290(x))
Eq(F_290(x), F_291(x) - F_293(x))
Eq(F_291(x), F_292(x)/F_39(x))
Eq(F_292(x), F_6(x))
Eq(F_293(x), F_157(x) + F_283(x))
Eq(F_294(x, k_0), F_49(x, k_0))
Eq(F_295(x, k_0), F_178(x, k_0) + F_296(x, k_0))
Eq(F_296(x, k_0), F_297(x, k_0))
Eq(F_297(x, k_0), F_166(x, k_0)*F_298(x))
Eq(F_298(x), F_138(x) + F_299(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_39(x))
Eq(F_301(x), F_277(x) + F_302(x))
Eq(F_302(x), F_289(x)*F_39(x))
Eq(F_303(x, k_0), F_304(x))
Eq(F_304(x), F_305(x) + F_307(x))
Eq(F_305(x), F_15(x) + F_306(x))
Eq(F_306(x), F_194(x, 1))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_309(x)*F_39(x))
Eq(F_309(x), F_173(x, 1))
Eq(F_310(x), F_4(x) + F_66(x))
Eq(F_311(x, k_0), F_312(x, k_0))
Eq(F_312(x, k_0), F_313(x, k_0)*F_39(x))
Eq(F_313(x, k_0), -F_314(x, 1) + (-k_0*F_314(x, k_0) + F_314(x, 1))/(1 - k_0))
Eq(F_97(x, k_0), F_314(x, k_0) + F_315(x))
Eq(F_315(x), F_316(x) + F_318(x))
Eq(F_316(x), F_317(x)*F_4(x))
Eq(F_317(x), F_0(x) + F_282(x))
Eq(F_318(x), F_101(x) + F_121(x))
Eq(F_319(x, k_0), F_320(x, k_0) + F_321(x, k_0))
Eq(F_320(x, k_0), F_120(x)*F_76(x, k_0))
Eq(F_321(x, k_0), F_322(x, k_0))
Eq(F_322(x, k_0), F_120(x)*F_39(x)*F_94(x, k_0))
Eq(F_323(x, k_0), F_317(x)*F_76(x, k_0))
Eq(F_324(x, k_0), F_325(x, k_0))
Eq(F_325(x, k_0), F_326(x, k_0)*F_39(x))
Eq(F_326(x, k_0), (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_120(x)*F_166(x, k_0)*F_39(x))
Eq(F_329(x, k_0), F_330(x, k_0))
Eq(F_330(x, k_0), F_23(x, k_0)*F_331(x, k_0)*F_39(x))
Eq(F_332(x, k_0), F_331(x, k_0)*F_39(x))
Eq(F_332(x, k_0), F_333(x, k_0))
Eq(F_333(x, k_0), F_334(x, k_0)*F_39(x))
Eq(F_335(x, k_0), F_27(x, k_0)*F_334(x, k_0))
Eq(F_335(x, k_0), F_123(x, k_0))
Eq(F_336(x), F_191(x, 1))
Eq(F_337(x), F_307(x) + F_43(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]]}], "iterative": false}
Specification JSON:
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"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": "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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "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": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"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": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "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], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "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, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "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": [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]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "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": "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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 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": [[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": "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": "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"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24864/
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[39,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[39,x]*F[8,x]
F[8,x] = F[337,x]+F[9,x]
F[9,x] = F[10,x]+F[336,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[39,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[11,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[39,x]
F[21,x,k[0]] = F[22,x,k[0]]+F[329,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[28,x]
F[23,x,k[0]] = F[0,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[27,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x] = F[0,x]+F[29,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[39,x]
F[32,x] = F[304,x]+F[33,x]
F[33,x] = F[34,x]+F[40,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[2,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[39,x]
F[38,x] = F[1,x]+F[36,x]
F[39,x] = x
F[40,x] = F[41,x]
F[41,x] = F[39,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[40,x]+F[5,x]
F[44,x] = F[45,x]
F[45,x] = F[39,x]*F[46,x]
F[46,x] = F[47,x,1]
F[48,x,k[0]] = F[39,x]*F[47,x,k[0]]*F[52,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[327,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[39,x]*F[52,x,k[0]]*F[55,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[27,x,k[0]]*F[52,x,k[0]]
F[55,x,k[0]] = F[324,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[203,x,k[0]]+F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[0,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[39,x]*F[61,x]
F[61,x] = F[44,x]+F[57,x]
F[62,x] = F[2,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[39,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[62,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[39,x]*F[69,x]
F[69,x] = F[44,x]+F[70,x]
F[70,x] = F[62,x]
F[71,x] = F[72,x]
F[72,x] = F[39,x]*F[73,x]
F[73,x] = F[74,x]+F[91,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[4,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[27,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[88,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]*F[87,x]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[0,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[39,x]*F[79,x,k[0]]
F[87,x] = F[1,x]+F[39,x]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[39,x]*F[52,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[58,x]+F[83,x,k[0]]
F[91,x] = F[92,x]
F[92,x] = F[39,x]*F[4,x]*F[93,x]
F[93,x] = F[94,x,1]
F[95,x,k[0]] = F[317,x]*F[39,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[323,x,k[0]]+F[96,x,k[0]]
F[97,x,k[0]] = F[319,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[123,x,k[0]]+F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[0,x]*F[4,x]
F[101,x] = F[102,x]
F[102,x] = F[0,x]*F[103,x]*F[39,x]
F[103,x] = 1/F[39,x]*F[104,x]
F[104,x] = F[105,x]
F[105,x] = -F[108,x]+F[106,x]
F[106,x] = 1/F[39,x]*F[107,x]
F[107,x] = F[63,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[2,x]+F[63,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[2,x]^2
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[39,x]
F[114,x] = F[115,x]+F[121,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[39,x]
F[118,x] = F[105,x]+F[119,x]
F[119,x] = F[110,x]+F[120,x]
F[120,x] = F[116,x]+F[2,x]
F[121,x] = F[122,x]
F[122,x] = F[103,x]*F[120,x]*F[39,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[311,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]+F[310,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[141,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]*F[134,x]*F[39,x]*F[52,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[134,x]*F[39,x]*F[52,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[4,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[27,x,k[0]]
F[133,x,k[0]] = F[132,x,k[0]]*F[39,x]
F[133,x,k[0]] = F[19,x,k[0]]
F[134,x] = F[135,x]+F[39,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]+F[2,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[39,x]
F[140,x] = F[2,x]+F[59,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[39,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[303,x,k[0]]
F[145,x,k[0]] = F[144,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[39,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[165,x,k[0]]
F[149,x,k[0]] = F[0,x]*F[148,x,k[0]]
F[150,x,k[0]] = F[149,x,k[0]]+F[163,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[39,x]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[160,x]
F[154,x,k[0]] = F[0,x]*F[155,x,k[0]]
F[155,x,k[0]] = F[156,x]+F[55,x,k[0]]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[2,x]+F[6,x]
F[158,x] = F[159,x]
F[159,x] = F[157,x]*F[38,x]*F[39,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[38,x]*F[4,x]
F[162,x] = F[138,x]+F[39,x]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[162,x]*F[38,x]*F[4,x]*F[52,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]*F[24,x,k[0]]
F[167,x,k[0]] = F[0,x]*F[166,x,k[0]]*F[39,x]
F[167,x,k[0]] = F[168,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]+F[295,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[39,x]
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[39,x]
F[172,x,k[0]] = F[173,x,k[0]]+F[294,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[39,x]
F[175,x,k[0]] = F[176,x,k[0]]+F[274,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[39,x]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[222,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]*F[2,x]
F[180,x,k[0]] = F[181,x,k[0]]+F[188,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[183,x,k[0]]
