02341_02413_02431_04213_04231_40213_40231
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3122, 17287, 97478, 556596, 3207368, 18612029, 108602988, 636569125, 3745209685, 22104636952, 130819311193, 776042034756, 4613134856146, 27472556812022, 163872288176391, 978904575230832, 5855166753432670, 35062807751902512, 210191092477802800, 1261246099616685009, 7574711074196257822, 45528162024769692705, 273850008787449834543, 1648306401570424539787, 9927327853471511656379, 59823950265043340150531, 360700927897249084103829, 2175864547139349061844406, 13131473320576768096610794, 79282631834507435889349807, 478864810214952230030473312, 2893386374481619684588218361, 17488314849841202472782172704, 105737197009362448673720655267, 639494774405063488084155567567, 3868720750842198004094536177895, 23410537915915288578274861447000, 141697460883917317063406706120070, 857853206984853126277351536624099, 5194672579722398429289668035003857, 31462422568869330321224440106860792, 190594257635710430399913577664372190, 1154798976443398457025424900516132327, 6998057119029642916259294114636412729, 42414952180825419048239246200173230869, 257114788950107603461856972464938881891, 1558827781041212009818159471437399901808, 9452112511452112128427883684382467022532, 57321318625375408915075851826957115995736, 347661888324442932845666995393232484736115, 2108865498044690824862084865213951925303860, 12793488862741465603537403553334296844107277, 77620246141934312072238665608300789209315059, 470982399062923227645189164121880405307812016, 2858089679120715756098771438971002103913271576, 17345488435324780228220061581514125499360302778, 105277323732933941020216194670365579189060569177, 639026663646270141137621973674675012853202751240, 3879156364417997915460520067079825107370339793649, 23549851372224231253880443480125693320920041705428, 142978302676479640158314795240859663663672094467897, 868124016588327789388875706681868929714882252388702, 5271348561783727298831091723325931140055224562206121, 32010227489321234179581552272068737806981498520849960, 194393460260938274911340742055470992729350554686057162, 1180590454148712924163811628786569489755125313889023208, 7170352952277446317704926475866484504692817146372050457, 43551631372250977542045737959762072859919640423960528770, 264539164946535658757106510548295837541554202427429852552, 1606927430889989600338474464070931912629257292594876204400, 9761631526053056334729827269732242459190138528720533660956, 59301760075993686007672450924911771675669308107836572154767, 360272399587676421950263703634617141519267581792964260617714, 2188829247017168942426331726225010651775043183662748764706742, 13298710715197061874326441318331253793816107123963687219689609, 80802216975574797682136859067028839803037636455012872737175501, 490967161738397763418147157905543496765686576794613957796233003, 2983296540844448911921860529102188912660493780934619694622345459, 18128197438480470516174363575131081880036920803951001312377547138, 110160646225002134387676783186315111435872639258263910367046197302, 669439667722797012451205531559031722472686493182442885110364221011, 4068262919951592972042033478976059156324528873603513806127199423412, 24723997549462678570115827188998307988513502913391709178259980288209, 150258833246469333976436020499469565551464121913509695068959841650106, 913213924468846803392632375255659866180502342761451926478744956641389, 5550291604953504739195237674550003673341312317836627966174202504753729, 33734123486275459160715448228404401421546639540180250089202562763488841, 205037369110469531972321016143984305153739829914761444927187922475143848, 1246252941453825518632539254789139178358293400171060909910074451170780623, 7575103969514627736041242191767137437902749039802462696745709583906892488, 46044724764133097791079883447698149330312641058067706183622993467020370882, 279885059809837857361266196293627534347662566299930901233471990924429705336, 1701326974867654966918760795616653901176452208632140945512327125243289673626, 10341982355217340454856666509315446166438347082302565971434134758755425668615
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25776/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[261,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[4,x]+F[8,x,k[0]]
F[8,x,k[0]] = F[89,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[16,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0]] = F[14,x,k[0]]+F[15,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[10,x,k[0]]
F[15,x,k[0]] = F[10,x,k[0]]
F[16,x,k[0]] = F[17,x]+F[18,x,k[0]]+F[58,x,k[0]]
F[17,x] = 0
F[18,x,k[0]] = F[12,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[44,x,k[0]]
F[20,x,k[0]] = F[16,x,k[0]]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[3,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[1,x]+F[21,x]
F[25,x] = F[26,x]+F[31,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[3,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[26,x]
F[30,x] = F[26,x]
F[31,x] = F[17,x]+F[32,x]+F[36,x]
F[32,x] = F[3,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[21,x]+F[31,x]
F[35,x] = F[31,x]
F[36,x] = F[3,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[26,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[3,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[21,x]+F[39,x]
F[43,x] = F[39,x]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[17,x]+F[46,x,k[0]]+F[50,x,k[0]]
F[46,x,k[0]] = F[12,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[21,x]+F[45,x,k[0]]
F[49,x,k[0]] = F[45,x,k[0]]
F[50,x,k[0]] = F[3,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[10,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[12,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]
F[56,x,k[0]] = F[21,x]+F[53,x,k[0]]
F[57,x,k[0]] = F[53,x,k[0]]
F[58,x,k[0]] = F[3,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[61,x,k[0]]
F[60,x,k[0]] = F[10,x,k[0]]+F[45,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[70,x,k[0]]
F[62,x,k[0]] = F[17,x]+F[63,x,k[0]]+F[66,x,k[0]]
F[63,x,k[0]] = F[12,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[26,x]+F[62,x,k[0]]
F[66,x,k[0]] = F[3,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[69,x,k[0]]
F[68,x,k[0]] = F[10,x,k[0]]
F[69,x,k[0]] = F[62,x,k[0]]
F[70,x,k[0]] = F[17,x]+F[71,x,k[0]]+F[74,x,k[0]]+F[78,x,k[0]]
F[71,x,k[0]] = F[12,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[31,x]+F[70,x,k[0]]
F[74,x,k[0]] = F[3,x]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[77,x,k[0]]
F[76,x,k[0]] = F[45,x,k[0]]
F[77,x,k[0]] = F[70,x,k[0]]
F[78,x,k[0]] = F[3,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[62,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = 2*F[17,x]+F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[12,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[39,x]+F[81,x,k[0]]
F[85,x,k[0]] = F[3,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]+F[88,x,k[0]]
F[87,x,k[0]] = F[53,x,k[0]]
F[88,x,k[0]] = F[81,x,k[0]]
F[89,x,k[0]] = F[165,x,k[0]]+F[17,x]+F[258,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[3,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[163,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[9,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[102,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[17,x]+F[95,x,k[0]]+F[98,x,k[0]]
F[95,x,k[0]] = F[3,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[10,x,k[0]]+F[94,x,k[0]]
F[98,x,k[0]] = F[12,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[101,x,k[0]]
F[100,x,k[0]] = F[26,x]
F[101,x,k[0]] = F[94,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]+F[129,x,k[0]]+F[17,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[3,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[102,x,k[0]]+F[16,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[109,x,k[0]]
F[108,x,k[0]] = F[31,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[114,x,k[0]]+F[118,x,k[0]]+F[17,x]
F[111,x,k[0]] = F[112,x,k[0]]*F[3,x]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[110,x,k[0]]+F[45,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[12,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[117,x,k[0]]
F[116,x,k[0]] = F[31,x]
F[117,x,k[0]] = F[110,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[3,x]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[94,x,k[0]]
F[121,x,k[0]] = 2*F[17,x]+F[122,x,k[0]]+F[125,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]*F[3,x]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[121,x,k[0]]+F[53,x,k[0]]
F[125,x,k[0]] = F[12,x,k[0]]*F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[128,x,k[0]]
F[127,x,k[0]] = F[39,x]