F[182,x,k[0]] = F[23,x,k[0]]*F[52,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[186,x,k[0]] = F[185,x,k[0]]*F[39,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[129,x,k[0]] = F[187,x,k[0]]+F[23,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[217,x,k[0]]
F[190,x,k[0]] = F[189,x,k[0]]*F[27,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[192,x,k[0]] = F[191,x,k[0]]+F[29,x]
F[192,x,k[0]] = F[193,x,k[0]]+F[194,x,k[0]]
F[193,x,k[0]] = F[2,x]*F[52,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[205,x,k[0]]
F[197,x,k[0]] = F[198,x]+F[201,x,k[0]]
F[198,x] = F[199,x]+F[29,x]
F[199,x] = F[200,x]
F[200,x] = F[39,x]*F[62,x]
F[201,x,k[0]] = F[202,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]*F[39,x]
F[126,x,k[0]] = F[203,x,k[0]]+F[204,x]
F[204,x] = F[0,x]+F[62,x]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]*F[39,x]
F[207,x,k[0]] = (F[208,x,k[0]]*k[0]-F[208,x,1])/(-1+k[0])
F[208,x,k[0]] = F[209,x,k[0]]+F[214,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[212,x,k[0]]
F[210,x,k[0]] = F[205,x,k[0]]+F[211,x,k[0]]
F[211,x,k[0]] = F[126,x,k[0]]+F[197,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[39,x]*F[55,x,k[0]]
F[215,x,k[0]] = F[212,x,k[0]]+F[214,x,k[0]]
F[216,x,k[0]] = F[215,x,k[0]]*F[39,x]*F[52,x,k[0]]
F[216,x,k[0]] = F[171,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]*F[39,x]
F[166,x,k[0]] = F[219,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]+F[26,x,k[0]]
F[166,x,k[0]] = F[181,x,k[0]]+F[221,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]*F[39,x]
F[224,x,k[0]] = F[225,x,k[0]]+F[226,x,k[0]]
F[225,x,k[0]] = F[118,x]*F[180,x,k[0]]
F[226,x,k[0]] = F[166,x,k[0]]*F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[229,x]*F[39,x]
F[229,x] = F[230,x]+F[231,x]
F[230,x] = F[120,x]*F[58,x]
F[231,x] = F[232,x]
F[232,x] = F[120,x]*F[233,x]*F[39,x]
F[233,x] = 1/F[0,x]/F[39,x]*F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[236,x]+F[62,x]
F[236,x] = -F[273,x]+F[237,x]
F[237,x] = F[238,x]
F[238,x] = F[239,x]*F[39,x]
F[239,x] = 1/F[250,x]/F[39,x]*F[240,x]
F[240,x] = -F[254,x]+F[241,x]
F[241,x] = 1/F[39,x]*F[242,x]
F[242,x] = F[243,x]
F[243,x] = -F[246,x]+F[244,x]
F[244,x] = 1/F[39,x]*F[245,x]
F[245,x] = F[63,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[248,x]
F[248,x] = F[249,x]*F[39,x]
F[249,x] = F[250,x]+F[251,x]
F[250,x] = F[1,x]+F[247,x]
F[251,x] = F[252,x]+F[39,x]
F[252,x] = F[253,x]
F[253,x] = F[247,x]*F[39,x]
F[254,x] = F[255,x,1]
F[255,x,k[0]] = F[256,x,k[0]]+F[73,x]
F[256,x,k[0]] = F[257,x,k[0]]
F[257,x,k[0]] = F[258,x,k[0]]*F[27,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[261,x]
F[259,x,k[0]] = F[255,x,k[0]]*F[260,x,k[0]]
F[260,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[261,x] = F[262,x]
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]
F[264,x] = F[265,x]*F[39,x]
F[265,x] = F[266,x]+F[267,x]
F[266,x] = F[38,x]*F[4,x]
F[267,x] = F[268,x]
F[268,x] = F[269,x]*F[38,x]*F[39,x]
F[269,x] = F[239,x]+F[270,x]
F[270,x] = F[271,x]*F[4,x]
F[271,x] = F[272,x]
F[272,x] = F[265,x]*F[39,x]
F[273,x] = F[0,x]*F[2,x]
F[274,x,k[0]] = F[275,x,k[0]]
F[275,x,k[0]] = F[166,x,k[0]]*F[276,x]
F[276,x] = F[263,x]+F[277,x]
F[277,x] = -F[288,x]+F[278,x]
F[278,x] = 1/F[39,x]*F[279,x]
F[279,x] = F[280,x]
F[280,x] = -F[287,x]+F[281,x]
F[281,x] = F[282,x]+F[283,x]
F[282,x] = F[116,x]+F[2,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]*F[39,x]
F[285,x] = F[286,x]
F[286,x] = F[233,x]*F[39,x]
F[287,x] = F[2,x]*F[87,x]
F[288,x] = F[289,x]*F[87,x]
F[289,x] = F[281,x]+F[290,x]
F[290,x] = -F[293,x]+F[291,x]
F[291,x] = 1/F[39,x]*F[292,x]
F[292,x] = F[6,x]
F[293,x] = F[157,x]+F[283,x]
F[294,x,k[0]] = F[49,x,k[0]]
F[295,x,k[0]] = F[178,x,k[0]]+F[296,x,k[0]]
F[296,x,k[0]] = F[297,x,k[0]]
F[297,x,k[0]] = F[166,x,k[0]]*F[298,x]
F[298,x] = F[138,x]+F[299,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[39,x]
F[301,x] = F[277,x]+F[302,x]
F[302,x] = F[289,x]*F[39,x]
F[303,x,k[0]] = F[304,x]
F[304,x] = F[305,x]+F[307,x]
F[305,x] = F[15,x]+F[306,x]
F[306,x] = F[194,x,1]
F[307,x] = F[308,x]
F[308,x] = F[309,x]*F[39,x]
F[309,x] = F[173,x,1]
F[310,x] = F[4,x]+F[66,x]
F[311,x,k[0]] = F[312,x,k[0]]
F[312,x,k[0]] = F[313,x,k[0]]*F[39,x]
F[313,x,k[0]] = -k[0]*(F[314,x,1]-F[314,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[314,x,k[0]]+F[315,x]
F[315,x] = F[316,x]+F[318,x]
F[316,x] = F[317,x]*F[4,x]
F[317,x] = F[0,x]+F[282,x]
F[318,x] = F[101,x]+F[121,x]
F[319,x,k[0]] = F[320,x,k[0]]+F[321,x,k[0]]
F[320,x,k[0]] = F[120,x]*F[76,x,k[0]]
F[321,x,k[0]] = F[322,x,k[0]]
F[322,x,k[0]] = F[120,x]*F[39,x]*F[94,x,k[0]]
F[323,x,k[0]] = F[317,x]*F[76,x,k[0]]
F[324,x,k[0]] = F[325,x,k[0]]
F[325,x,k[0]] = F[326,x,k[0]]*F[39,x]
F[326,x,k[0]] = (F[47,x,k[0]]*k[0]-F[47,x,1])/(-1+k[0])
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[120,x]*F[166,x,k[0]]*F[39,x]
F[329,x,k[0]] = F[330,x,k[0]]
F[330,x,k[0]] = F[23,x,k[0]]*F[331,x,k[0]]*F[39,x]
F[332,x,k[0]] = F[331,x,k[0]]*F[39,x]
F[332,x,k[0]] = F[333,x,k[0]]
F[333,x,k[0]] = F[334,x,k[0]]*F[39,x]
F[335,x,k[0]] = F[27,x,k[0]]*F[334,x,k[0]]
F[335,x,k[0]] = F[123,x,k[0]]
F[336,x] = F[191,x,1]
F[337,x] = F[307,x]+F[43,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_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{337}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{336}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{39}\! \left(x \right)
F_{32}\! \left(x \right) = F_{304}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{40}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = x
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{47}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{327}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{39}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{39}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{39}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{44}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{62}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{39}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{91}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{52}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{95}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{39}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{319}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{0}\! \left(x \right) F_{103}\! \left(x \right) F_{39}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{63}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{39}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{121}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{39}\! \left(x \right)
F_{118}\! \left(x \right) = F_{105}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{110}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{103}\! \left(x \right) F_{120}\! \left(x \right) F_{39}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{310}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{134}\! \left(x \right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{134}\! \left(x \right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{39}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{39}\! \left(x \right)
F_{140}\! \left(x \right) = F_{2}\! \left(x \right)+F_{59}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{160}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{157}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{138}\! \left(x \right)+F_{39}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{162}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{166}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{295}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x \right)+F_{201}\! \left(x , y\right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{29}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{39}\! \left(x \right) F_{62}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{0}\! \left(x \right)+F_{62}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{207}\! \left(x , y\right) = -\frac{-F_{208}\! \left(x , y\right) y +F_{208}\! \left(x , 1\right)}{-1+y}
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{39}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{215}\! \left(x , y\right) F_{39}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{118}\! \left(x \right) F_{180}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{39}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{231}\! \left(x \right)
F_{230}\! \left(x \right) = F_{120}\! \left(x \right) F_{58}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{120}\! \left(x \right) F_{233}\! \left(x \right) F_{39}\! \left(x \right)