F[128,x,k[0]] = F[121,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[3,x]
F[130,x,k[0]] = F[131,x,k[0]]+F[132,x,k[0]]
F[131,x,k[0]] = F[110,x,k[0]]+F[94,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[142,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[137,x,k[0]]+F[138,x,k[0]]+F[17,x]
F[134,x,k[0]] = F[135,x,k[0]]*F[3,x]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[133,x,k[0]]+F[62,x,k[0]]
F[137,x,k[0]] = 0
F[138,x,k[0]] = F[139,x,k[0]]*F[3,x]
F[139,x,k[0]] = F[140,x,k[0]]+F[141,x,k[0]]
F[140,x,k[0]] = F[94,x,k[0]]
F[141,x,k[0]] = F[133,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]+F[146,x,k[0]]+F[147,x,k[0]]+F[151,x,k[0]]+F[17,x]
F[143,x,k[0]] = F[144,x,k[0]]*F[3,x]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[142,x,k[0]]+F[70,x,k[0]]
F[146,x,k[0]] = 0
F[147,x,k[0]] = F[148,x,k[0]]*F[3,x]
F[148,x,k[0]] = F[149,x,k[0]]+F[150,x,k[0]]
F[149,x,k[0]] = F[110,x,k[0]]
F[150,x,k[0]] = F[142,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[3,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[133,x,k[0]]+F[154,x,k[0]]
F[154,x,k[0]] = 2*F[17,x]+F[155,x,k[0]]+F[158,x,k[0]]+F[159,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[3,x]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[154,x,k[0]]+F[81,x,k[0]]
F[158,x,k[0]] = 0
F[159,x,k[0]] = F[160,x,k[0]]*F[3,x]
F[160,x,k[0]] = F[161,x,k[0]]+F[162,x,k[0]]
F[161,x,k[0]] = F[121,x,k[0]]
F[162,x,k[0]] = F[154,x,k[0]]
F[163,x,k[0]] = F[164,x,1,k[0]]
F[164,x,k[0],k[1]] = k[1]*(F[89,x,k[0]]-F[89,x,k[1]])/(-k[1]+k[0])
F[165,x,k[0]] = F[12,x,k[0]]*F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]+F[257,x,k[0]]
F[167,x,k[0]] = F[168,x]+F[89,x,k[0]]
F[168,x] = F[169,x]+F[17,x]+F[5,x]
F[169,x] = F[170,x,1]
F[170,x,k[0]] = F[171,x,k[0]]*F[3,x]
F[171,x,k[0]] = F[17,x]+F[172,x,k[0]]+F[193,x,k[0]]+F[238,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]*F[3,x]
F[173,x,k[0]] = F[174,x,k[0]]+F[6,x]
F[174,x,k[0]] = F[17,x]+F[175,x,k[0]]+F[224,x,k[0]]+F[225,x,k[0]]+F[235,x,k[0]]
F[175,x,k[0]] = F[176,x,1,k[0]]
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]*F[3,x]
F[177,x,k[0],k[1]] = F[178,x,1,k[0],k[1]]
F[178,x,k[0],k[1],k[2]] = (F[179,x,k[0],k[2]]*k[0]-F[179,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[179,x,k[0],k[1]] = F[17,x]+F[176,x,k[0],k[1]]+F[180,x,k[0],k[1]]+F[182,x,k[1],k[0]]+F[222,x,k[0],k[1]]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]
F[181,x,k[0],k[1]] = F[12,x,k[0]]*F[179,x,k[0],k[1]]
F[182,x,k[0],k[1]] = F[12,x,k[0]]*F[183,x,k[1],k[0]]
F[183,x,k[0],k[1]] = (-F[184,x,1,k[1]]*k[1]+F[184,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[184,x,k[0],k[1]] = F[185,x,k[0],k[1]]+F[188,x,k[0],k[1]]
F[185,x,k[0],k[1]] = F[186,x,k[1]]+F[187,x,k[0],k[1]]
F[186,x,k[0]] = F[24,x]+F[60,x,k[0]]
F[187,x,k[0],k[1]] = F[60,x,k[0]*k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1],1]
F[189,x,k[0],k[1],k[2]] = F[171,x,k[0]*k[1]]+F[190,x,k[0],k[1],k[2]]
F[190,x,k[0],k[1],k[2]] = F[191,x,k[1]*k[2]]
F[191,x,k[0]] = F[17,x]+F[192,x,k[0]]+F[193,x,k[0]]+F[197,x,k[0]]
F[192,x,k[0]] = F[181,x,1,k[0]]
F[193,x,k[0]] = F[12,x,k[0]]*F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0],1]
F[196,x,k[0],k[1]] = F[188,x,k[1],k[0]]
F[197,x,k[0]] = F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]*F[3,x]
F[199,x,k[0]] = 2*F[17,x]+F[200,x,k[0]]+F[218,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]*F[3,x]
F[201,x,k[0]] = 2*F[17,x]+F[202,x,k[0]]+F[216,x,k[0]]+F[217,x,k[0]]
F[202,x,k[0]] = F[203,x,k[0]]*F[3,x]
F[203,x,k[0]] = F[204,x,1,k[0]]
F[204,x,k[0],k[1]] = 1/(-1+k[0])*(F[205,x,k[0],k[1]]*k[0]-F[205,x,1,k[1]])
F[205,x,k[0],k[1]] = 2*F[17,x]+F[206,x,k[0],k[1]]+F[207,x,k[0],k[1]]+F[209,x,k[1],k[0]]
F[206,x,k[0],k[1]] = F[204,x,k[0],k[1]]*F[3,x]
F[207,x,k[0],k[1]] = F[208,x,k[0],k[1]]
F[208,x,k[0],k[1]] = F[12,x,k[0]]*F[205,x,k[0],k[1]]
F[209,x,k[0],k[1]] = F[12,x,k[0]]*F[210,x,k[1],k[0]]
F[210,x,k[0],k[1]] = F[211,x,k[0],k[1]]+F[214,x,k[0],k[1]]
F[211,x,k[0],k[1]] = F[212,x,k[0]]+F[213,x,k[0],k[1]]
F[212,x,k[0]] = F[171,x,k[0]]+F[186,x,k[0]]
F[213,x,k[0],k[1]] = F[205,x,k[0],k[1]]
F[214,x,k[0],k[1]] = F[215,x,k[1]]
F[215,x,k[0]] = F[199,x,k[0]]+F[52,x,k[0]]
F[216,x,k[0]] = F[200,x,k[0]]
F[217,x,k[0]] = F[209,x,k[0],1]
F[218,x,k[0]] = F[12,x,k[0]]*F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]+F[221,x,k[0]]