F_{233}\! \left(x \right) = \frac{F_{234}\! \left(x \right)}{F_{0}\! \left(x \right) F_{39}\! \left(x \right)}
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{62}\! \left(x \right)
F_{236}\! \left(x \right) = -F_{273}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right) F_{39}\! \left(x \right)
F_{239}\! \left(x \right) = \frac{F_{240}\! \left(x \right)}{F_{250}\! \left(x \right) F_{39}\! \left(x \right)}
F_{240}\! \left(x \right) = -F_{254}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = \frac{F_{242}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = -F_{246}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{245}\! \left(x \right) = F_{63}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right) F_{39}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{251}\! \left(x \right)
F_{250}\! \left(x \right) = F_{1}\! \left(x \right)+F_{247}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{39}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{247}\! \left(x \right) F_{39}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x , 1\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{261}\! \left(x \right)
F_{259}\! \left(x , y\right) = F_{255}\! \left(x , y\right) F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right) F_{39}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)+F_{267}\! \left(x \right)
F_{266}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{269}\! \left(x \right) = F_{239}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right) F_{4}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{265}\! \left(x \right) F_{39}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{263}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = \frac{F_{279}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{283}\! \left(x \right)
F_{282}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right) F_{39}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = F_{233}\! \left(x \right) F_{39}\! \left(x \right)
F_{287}\! \left(x \right) = F_{2}\! \left(x \right) F_{87}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right) F_{87}\! \left(x \right)
F_{289}\! \left(x \right) = F_{281}\! \left(x \right)+F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = \frac{F_{292}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{292}\! \left(x \right) = F_{6}\! \left(x \right)
F_{293}\! \left(x \right) = F_{157}\! \left(x \right)+F_{283}\! \left(x \right)
F_{294}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{138}\! \left(x \right)+F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{39}\! \left(x \right)
F_{301}\! \left(x \right) = F_{277}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{289}\! \left(x \right) F_{39}\! \left(x \right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{307}\! \left(x \right)
F_{305}\! \left(x \right) = F_{15}\! \left(x \right)+F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right) F_{39}\! \left(x \right)
F_{309}\! \left(x \right) = F_{173}\! \left(x , 1\right)
F_{310}\! \left(x \right) = F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{311}\! \left(x , y\right) = F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{313}\! \left(x , y\right) = -\frac{y \left(F_{314}\! \left(x , 1\right)-F_{314}\! \left(x , y\right)\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{314}\! \left(x , y\right)+F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)+F_{318}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{4}\! \left(x \right)
F_{317}\! \left(x \right) = F_{0}\! \left(x \right)+F_{282}\! \left(x \right)
F_{318}\! \left(x \right) = F_{101}\! \left(x \right)+F_{121}\! \left(x \right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{321}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{39}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{326}\! \left(x , y\right) = -\frac{-y F_{47}\! \left(x , y\right)+F_{47}\! \left(x , 1\right)}{-1+y}
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{166}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{331}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{331}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{335}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{334}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{336}\! \left(x \right) = F_{191}\! \left(x , 1\right)
F_{337}\! \left(x \right) = F_{307}\! \left(x \right)+F_{43}\! \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_39(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_39(x)*F_8(x))
Eq(F_8(x), F_337(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_336(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_39(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_11(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_39(x))
Eq(F_21(x, k_0), F_22(x, k_0) + F_329(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_28(x))
Eq(F_23(x, k_0), F_0(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_27(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x), F_0(x) + F_29(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_39(x))
Eq(F_32(x), F_304(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_40(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_2(x)*F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_39(x))
Eq(F_38(x), F_1(x) + F_36(x))
Eq(F_39(x), x)
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_39(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_40(x) + F_5(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_39(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_48(x, k_0), F_39(x)*F_47(x, k_0)*F_52(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_327(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_39(x)*F_52(x, k_0)*F_55(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_27(x, k_0)*F_52(x, k_0))
Eq(F_55(x, k_0), F_324(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_203(x, k_0) + F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_0(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_39(x)*F_61(x))
Eq(F_61(x), F_44(x) + F_57(x))
Eq(F_62(x), F_2(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_39(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_62(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_39(x)*F_69(x))
Eq(F_69(x), F_44(x) + F_70(x))
Eq(F_70(x), F_62(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_39(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_91(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_4(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_27(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_88(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0)*F_87(x))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_0(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_39(x)*F_79(x, k_0))
Eq(F_87(x), F_1(x) + F_39(x))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_39(x)*F_52(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_58(x) + F_83(x, k_0))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_39(x)*F_4(x)*F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_95(x, k_0), F_317(x)*F_39(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_323(x, k_0) + F_96(x, k_0))
Eq(F_97(x, k_0), F_319(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_123(x, k_0) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_0(x)*F_4(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_0(x)*F_103(x)*F_39(x))
Eq(F_103(x), F_104(x)/F_39(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_108(x))
Eq(F_106(x), F_107(x)/F_39(x))
Eq(F_107(x), F_63(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_2(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_2(x)**2)
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_39(x))
Eq(F_114(x), F_115(x) + F_121(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_39(x))
Eq(F_118(x), F_105(x) + F_119(x))
Eq(F_119(x), F_110(x) + F_120(x))
Eq(F_120(x), F_116(x) + F_2(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_103(x)*F_120(x)*F_39(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_311(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0) + F_310(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_141(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0)*F_134(x)*F_39(x)*F_52(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_134(x)*F_39(x)*F_52(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_4(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_27(x, k_0))
Eq(F_133(x, k_0), F_132(x, k_0)*F_39(x))
Eq(F_133(x, k_0), F_19(x, k_0))