F[220,x,k[0]] = F[168,x]+F[199,x,k[0]]
F[221,x,k[0]] = F[199,x,k[0]]
F[222,x,k[0],k[1]] = F[223,x,k[0],k[1]]
F[223,x,k[0],k[1]] = F[213,x,k[0],k[1]]*F[3,x]
F[224,x,k[0]] = F[192,x,k[0]]
F[225,x,k[0]] = F[12,x,k[0]]*F[226,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]+F[233,x,k[0]]
F[227,x,k[0]] = F[228,x,k[0]]+F[230,x,k[0]]
F[228,x,k[0]] = F[186,x,k[0]]+F[229,x,k[0]]
F[229,x,k[0]] = F[60,x,k[0]]
F[230,x,k[0]] = F[231,x,k[0]]+F[232,x,k[0]]
F[231,x,k[0]] = F[25,x]
F[232,x,k[0]] = F[131,x,k[0]]
F[233,x,k[0]] = F[234,x,1,k[0]]
F[234,x,k[0],k[1]] = (-F[188,x,1,k[1]]*k[1]+F[188,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[235,x,k[0]] = F[236,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]*F[3,x]
F[237,x,k[0]] = F[201,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]*F[3,x]
F[239,x,k[0]] = F[17,x]+F[218,x,k[0]]+F[240,x,k[0]]+F[247,x]+F[248,x]
F[240,x,k[0]] = F[241,x,k[0]]*F[3,x]
F[241,x,k[0]] = F[242,x,k[0]]+F[244,x,k[0]]
F[242,x,k[0]] = F[243,x,1,k[0]]
F[243,x,k[0],k[1]] = F[205,x,k[0],k[1]]+F[7,x,k[0]]
F[244,x,k[0]] = F[245,x]
F[245,x] = F[246,x,1]
F[246,x,k[0]] = F[174,x,k[0]]
F[247,x] = F[193,x,1]
F[248,x] = F[249,x]*F[3,x]
F[249,x] = F[250,x]
F[250,x] = F[251,x,1]
F[251,x,k[0]] = F[252,x,k[0]]
F[252,x,k[0]] = F[253,x]+F[256,x,k[0]]
F[253,x] = F[254,x]
F[254,x] = F[255,x,1]
F[255,x,k[0]] = F[220,x,k[0]]
F[256,x,k[0]] = F[191,x,k[0]]
F[257,x,k[0]] = F[191,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]*F[3,x]
F[259,x,k[0]] = F[260,x,k[0],1]
F[260,x,k[0],k[1]] = k[0]*(F[191,x,k[0]]-F[191,x,k[1]])/(-k[1]+k[0])
F[261,x] = F[262,x,1]
F[262,x,k[0]] = F[212,x,k[0]]*F[3,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{261}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{89}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{18}\! \left(x , y_{0}\right)+F_{58}\! \left(x , y_{0}\right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{3}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{3}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{3}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{26}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)
F_{44}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)+F_{50}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right)+F_{45}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)+F_{70}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{63}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{26}\! \left(x \right)+F_{62}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{71}\! \left(x , y_{0}\right)+F_{74}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{72}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = F_{73}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{31}\! \left(x \right)+F_{70}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = 2 F_{17}\! \left(x \right)+F_{82}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{39}\! \left(x \right)+F_{81}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{86}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{87}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{81}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{165}\! \left(x , y_{0}\right)+F_{17}\! \left(x \right)+F_{258}\! \left(x , y_{0}\right)+F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{91}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{163}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{9}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{95}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right)+F_{101}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{26}\! \left(x \right)
F_{101}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right)+F_{106}\! \left(x , y_{0}\right)+F_{129}\! \left(x , y_{0}\right)+F_{17}\! \left(x \right)
F_{103}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x , y_{0}\right) F_{12}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)+F_{109}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{31}\! \left(x \right)
F_{109}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right)+F_{114}\! \left(x , y_{0}\right)+F_{118}\! \left(x , y_{0}\right)+F_{17}\! \left(x \right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{112}\! \left(x , y_{0}\right) = F_{113}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}\right) = F_{115}\! \left(x , y_{0}\right) F_{12}\! \left(x , y_{0}\right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right)+F_{117}\! \left(x , y_{0}\right)