Eq(F_134(x), F_135(x) + F_39(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x) + F_2(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_39(x))
Eq(F_140(x), F_2(x) + F_59(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_39(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_303(x, k_0))
Eq(F_145(x, k_0), F_144(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_39(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_165(x, k_0))
Eq(F_149(x, k_0), F_0(x)*F_148(x, k_0))
Eq(F_150(x, k_0), F_149(x, k_0) + F_163(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_39(x))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_160(x))
Eq(F_154(x, k_0), F_0(x)*F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x) + F_55(x, k_0))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_2(x) + F_6(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_157(x)*F_38(x)*F_39(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_38(x)*F_4(x))
Eq(F_162(x), F_138(x) + F_39(x))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_162(x)*F_38(x)*F_4(x)*F_52(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0)*F_24(x, k_0))
Eq(F_167(x, k_0), F_0(x)*F_166(x, k_0)*F_39(x))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0) + F_295(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_39(x))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_39(x))
Eq(F_172(x, k_0), F_173(x, k_0) + F_294(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_39(x))
Eq(F_175(x, k_0), F_176(x, k_0) + F_274(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_39(x))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_222(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0)*F_2(x))
Eq(F_180(x, k_0), F_181(x, k_0) + F_188(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_183(x, k_0))
Eq(F_182(x, k_0), F_23(x, k_0)*F_52(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_186(x, k_0), F_185(x, k_0)*F_39(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_129(x, k_0), F_187(x, k_0) + F_23(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_217(x, k_0))
Eq(F_190(x, k_0), F_189(x, k_0)*F_27(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_192(x, k_0), F_191(x, k_0) + F_29(x))
Eq(F_192(x, k_0), F_193(x, k_0) + F_194(x, k_0))
Eq(F_193(x, k_0), F_2(x)*F_52(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_205(x, k_0))
Eq(F_197(x, k_0), F_198(x) + F_201(x, k_0))
Eq(F_198(x), F_199(x) + F_29(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_39(x)*F_62(x))
Eq(F_201(x, k_0), F_202(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0)*F_39(x))
Eq(F_126(x, k_0), F_203(x, k_0) + F_204(x))
Eq(F_204(x), F_0(x) + F_62(x))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0)*F_39(x))
Eq(F_207(x, k_0), (-k_0*F_208(x, k_0) + F_208(x, 1))/(1 - k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_214(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_212(x, k_0))
Eq(F_210(x, k_0), F_205(x, k_0) + F_211(x, k_0))
Eq(F_211(x, k_0), F_126(x, k_0) + F_197(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_39(x)*F_55(x, k_0))
Eq(F_215(x, k_0), F_212(x, k_0) + F_214(x, k_0))
Eq(F_216(x, k_0), F_215(x, k_0)*F_39(x)*F_52(x, k_0))
Eq(F_216(x, k_0), F_171(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0)*F_39(x))
Eq(F_166(x, k_0), F_219(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0) + F_26(x, k_0))
Eq(F_166(x, k_0), F_181(x, k_0) + F_221(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0)*F_39(x))
Eq(F_224(x, k_0), F_225(x, k_0) + F_226(x, k_0))
Eq(F_225(x, k_0), F_118(x)*F_180(x, k_0))
Eq(F_226(x, k_0), F_166(x, k_0)*F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_229(x)*F_39(x))
Eq(F_229(x), F_230(x) + F_231(x))
Eq(F_230(x), F_120(x)*F_58(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_120(x)*F_233(x)*F_39(x))
Eq(F_233(x), F_234(x)/(F_0(x)*F_39(x)))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_236(x) + F_62(x))
Eq(F_236(x), F_237(x) - F_273(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_239(x)*F_39(x))
Eq(F_239(x), F_240(x)/(F_250(x)*F_39(x)))
Eq(F_240(x), F_241(x) - F_254(x))
Eq(F_241(x), F_242(x)/F_39(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_244(x) - F_246(x))
Eq(F_244(x), F_245(x)/F_39(x))
Eq(F_245(x), F_63(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_249(x)*F_39(x))
Eq(F_249(x), F_250(x) + F_251(x))
Eq(F_250(x), F_1(x) + F_247(x))
Eq(F_251(x), F_252(x) + F_39(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_247(x)*F_39(x))
Eq(F_254(x), F_255(x, 1))
Eq(F_255(x, k_0), F_256(x, k_0) + F_73(x))
Eq(F_256(x, k_0), F_257(x, k_0))
Eq(F_257(x, k_0), F_258(x, k_0)*F_27(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_261(x))
Eq(F_259(x, k_0), F_255(x, k_0)*F_260(x, k_0))
Eq(F_260(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_261(x), F_262(x))
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_265(x)*F_39(x))
Eq(F_265(x), F_266(x) + F_267(x))
Eq(F_266(x), F_38(x)*F_4(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_269(x)*F_38(x)*F_39(x))
Eq(F_269(x), F_239(x) + F_270(x))
Eq(F_270(x), F_271(x)*F_4(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_265(x)*F_39(x))
Eq(F_273(x), F_0(x)*F_2(x))
Eq(F_274(x, k_0), F_275(x, k_0))
Eq(F_275(x, k_0), F_166(x, k_0)*F_276(x))
Eq(F_276(x), F_263(x) + F_277(x))
Eq(F_277(x), F_278(x) - F_288(x))
Eq(F_278(x), F_279(x)/F_39(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_281(x) - F_287(x))
Eq(F_281(x), F_282(x) + F_283(x))
Eq(F_282(x), F_116(x) + F_2(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x)*F_39(x))
Eq(F_285(x), F_286(x))
Eq(F_286(x), F_233(x)*F_39(x))
Eq(F_287(x), F_2(x)*F_87(x))
Eq(F_288(x), F_289(x)*F_87(x))
Eq(F_289(x), F_281(x) + F_290(x))
Eq(F_290(x), F_291(x) - F_293(x))
Eq(F_291(x), F_292(x)/F_39(x))
Eq(F_292(x), F_6(x))
Eq(F_293(x), F_157(x) + F_283(x))
Eq(F_294(x, k_0), F_49(x, k_0))
Eq(F_295(x, k_0), F_178(x, k_0) + F_296(x, k_0))
Eq(F_296(x, k_0), F_297(x, k_0))
Eq(F_297(x, k_0), F_166(x, k_0)*F_298(x))
Eq(F_298(x), F_138(x) + F_299(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_39(x))
Eq(F_301(x), F_277(x) + F_302(x))
Eq(F_302(x), F_289(x)*F_39(x))
Eq(F_303(x, k_0), F_304(x))
Eq(F_304(x), F_305(x) + F_307(x))
Eq(F_305(x), F_15(x) + F_306(x))
Eq(F_306(x), F_194(x, 1))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_309(x)*F_39(x))
Eq(F_309(x), F_173(x, 1))
Eq(F_310(x), F_4(x) + F_66(x))
Eq(F_311(x, k_0), F_312(x, k_0))
Eq(F_312(x, k_0), F_313(x, k_0)*F_39(x))
Eq(F_313(x, k_0), -F_314(x, 1) + (-k_0*F_314(x, k_0) + F_314(x, 1))/(1 - k_0))
Eq(F_97(x, k_0), F_314(x, k_0) + F_315(x))
Eq(F_315(x), F_316(x) + F_318(x))
Eq(F_316(x), F_317(x)*F_4(x))
Eq(F_317(x), F_0(x) + F_282(x))
Eq(F_318(x), F_101(x) + F_121(x))
Eq(F_319(x, k_0), F_320(x, k_0) + F_321(x, k_0))
Eq(F_320(x, k_0), F_120(x)*F_76(x, k_0))
Eq(F_321(x, k_0), F_322(x, k_0))
Eq(F_322(x, k_0), F_120(x)*F_39(x)*F_94(x, k_0))
Eq(F_323(x, k_0), F_317(x)*F_76(x, k_0))
Eq(F_324(x, k_0), F_325(x, k_0))
Eq(F_325(x, k_0), F_326(x, k_0)*F_39(x))
Eq(F_326(x, k_0), (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_120(x)*F_166(x, k_0)*F_39(x))
Eq(F_329(x, k_0), F_330(x, k_0))
Eq(F_330(x, k_0), F_23(x, k_0)*F_331(x, k_0)*F_39(x))
Eq(F_332(x, k_0), F_331(x, k_0)*F_39(x))
Eq(F_332(x, k_0), F_333(x, k_0))
Eq(F_333(x, k_0), F_334(x, k_0)*F_39(x))
Eq(F_335(x, k_0), F_27(x, k_0)*F_334(x, k_0))
Eq(F_335(x, k_0), F_123(x, k_0))
Eq(F_336(x), F_191(x, 1))
Eq(F_337(x), F_307(x) + F_43(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": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "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": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "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": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 2], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 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": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 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": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 2], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 2], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 1], [2, 2], [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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[2, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": 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"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": "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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "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": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"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": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "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], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "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, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "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": [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]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "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": "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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 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": [[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": "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": "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"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25141/