F_{116}\! \left(x , y_{0}\right) = F_{31}\! \left(x \right)
F_{117}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{119}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{119}\! \left(x , y_{0}\right) = F_{120}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}\right) = 2 F_{17}\! \left(x \right)+F_{122}\! \left(x , y_{0}\right)+F_{125}\! \left(x , y_{0}\right)
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{123}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right)
F_{124}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{125}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{126}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)+F_{128}\! \left(x , y_{0}\right)
F_{127}\! \left(x , y_{0}\right) = F_{39}\! \left(x \right)
F_{128}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right)
F_{129}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)+F_{132}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)
F_{132}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)+F_{142}\! \left(x , y_{0}\right)
F_{133}\! \left(x , y_{0}\right) = F_{134}\! \left(x , y_{0}\right)+F_{137}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}\right)+F_{17}\! \left(x \right)
F_{134}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{135}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)
F_{136}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)
F_{137}\! \left(x , y_{0}\right) = 0
F_{138}\! \left(x , y_{0}\right) = F_{139}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{139}\! \left(x , y_{0}\right) = F_{140}\! \left(x , y_{0}\right)+F_{141}\! \left(x , y_{0}\right)
F_{140}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{141}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)
F_{142}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)+F_{146}\! \left(x , y_{0}\right)+F_{147}\! \left(x , y_{0}\right)+F_{151}\! \left(x , y_{0}\right)+F_{17}\! \left(x \right)
F_{143}\! \left(x , y_{0}\right) = F_{144}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{144}\! \left(x , y_{0}\right) = F_{145}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}\right) = F_{142}\! \left(x , y_{0}\right)+F_{70}\! \left(x , y_{0}\right)
F_{146}\! \left(x , y_{0}\right) = 0
F_{147}\! \left(x , y_{0}\right) = F_{148}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)
F_{149}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{142}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)
F_{153}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)+F_{154}\! \left(x , y_{0}\right)
F_{154}\! \left(x , y_{0}\right) = 2 F_{17}\! \left(x \right)+F_{155}\! \left(x , y_{0}\right)+F_{158}\! \left(x , y_{0}\right)+F_{159}\! \left(x , y_{0}\right)
F_{155}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{156}\! \left(x , y_{0}\right) = F_{157}\! \left(x , y_{0}\right)
F_{157}\! \left(x , y_{0}\right) = F_{154}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = 0
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{160}\! \left(x , y_{0}\right) = F_{161}\! \left(x , y_{0}\right)+F_{162}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{154}\! \left(x , y_{0}\right)
F_{163}\! \left(x , y_{0}\right) = F_{164}\! \left(x , 1, y_{0}\right)
F_{164}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{89}\! \left(x , y_{0}\right)-F_{89}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{165}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{166}\! \left(x , y_{0}\right)
F_{166}\! \left(x , y_{0}\right) = F_{167}\! \left(x , y_{0}\right)+F_{257}\! \left(x , y_{0}\right)
F_{167}\! \left(x , y_{0}\right) = F_{168}\! \left(x \right)+F_{89}\! \left(x , y_{0}\right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{17}\! \left(x \right)+F_{5}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x , 1\right)
F_{170}\! \left(x , y_{0}\right) = F_{171}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{171}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{172}\! \left(x , y_{0}\right)+F_{193}\! \left(x , y_{0}\right)+F_{238}\! \left(x , y_{0}\right)
F_{172}\! \left(x , y_{0}\right) = F_{173}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{173}\! \left(x , y_{0}\right) = F_{174}\! \left(x , y_{0}\right)+F_{6}\! \left(x \right)