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[38,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[38,x]*F[8,x]
F[8,x] = F[337,x]+F[9,x]
F[9,x] = F[10,x]+F[336,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[38,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[11,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[38,x]
F[21,x,k[0]] = F[22,x,k[0]]+F[329,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[28,x]
F[23,x,k[0]] = F[0,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[27,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x] = F[0,x]+F[29,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[38,x]
F[32,x] = F[304,x]+F[33,x]
F[33,x] = F[34,x]+F[40,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[2,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[39,x]
F[38,x] = x
F[39,x] = F[1,x]+F[36,x]
F[40,x] = F[41,x]
F[41,x] = F[38,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[40,x]+F[5,x]
F[44,x] = F[45,x]
F[45,x] = F[38,x]*F[46,x]
F[46,x] = F[47,x,1]
F[48,x,k[0]] = F[38,x]*F[47,x,k[0]]*F[52,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[327,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[38,x]*F[52,x,k[0]]*F[55,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[27,x,k[0]]*F[52,x,k[0]]
F[55,x,k[0]] = F[324,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[203,x,k[0]]+F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[0,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[38,x]*F[61,x]
F[61,x] = F[44,x]+F[57,x]
F[62,x] = F[2,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[38,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[62,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[38,x]*F[69,x]
F[69,x] = F[44,x]+F[70,x]
F[70,x] = F[62,x]
F[71,x] = F[72,x]
F[72,x] = F[38,x]*F[73,x]
F[73,x] = F[74,x]+F[91,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[4,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[27,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[88,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]*F[87,x]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[0,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[27,x,k[0]]*F[81,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[38,x]*F[79,x,k[0]]
F[87,x] = F[1,x]+F[38,x]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[38,x]*F[52,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[58,x]+F[83,x,k[0]]
F[91,x] = F[92,x]
F[92,x] = F[38,x]*F[4,x]*F[93,x]
F[93,x] = F[94,x,1]
F[95,x,k[0]] = F[317,x]*F[38,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[323,x,k[0]]+F[96,x,k[0]]
F[97,x,k[0]] = F[319,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[123,x,k[0]]+F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[0,x]*F[4,x]
F[101,x] = F[102,x]
F[102,x] = F[0,x]*F[103,x]*F[38,x]
F[103,x] = 1/F[38,x]*F[104,x]
F[104,x] = F[105,x]
F[105,x] = -F[108,x]+F[106,x]
F[106,x] = 1/F[38,x]*F[107,x]
F[107,x] = F[63,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[2,x]+F[63,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[2,x]^2
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[38,x]
F[114,x] = F[115,x]+F[121,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[38,x]
F[118,x] = F[105,x]+F[119,x]
F[119,x] = F[110,x]+F[120,x]
F[120,x] = F[116,x]+F[2,x]
F[121,x] = F[122,x]
F[122,x] = F[103,x]*F[120,x]*F[38,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[311,x,k[0]]
F[125,x,k[0]] = F[124,x,k[0]]+F[310,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[141,x,k[0]]
F[127,x,k[0]] = F[126,x,k[0]]*F[134,x]*F[38,x]*F[52,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[134,x]*F[38,x]*F[52,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[4,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[27,x,k[0]]
F[133,x,k[0]] = F[132,x,k[0]]*F[38,x]
F[133,x,k[0]] = F[19,x,k[0]]
F[134,x] = F[135,x]+F[38,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]+F[2,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[38,x]
F[140,x] = F[2,x]+F[59,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[38,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[303,x,k[0]]
F[145,x,k[0]] = F[144,x,k[0]]*F[38,x]*F[52,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[38,x]
F[147,x,k[0]] = F[148,x,k[0]]+F[165,x,k[0]]
F[149,x,k[0]] = F[0,x]*F[148,x,k[0]]
F[150,x,k[0]] = F[149,x,k[0]]+F[163,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[38,x]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]*F[38,x]*F[52,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[160,x]
F[154,x,k[0]] = F[0,x]*F[155,x,k[0]]
F[155,x,k[0]] = F[156,x]+F[55,x,k[0]]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[2,x]+F[6,x]
F[158,x] = F[159,x]
F[159,x] = F[157,x]*F[38,x]*F[39,x]
F[160,x] = F[161,x]
F[161,x] = F[162,x]*F[39,x]*F[4,x]
F[162,x] = F[138,x]+F[38,x]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[162,x]*F[39,x]*F[4,x]*F[52,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]*F[24,x,k[0]]
F[167,x,k[0]] = F[0,x]*F[166,x,k[0]]*F[38,x]
F[167,x,k[0]] = F[168,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]+F[295,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[38,x]
F[170,x,k[0]] = F[171,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[38,x]
F[172,x,k[0]] = F[173,x,k[0]]+F[294,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[38,x]
F[175,x,k[0]] = F[176,x,k[0]]+F[274,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[38,x]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]+F[222,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]*F[2,x]
F[180,x,k[0]] = F[181,x,k[0]]+F[188,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[183,x,k[0]]
F[182,x,k[0]] = F[23,x,k[0]]*F[52,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[38,x]*F[52,x,k[0]]
F[186,x,k[0]] = F[185,x,k[0]]*F[38,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[129,x,k[0]] = F[187,x,k[0]]+F[23,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[217,x,k[0]]
F[190,x,k[0]] = F[189,x,k[0]]*F[27,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]
F[192,x,k[0]] = F[191,x,k[0]]+F[29,x]
F[192,x,k[0]] = F[193,x,k[0]]+F[194,x,k[0]]
F[193,x,k[0]] = F[2,x]*F[52,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[38,x]*F[52,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[205,x,k[0]]
F[197,x,k[0]] = F[198,x]+F[201,x,k[0]]
F[198,x] = F[199,x]+F[29,x]
F[199,x] = F[200,x]
F[200,x] = F[38,x]*F[62,x]
F[201,x,k[0]] = F[202,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]*F[38,x]
F[126,x,k[0]] = F[203,x,k[0]]+F[204,x]
F[204,x] = F[0,x]+F[62,x]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]*F[38,x]
F[207,x,k[0]] = (F[208,x,k[0]]*k[0]-F[208,x,1])/(-1+k[0])
F[208,x,k[0]] = F[209,x,k[0]]+F[214,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]+F[212,x,k[0]]
F[210,x,k[0]] = F[205,x,k[0]]+F[211,x,k[0]]
F[211,x,k[0]] = F[126,x,k[0]]+F[197,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[38,x]*F[55,x,k[0]]
F[215,x,k[0]] = F[212,x,k[0]]+F[214,x,k[0]]
F[216,x,k[0]] = F[215,x,k[0]]*F[38,x]*F[52,x,k[0]]
F[216,x,k[0]] = F[171,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]*F[38,x]
F[166,x,k[0]] = F[219,x,k[0]]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]+F[26,x,k[0]]
F[166,x,k[0]] = F[181,x,k[0]]+F[221,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]*F[38,x]
F[224,x,k[0]] = F[225,x,k[0]]+F[226,x,k[0]]
F[225,x,k[0]] = F[118,x]*F[180,x,k[0]]
F[226,x,k[0]] = F[166,x,k[0]]*F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[229,x]*F[38,x]
F[229,x] = F[230,x]+F[231,x]
F[230,x] = F[120,x]*F[58,x]
F[231,x] = F[232,x]
F[232,x] = F[120,x]*F[233,x]*F[38,x]
F[233,x] = 1/F[0,x]/F[38,x]*F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[236,x]+F[62,x]
F[236,x] = -F[273,x]+F[237,x]
F[237,x] = F[238,x]
F[238,x] = F[239,x]*F[38,x]
F[239,x] = 1/F[250,x]/F[38,x]*F[240,x]
F[240,x] = -F[254,x]+F[241,x]
F[241,x] = 1/F[38,x]*F[242,x]
F[242,x] = F[243,x]
F[243,x] = -F[246,x]+F[244,x]
F[244,x] = 1/F[38,x]*F[245,x]
F[245,x] = F[63,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[248,x]
F[248,x] = F[249,x]*F[38,x]
F[249,x] = F[250,x]+F[251,x]
F[250,x] = F[1,x]+F[247,x]
F[251,x] = F[252,x]+F[38,x]
F[252,x] = F[253,x]
F[253,x] = F[247,x]*F[38,x]
F[254,x] = F[255,x,1]
F[255,x,k[0]] = F[256,x,k[0]]+F[73,x]
F[256,x,k[0]] = F[257,x,k[0]]
F[257,x,k[0]] = F[258,x,k[0]]*F[27,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[261,x]
F[259,x,k[0]] = F[255,x,k[0]]*F[260,x,k[0]]
F[260,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[261,x] = F[262,x]
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]
F[264,x] = F[265,x]*F[38,x]
F[265,x] = F[266,x]+F[267,x]
F[266,x] = F[39,x]*F[4,x]
F[267,x] = F[268,x]
F[268,x] = F[269,x]*F[38,x]*F[39,x]
F[269,x] = F[239,x]+F[270,x]
F[270,x] = F[271,x]*F[4,x]
F[271,x] = F[272,x]
F[272,x] = F[265,x]*F[38,x]
F[273,x] = F[0,x]*F[2,x]
F[274,x,k[0]] = F[275,x,k[0]]
F[275,x,k[0]] = F[166,x,k[0]]*F[276,x]
F[276,x] = F[263,x]+F[277,x]
F[277,x] = -F[288,x]+F[278,x]
F[278,x] = 1/F[38,x]*F[279,x]
F[279,x] = F[280,x]
F[280,x] = -F[287,x]+F[281,x]
F[281,x] = F[282,x]+F[283,x]
F[282,x] = F[116,x]+F[2,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]*F[38,x]
F[285,x] = F[286,x]
F[286,x] = F[233,x]*F[38,x]
F[287,x] = F[2,x]*F[87,x]
F[288,x] = F[289,x]*F[87,x]
F[289,x] = F[281,x]+F[290,x]
F[290,x] = -F[293,x]+F[291,x]
F[291,x] = 1/F[38,x]*F[292,x]
F[292,x] = F[6,x]
F[293,x] = F[157,x]+F[283,x]
F[294,x,k[0]] = F[49,x,k[0]]
F[295,x,k[0]] = F[178,x,k[0]]+F[296,x,k[0]]
F[296,x,k[0]] = F[297,x,k[0]]
F[297,x,k[0]] = F[166,x,k[0]]*F[298,x]
F[298,x] = F[138,x]+F[299,x]
F[299,x] = F[300,x]
F[300,x] = F[301,x]*F[38,x]
F[301,x] = F[277,x]+F[302,x]
F[302,x] = F[289,x]*F[38,x]
F[303,x,k[0]] = F[304,x]
F[304,x] = F[305,x]+F[307,x]
F[305,x] = F[15,x]+F[306,x]
F[306,x] = F[194,x,1]
F[307,x] = F[308,x]
F[308,x] = F[309,x]*F[38,x]
F[309,x] = F[173,x,1]
F[310,x] = F[4,x]+F[66,x]
F[311,x,k[0]] = F[312,x,k[0]]
F[312,x,k[0]] = F[313,x,k[0]]*F[38,x]
F[313,x,k[0]] = -k[0]*(F[314,x,1]-F[314,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[314,x,k[0]]+F[315,x]
F[315,x] = F[316,x]+F[318,x]
F[316,x] = F[317,x]*F[4,x]
F[317,x] = F[0,x]+F[282,x]
F[318,x] = F[101,x]+F[121,x]
F[319,x,k[0]] = F[320,x,k[0]]+F[321,x,k[0]]
F[320,x,k[0]] = F[120,x]*F[76,x,k[0]]
F[321,x,k[0]] = F[322,x,k[0]]
F[322,x,k[0]] = F[120,x]*F[38,x]*F[94,x,k[0]]
F[323,x,k[0]] = F[317,x]*F[76,x,k[0]]
F[324,x,k[0]] = F[325,x,k[0]]
F[325,x,k[0]] = F[326,x,k[0]]*F[38,x]
F[326,x,k[0]] = (F[47,x,k[0]]*k[0]-F[47,x,1])/(-1+k[0])
F[327,x,k[0]] = F[328,x,k[0]]
F[328,x,k[0]] = F[120,x]*F[166,x,k[0]]*F[38,x]
F[329,x,k[0]] = F[330,x,k[0]]
F[330,x,k[0]] = F[23,x,k[0]]*F[331,x,k[0]]*F[38,x]
F[332,x,k[0]] = F[331,x,k[0]]*F[38,x]
F[332,x,k[0]] = F[333,x,k[0]]
F[333,x,k[0]] = F[334,x,k[0]]*F[38,x]
F[335,x,k[0]] = F[27,x,k[0]]*F[334,x,k[0]]
F[335,x,k[0]] = F[123,x,k[0]]
F[336,x] = F[191,x,1]
F[337,x] = F[307,x]+F[43,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_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{337}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{336}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{38}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x \right) = F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{38}\! \left(x \right)
F_{32}\! \left(x \right) = F_{304}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{40}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = x
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{38}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{47}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{327}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{324}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{38}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{38}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{38}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{44}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{62}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{91}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{87}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{52}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{95}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{38}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{323}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{319}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{0}\! \left(x \right) F_{103}\! \left(x \right) F_{38}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{63}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{2} \left(x \right)^{2}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{38}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{121}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{38}\! \left(x \right)
F_{118}\! \left(x \right) = F_{105}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{110}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{103}\! \left(x \right) F_{120}\! \left(x \right) F_{38}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{311}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{310}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{134}\! \left(x \right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{134}\! \left(x \right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{38}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{38}\! \left(x \right)
F_{140}\! \left(x \right) = F_{2}\! \left(x \right)+F_{59}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{148}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{160}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{157}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{138}\! \left(x \right)+F_{38}\! \left(x \right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{162}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{166}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{295}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{189}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{191}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x \right)+F_{201}\! \left(x , y\right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{29}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{38}\! \left(x \right) F_{62}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{203}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{203}\! \left(x , y\right)+F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{0}\! \left(x \right)+F_{62}\! \left(x \right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{207}\! \left(x , y\right) = -\frac{-F_{208}\! \left(x , y\right) y +F_{208}\! \left(x , 1\right)}{-1+y}
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{215}\! \left(x , y\right) F_{38}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right)+F_{226}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{118}\! \left(x \right) F_{180}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{38}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{231}\! \left(x \right)
F_{230}\! \left(x \right) = F_{120}\! \left(x \right) F_{58}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{120}\! \left(x \right) F_{233}\! \left(x \right) F_{38}\! \left(x \right)
F_{233}\! \left(x \right) = \frac{F_{234}\! \left(x \right)}{F_{0}\! \left(x \right) F_{38}\! \left(x \right)}
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{62}\! \left(x \right)
F_{236}\! \left(x \right) = -F_{273}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right) F_{38}\! \left(x \right)
F_{239}\! \left(x \right) = \frac{F_{240}\! \left(x \right)}{F_{250}\! \left(x \right) F_{38}\! \left(x \right)}
F_{240}\! \left(x \right) = -F_{254}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = \frac{F_{242}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = -F_{246}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = \frac{F_{245}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{245}\! \left(x \right) = F_{63}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right) F_{38}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{251}\! \left(x \right)
F_{250}\! \left(x \right) = F_{1}\! \left(x \right)+F_{247}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{38}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{247}\! \left(x \right) F_{38}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x , 1\right)