F_{174}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{175}\! \left(x , y_{0}\right)+F_{224}\! \left(x , y_{0}\right)+F_{225}\! \left(x , y_{0}\right)+F_{235}\! \left(x , y_{0}\right)
F_{175}\! \left(x , y_{0}\right) = F_{176}\! \left(x , 1, y_{0}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{178}\! \left(x , 1, y_{0}, y_{1}\right)
F_{178}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{179}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{179}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{179}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x \right)+F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{180}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , y_{1}, y_{0}\right)+F_{222}\! \left(x , y_{0}, y_{1}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{179}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{183}\! \left(x , y_{1}, y_{0}\right)
F_{183}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{184}\! \left(x , 1, y_{1}\right) y_{1}-F_{184}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{184}\! \left(x , y_{0}, y_{1}\right) = F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{188}\! \left(x , y_{0}, y_{1}\right)
F_{185}\! \left(x , y_{0}, y_{1}\right) = F_{186}\! \left(x , y_{1}\right)+F_{187}\! \left(x , y_{0}, y_{1}\right)
F_{186}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)
F_{187}\! \left(x , y_{0}, y_{1}\right) = F_{60}\! \left(x , y_{0} y_{1}\right)
F_{188}\! \left(x , y_{0}, y_{1}\right) = F_{189}\! \left(x , y_{0}, y_{1}, 1\right)
F_{189}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{171}\! \left(x , y_{0} y_{1}\right)+F_{190}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{190}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{191}\! \left(x , y_{1} y_{2}\right)
F_{191}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{192}\! \left(x , y_{0}\right)+F_{193}\! \left(x , y_{0}\right)+F_{197}\! \left(x , y_{0}\right)
F_{192}\! \left(x , y_{0}\right) = F_{181}\! \left(x , 1, y_{0}\right)
F_{193}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{194}\! \left(x , y_{0}\right)
F_{194}\! \left(x , y_{0}\right) = F_{195}\! \left(x , y_{0}\right)
F_{195}\! \left(x , y_{0}\right) = F_{196}\! \left(x , y_{0}, 1\right)
F_{196}\! \left(x , y_{0}, y_{1}\right) = F_{188}\! \left(x , y_{1}, y_{0}\right)
F_{197}\! \left(x , y_{0}\right) = F_{198}\! \left(x , y_{0}\right)
F_{198}\! \left(x , y_{0}\right) = F_{199}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{199}\! \left(x , y_{0}\right) = 2 F_{17}\! \left(x \right)+F_{200}\! \left(x , y_{0}\right)+F_{218}\! \left(x , y_{0}\right)
F_{200}\! \left(x , y_{0}\right) = F_{201}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{201}\! \left(x , y_{0}\right) = 2 F_{17}\! \left(x \right)+F_{202}\! \left(x , y_{0}\right)+F_{216}\! \left(x , y_{0}\right)+F_{217}\! \left(x , y_{0}\right)
F_{202}\! \left(x , y_{0}\right) = F_{203}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{203}\! \left(x , y_{0}\right) = F_{204}\! \left(x , 1, y_{0}\right)
F_{204}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{205}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{205}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{205}\! \left(x , y_{0}, y_{1}\right) = 2 F_{17}\! \left(x \right)+F_{206}\! \left(x , y_{0}, y_{1}\right)+F_{207}\! \left(x , y_{0}, y_{1}\right)+F_{209}\! \left(x , y_{1}, y_{0}\right)
F_{206}\! \left(x , y_{0}, y_{1}\right) = F_{204}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{207}\! \left(x , y_{0}, y_{1}\right) = F_{208}\! \left(x , y_{0}, y_{1}\right)
F_{208}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{205}\! \left(x , y_{0}, y_{1}\right)
F_{209}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{210}\! \left(x , y_{1}, y_{0}\right)
F_{210}\! \left(x , y_{0}, y_{1}\right) = F_{211}\! \left(x , y_{0}, y_{1}\right)+F_{214}\! \left(x , y_{0}, y_{1}\right)
F_{211}\! \left(x , y_{0}, y_{1}\right) = F_{212}\! \left(x , y_{0}\right)+F_{213}\! \left(x , y_{0}, y_{1}\right)
F_{212}\! \left(x , y_{0}\right) = F_{171}\! \left(x , y_{0}\right)+F_{186}\! \left(x , y_{0}\right)
F_{213}\! \left(x , y_{0}, y_{1}\right) = F_{205}\! \left(x , y_{0}, y_{1}\right)
F_{214}\! \left(x , y_{0}, y_{1}\right) = F_{215}\! \left(x , y_{1}\right)