F_{255}\! \left(x , y\right) = F_{256}\! \left(x , y\right)+F_{73}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{261}\! \left(x \right)
F_{259}\! \left(x , y\right) = F_{255}\! \left(x , y\right) F_{260}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{265}\! \left(x \right) F_{38}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)+F_{267}\! \left(x \right)
F_{266}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right) F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{269}\! \left(x \right) = F_{239}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right) F_{4}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{265}\! \left(x \right) F_{38}\! \left(x \right)
F_{273}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{274}\! \left(x , y\right) = F_{275}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{263}\! \left(x \right)+F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = -F_{288}\! \left(x \right)+F_{278}\! \left(x \right)
F_{278}\! \left(x \right) = \frac{F_{279}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{281}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{283}\! \left(x \right)
F_{282}\! \left(x \right) = F_{116}\! \left(x \right)+F_{2}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right) F_{38}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = F_{233}\! \left(x \right) F_{38}\! \left(x \right)
F_{287}\! \left(x \right) = F_{2}\! \left(x \right) F_{87}\! \left(x \right)
F_{288}\! \left(x \right) = F_{289}\! \left(x \right) F_{87}\! \left(x \right)
F_{289}\! \left(x \right) = F_{281}\! \left(x \right)+F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = \frac{F_{292}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{292}\! \left(x \right) = F_{6}\! \left(x \right)
F_{293}\! \left(x \right) = F_{157}\! \left(x \right)+F_{283}\! \left(x \right)
F_{294}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{138}\! \left(x \right)+F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)
F_{300}\! \left(x \right) = F_{301}\! \left(x \right) F_{38}\! \left(x \right)
F_{301}\! \left(x \right) = F_{277}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{289}\! \left(x \right) F_{38}\! \left(x \right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{307}\! \left(x \right)
F_{305}\! \left(x \right) = F_{15}\! \left(x \right)+F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right) F_{38}\! \left(x \right)
F_{309}\! \left(x \right) = F_{173}\! \left(x , 1\right)
F_{310}\! \left(x \right) = F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{311}\! \left(x , y\right) = F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{313}\! \left(x , y\right) = -\frac{y \left(F_{314}\! \left(x , 1\right)-F_{314}\! \left(x , y\right)\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{314}\! \left(x , y\right)+F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)+F_{318}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{4}\! \left(x \right)
F_{317}\! \left(x \right) = F_{0}\! \left(x \right)+F_{282}\! \left(x \right)
F_{318}\! \left(x \right) = F_{101}\! \left(x \right)+F_{121}\! \left(x \right)
F_{319}\! \left(x , y\right) = F_{320}\! \left(x , y\right)+F_{321}\! \left(x , y\right)
F_{320}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{321}\! \left(x , y\right) = F_{322}\! \left(x , y\right)
F_{322}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{38}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{317}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = F_{325}\! \left(x , y\right)
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{326}\! \left(x , y\right) = -\frac{-y F_{47}\! \left(x , y\right)+F_{47}\! \left(x , 1\right)}{-1+y}
F_{327}\! \left(x , y\right) = F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = F_{120}\! \left(x \right) F_{166}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{329}\! \left(x , y\right) = F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{331}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{331}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{335}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{334}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{336}\! \left(x \right) = F_{191}\! \left(x , 1\right)
F_{337}\! \left(x \right) = F_{307}\! \left(x \right)+F_{43}\! \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_38(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_38(x)*F_8(x))
Eq(F_8(x), F_337(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_336(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_38(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_11(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_38(x))
Eq(F_21(x, k_0), F_22(x, k_0) + F_329(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_28(x))
Eq(F_23(x, k_0), F_0(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_27(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x), F_0(x) + F_29(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_38(x))
Eq(F_32(x), F_304(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_40(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_2(x)*F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_39(x))
Eq(F_38(x), x)
Eq(F_39(x), F_1(x) + F_36(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_38(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_40(x) + F_5(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_38(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_48(x, k_0), F_38(x)*F_47(x, k_0)*F_52(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_327(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_38(x)*F_52(x, k_0)*F_55(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_27(x, k_0)*F_52(x, k_0))
Eq(F_55(x, k_0), F_324(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_203(x, k_0) + F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_0(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_38(x)*F_61(x))
Eq(F_61(x), F_44(x) + F_57(x))
Eq(F_62(x), F_2(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_38(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_62(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_38(x)*F_69(x))
Eq(F_69(x), F_44(x) + F_70(x))
Eq(F_70(x), F_62(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_38(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_91(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_4(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_27(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_88(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0)*F_87(x))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_0(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_27(x, k_0)*F_81(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_38(x)*F_79(x, k_0))
Eq(F_87(x), F_1(x) + F_38(x))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_38(x)*F_52(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_58(x) + F_83(x, k_0))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_38(x)*F_4(x)*F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_95(x, k_0), F_317(x)*F_38(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_323(x, k_0) + F_96(x, k_0))
Eq(F_97(x, k_0), F_319(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_123(x, k_0) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_0(x)*F_4(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_0(x)*F_103(x)*F_38(x))
Eq(F_103(x), F_104(x)/F_38(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_108(x))
Eq(F_106(x), F_107(x)/F_38(x))
Eq(F_107(x), F_63(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_2(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_2(x)**2)
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_38(x))
Eq(F_114(x), F_115(x) + F_121(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_38(x))
Eq(F_118(x), F_105(x) + F_119(x))
Eq(F_119(x), F_110(x) + F_120(x))
Eq(F_120(x), F_116(x) + F_2(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_103(x)*F_120(x)*F_38(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_311(x, k_0))
Eq(F_125(x, k_0), F_124(x, k_0) + F_310(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_141(x, k_0))
Eq(F_127(x, k_0), F_126(x, k_0)*F_134(x)*F_38(x)*F_52(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_134(x)*F_38(x)*F_52(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_4(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_27(x, k_0))
Eq(F_133(x, k_0), F_132(x, k_0)*F_38(x))
Eq(F_133(x, k_0), F_19(x, k_0))
Eq(F_134(x), F_135(x) + F_38(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x) + F_2(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_38(x))