F_{215}\! \left(x , y_{0}\right) = F_{199}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)
F_{216}\! \left(x , y_{0}\right) = F_{200}\! \left(x , y_{0}\right)
F_{217}\! \left(x , y_{0}\right) = F_{209}\! \left(x , y_{0}, 1\right)
F_{218}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{219}\! \left(x , y_{0}\right)
F_{219}\! \left(x , y_{0}\right) = F_{220}\! \left(x , y_{0}\right)+F_{221}\! \left(x , y_{0}\right)
F_{220}\! \left(x , y_{0}\right) = F_{168}\! \left(x \right)+F_{199}\! \left(x , y_{0}\right)
F_{221}\! \left(x , y_{0}\right) = F_{199}\! \left(x , y_{0}\right)
F_{222}\! \left(x , y_{0}, y_{1}\right) = F_{223}\! \left(x , y_{0}, y_{1}\right)
F_{223}\! \left(x , y_{0}, y_{1}\right) = F_{213}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{224}\! \left(x , y_{0}\right) = F_{192}\! \left(x , y_{0}\right)
F_{225}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{226}\! \left(x , y_{0}\right)
F_{226}\! \left(x , y_{0}\right) = F_{227}\! \left(x , y_{0}\right)+F_{233}\! \left(x , y_{0}\right)
F_{227}\! \left(x , y_{0}\right) = F_{228}\! \left(x , y_{0}\right)+F_{230}\! \left(x , y_{0}\right)
F_{228}\! \left(x , y_{0}\right) = F_{186}\! \left(x , y_{0}\right)+F_{229}\! \left(x , y_{0}\right)
F_{229}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)
F_{230}\! \left(x , y_{0}\right) = F_{231}\! \left(x , y_{0}\right)+F_{232}\! \left(x , y_{0}\right)
F_{231}\! \left(x , y_{0}\right) = F_{25}\! \left(x \right)
F_{232}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)
F_{233}\! \left(x , y_{0}\right) = F_{234}\! \left(x , 1, y_{0}\right)
F_{234}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{188}\! \left(x , 1, y_{1}\right)-y_{0} F_{188}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{235}\! \left(x , y_{0}\right) = F_{236}\! \left(x , y_{0}\right)
F_{236}\! \left(x , y_{0}\right) = F_{237}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{237}\! \left(x , y_{0}\right) = F_{201}\! \left(x , y_{0}\right)
F_{238}\! \left(x , y_{0}\right) = F_{239}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{239}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right)+F_{218}\! \left(x , y_{0}\right)+F_{240}\! \left(x , y_{0}\right)+F_{247}\! \left(x \right)+F_{248}\! \left(x \right)
F_{240}\! \left(x , y_{0}\right) = F_{241}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{241}\! \left(x , y_{0}\right) = F_{242}\! \left(x , y_{0}\right)+F_{244}\! \left(x , y_{0}\right)
F_{242}\! \left(x , y_{0}\right) = F_{243}\! \left(x , 1, y_{0}\right)
F_{243}\! \left(x , y_{0}, y_{1}\right) = F_{205}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{0}\right)
F_{244}\! \left(x , y_{0}\right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x , 1\right)
F_{246}\! \left(x , y_{0}\right) = F_{174}\! \left(x , y_{0}\right)
F_{247}\! \left(x \right) = F_{193}\! \left(x , 1\right)
F_{248}\! \left(x \right) = F_{249}\! \left(x \right) F_{3}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x , 1\right)
F_{251}\! \left(x , y_{0}\right) = F_{252}\! \left(x , y_{0}\right)
F_{252}\! \left(x , y_{0}\right) = F_{253}\! \left(x \right)+F_{256}\! \left(x , y_{0}\right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x , 1\right)
F_{255}\! \left(x , y_{0}\right) = F_{220}\! \left(x , y_{0}\right)
F_{256}\! \left(x , y_{0}\right) = F_{191}\! \left(x , y_{0}\right)
F_{257}\! \left(x , y_{0}\right) = F_{191}\! \left(x , y_{0}\right)
F_{258}\! \left(x , y_{0}\right) = F_{259}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{259}\! \left(x , y_{0}\right) = F_{260}\! \left(x , y_{0}, 1\right)
F_{260}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} \left(F_{191}\! \left(x , y_{0}\right)-F_{191}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{261}\! \left(x \right) = F_{262}\! \left(x , 1\right)
F_{262}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right) F_{3}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_261(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_4(x) + F_8(x, k_0))
Eq(F_8(x, k_0), F_89(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_16(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0), F_14(x, k_0) + F_15(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_10(x, k_0))
Eq(F_15(x, k_0), F_10(x, k_0))
Eq(F_16(x, k_0), F_17(x) + F_18(x, k_0) + F_58(x, k_0))