Eq(F_140(x), F_2(x) + F_59(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_38(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_303(x, k_0))
Eq(F_145(x, k_0), F_144(x, k_0)*F_38(x)*F_52(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_38(x))
Eq(F_147(x, k_0), F_148(x, k_0) + F_165(x, k_0))
Eq(F_149(x, k_0), F_0(x)*F_148(x, k_0))
Eq(F_150(x, k_0), F_149(x, k_0) + F_163(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_38(x))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_38(x)*F_52(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_160(x))
Eq(F_154(x, k_0), F_0(x)*F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x) + F_55(x, k_0))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_2(x) + F_6(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_157(x)*F_38(x)*F_39(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_162(x)*F_39(x)*F_4(x))
Eq(F_162(x), F_138(x) + F_38(x))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_162(x)*F_39(x)*F_4(x)*F_52(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0)*F_24(x, k_0))
Eq(F_167(x, k_0), F_0(x)*F_166(x, k_0)*F_38(x))
Eq(F_167(x, k_0), F_168(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0) + F_295(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_38(x))
Eq(F_170(x, k_0), F_171(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_38(x))
Eq(F_172(x, k_0), F_173(x, k_0) + F_294(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_38(x))
Eq(F_175(x, k_0), F_176(x, k_0) + F_274(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_38(x))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0) + F_222(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0)*F_2(x))
Eq(F_180(x, k_0), F_181(x, k_0) + F_188(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_183(x, k_0))
Eq(F_182(x, k_0), F_23(x, k_0)*F_52(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_38(x)*F_52(x, k_0))
Eq(F_186(x, k_0), F_185(x, k_0)*F_38(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_129(x, k_0), F_187(x, k_0) + F_23(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_217(x, k_0))
Eq(F_190(x, k_0), F_189(x, k_0)*F_27(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0))
Eq(F_192(x, k_0), F_191(x, k_0) + F_29(x))
Eq(F_192(x, k_0), F_193(x, k_0) + F_194(x, k_0))
Eq(F_193(x, k_0), F_2(x)*F_52(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_38(x)*F_52(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_205(x, k_0))
Eq(F_197(x, k_0), F_198(x) + F_201(x, k_0))
Eq(F_198(x), F_199(x) + F_29(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_38(x)*F_62(x))
Eq(F_201(x, k_0), F_202(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0)*F_38(x))
Eq(F_126(x, k_0), F_203(x, k_0) + F_204(x))
Eq(F_204(x), F_0(x) + F_62(x))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0)*F_38(x))
Eq(F_207(x, k_0), (-k_0*F_208(x, k_0) + F_208(x, 1))/(1 - k_0))
Eq(F_208(x, k_0), F_209(x, k_0) + F_214(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_212(x, k_0))
Eq(F_210(x, k_0), F_205(x, k_0) + F_211(x, k_0))
Eq(F_211(x, k_0), F_126(x, k_0) + F_197(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_38(x)*F_55(x, k_0))
Eq(F_215(x, k_0), F_212(x, k_0) + F_214(x, k_0))
Eq(F_216(x, k_0), F_215(x, k_0)*F_38(x)*F_52(x, k_0))
Eq(F_216(x, k_0), F_171(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0))
Eq(F_218(x, k_0), F_219(x, k_0)*F_38(x))
Eq(F_166(x, k_0), F_219(x, k_0) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0) + F_26(x, k_0))
Eq(F_166(x, k_0), F_181(x, k_0) + F_221(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0)*F_38(x))
Eq(F_224(x, k_0), F_225(x, k_0) + F_226(x, k_0))
Eq(F_225(x, k_0), F_118(x)*F_180(x, k_0))
Eq(F_226(x, k_0), F_166(x, k_0)*F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_229(x)*F_38(x))
Eq(F_229(x), F_230(x) + F_231(x))
Eq(F_230(x), F_120(x)*F_58(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_120(x)*F_233(x)*F_38(x))
Eq(F_233(x), F_234(x)/(F_0(x)*F_38(x)))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_236(x) + F_62(x))
Eq(F_236(x), F_237(x) - F_273(x))
Eq(F_237(x), F_238(x))
Eq(F_238(x), F_239(x)*F_38(x))
Eq(F_239(x), F_240(x)/(F_250(x)*F_38(x)))
Eq(F_240(x), F_241(x) - F_254(x))
Eq(F_241(x), F_242(x)/F_38(x))
Eq(F_242(x), F_243(x))
Eq(F_243(x), F_244(x) - F_246(x))
Eq(F_244(x), F_245(x)/F_38(x))
Eq(F_245(x), F_63(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_249(x)*F_38(x))
Eq(F_249(x), F_250(x) + F_251(x))
Eq(F_250(x), F_1(x) + F_247(x))
Eq(F_251(x), F_252(x) + F_38(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_247(x)*F_38(x))
Eq(F_254(x), F_255(x, 1))
Eq(F_255(x, k_0), F_256(x, k_0) + F_73(x))
Eq(F_256(x, k_0), F_257(x, k_0))
Eq(F_257(x, k_0), F_258(x, k_0)*F_27(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_261(x))
Eq(F_259(x, k_0), F_255(x, k_0)*F_260(x, k_0))
Eq(F_260(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_261(x), F_262(x))
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_265(x)*F_38(x))
Eq(F_265(x), F_266(x) + F_267(x))
Eq(F_266(x), F_39(x)*F_4(x))
Eq(F_267(x), F_268(x))
Eq(F_268(x), F_269(x)*F_38(x)*F_39(x))
Eq(F_269(x), F_239(x) + F_270(x))
Eq(F_270(x), F_271(x)*F_4(x))
Eq(F_271(x), F_272(x))
Eq(F_272(x), F_265(x)*F_38(x))
Eq(F_273(x), F_0(x)*F_2(x))
Eq(F_274(x, k_0), F_275(x, k_0))
Eq(F_275(x, k_0), F_166(x, k_0)*F_276(x))
Eq(F_276(x), F_263(x) + F_277(x))
Eq(F_277(x), F_278(x) - F_288(x))
Eq(F_278(x), F_279(x)/F_38(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_281(x) - F_287(x))
Eq(F_281(x), F_282(x) + F_283(x))
Eq(F_282(x), F_116(x) + F_2(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x)*F_38(x))
Eq(F_285(x), F_286(x))
Eq(F_286(x), F_233(x)*F_38(x))
Eq(F_287(x), F_2(x)*F_87(x))
Eq(F_288(x), F_289(x)*F_87(x))
Eq(F_289(x), F_281(x) + F_290(x))
Eq(F_290(x), F_291(x) - F_293(x))
Eq(F_291(x), F_292(x)/F_38(x))
Eq(F_292(x), F_6(x))
Eq(F_293(x), F_157(x) + F_283(x))
Eq(F_294(x, k_0), F_49(x, k_0))
Eq(F_295(x, k_0), F_178(x, k_0) + F_296(x, k_0))
Eq(F_296(x, k_0), F_297(x, k_0))
Eq(F_297(x, k_0), F_166(x, k_0)*F_298(x))
Eq(F_298(x), F_138(x) + F_299(x))
Eq(F_299(x), F_300(x))
Eq(F_300(x), F_301(x)*F_38(x))
Eq(F_301(x), F_277(x) + F_302(x))
Eq(F_302(x), F_289(x)*F_38(x))
Eq(F_303(x, k_0), F_304(x))
Eq(F_304(x), F_305(x) + F_307(x))
Eq(F_305(x), F_15(x) + F_306(x))
Eq(F_306(x), F_194(x, 1))
Eq(F_307(x), F_308(x))
Eq(F_308(x), F_309(x)*F_38(x))
Eq(F_309(x), F_173(x, 1))
Eq(F_310(x), F_4(x) + F_66(x))
Eq(F_311(x, k_0), F_312(x, k_0))
Eq(F_312(x, k_0), F_313(x, k_0)*F_38(x))
Eq(F_313(x, k_0), -F_314(x, 1) + (-k_0*F_314(x, k_0) + F_314(x, 1))/(1 - k_0))
Eq(F_97(x, k_0), F_314(x, k_0) + F_315(x))
Eq(F_315(x), F_316(x) + F_318(x))
Eq(F_316(x), F_317(x)*F_4(x))
Eq(F_317(x), F_0(x) + F_282(x))
Eq(F_318(x), F_101(x) + F_121(x))
Eq(F_319(x, k_0), F_320(x, k_0) + F_321(x, k_0))
Eq(F_320(x, k_0), F_120(x)*F_76(x, k_0))
Eq(F_321(x, k_0), F_322(x, k_0))
Eq(F_322(x, k_0), F_120(x)*F_38(x)*F_94(x, k_0))
Eq(F_323(x, k_0), F_317(x)*F_76(x, k_0))
Eq(F_324(x, k_0), F_325(x, k_0))
Eq(F_325(x, k_0), F_326(x, k_0)*F_38(x))
Eq(F_326(x, k_0), (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_327(x, k_0), F_328(x, k_0))
Eq(F_328(x, k_0), F_120(x)*F_166(x, k_0)*F_38(x))
Eq(F_329(x, k_0), F_330(x, k_0))
Eq(F_330(x, k_0), F_23(x, k_0)*F_331(x, k_0)*F_38(x))
Eq(F_332(x, k_0), F_331(x, k_0)*F_38(x))
Eq(F_332(x, k_0), F_333(x, k_0))
Eq(F_333(x, k_0), F_334(x, k_0)*F_38(x))
Eq(F_335(x, k_0), F_27(x, k_0)*F_334(x, k_0))
Eq(F_335(x, k_0), F_123(x, k_0))
Eq(F_336(x), F_191(x, 1))
Eq(F_337(x), F_307(x) + F_43(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "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": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "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": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 2], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 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": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 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": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 2], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 2], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 1], [2, 2], [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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 2], [2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 1], [2, 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[2, 2], [2, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2], [2, 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