Eq(F_17(x), 0)
Eq(F_18(x, k_0), F_12(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_44(x, k_0))
Eq(F_20(x, k_0), F_16(x, k_0) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_3(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_1(x) + F_21(x))
Eq(F_25(x), F_26(x) + F_31(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_3(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_26(x))
Eq(F_30(x), F_26(x))
Eq(F_31(x), F_17(x) + F_32(x) + F_36(x))
Eq(F_32(x), F_3(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_21(x) + F_31(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_3(x)*F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_26(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_3(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_21(x) + F_39(x))
Eq(F_43(x), F_39(x))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_17(x) + F_46(x, k_0) + F_50(x, k_0))
Eq(F_46(x, k_0), F_12(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_21(x) + F_45(x, k_0))
Eq(F_49(x, k_0), F_45(x, k_0))
Eq(F_50(x, k_0), F_3(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_10(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_12(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_57(x, k_0))
Eq(F_56(x, k_0), F_21(x) + F_53(x, k_0))
Eq(F_57(x, k_0), F_53(x, k_0))
Eq(F_58(x, k_0), F_3(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_61(x, k_0))
Eq(F_60(x, k_0), F_10(x, k_0) + F_45(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_70(x, k_0))
Eq(F_62(x, k_0), F_17(x) + F_63(x, k_0) + F_66(x, k_0))
Eq(F_63(x, k_0), F_12(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_26(x) + F_62(x, k_0))
Eq(F_66(x, k_0), F_3(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_69(x, k_0))
Eq(F_68(x, k_0), F_10(x, k_0))
Eq(F_69(x, k_0), F_62(x, k_0))
Eq(F_70(x, k_0), F_17(x) + F_71(x, k_0) + F_74(x, k_0) + F_78(x, k_0))
Eq(F_71(x, k_0), F_12(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_31(x) + F_70(x, k_0))
Eq(F_74(x, k_0), F_3(x)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_77(x, k_0))
Eq(F_76(x, k_0), F_45(x, k_0))
Eq(F_77(x, k_0), F_70(x, k_0))
Eq(F_78(x, k_0), F_3(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_62(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), 2*F_17(x) + F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_12(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_39(x) + F_81(x, k_0))
Eq(F_85(x, k_0), F_3(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0) + F_88(x, k_0))
Eq(F_87(x, k_0), F_53(x, k_0))
Eq(F_88(x, k_0), F_81(x, k_0))
Eq(F_89(x, k_0), F_165(x, k_0) + F_17(x) + F_258(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_3(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_163(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_9(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_102(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_17(x) + F_95(x, k_0) + F_98(x, k_0))
Eq(F_95(x, k_0), F_3(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_10(x, k_0) + F_94(x, k_0))
Eq(F_98(x, k_0), F_12(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_101(x, k_0))
Eq(F_100(x, k_0), F_26(x))
Eq(F_101(x, k_0), F_94(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_106(x, k_0) + F_129(x, k_0) + F_17(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_3(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_102(x, k_0) + F_16(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_109(x, k_0))
Eq(F_108(x, k_0), F_31(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_114(x, k_0) + F_118(x, k_0) + F_17(x))
Eq(F_111(x, k_0), F_112(x, k_0)*F_3(x))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_110(x, k_0) + F_45(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_12(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_117(x, k_0))
Eq(F_116(x, k_0), F_31(x))
Eq(F_117(x, k_0), F_110(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_3(x))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_94(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_125(x, k_0) + 2*F_17(x))
Eq(F_122(x, k_0), F_123(x, k_0)*F_3(x))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_121(x, k_0) + F_53(x, k_0))
Eq(F_125(x, k_0), F_12(x, k_0)*F_126(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_128(x, k_0))
Eq(F_127(x, k_0), F_39(x))
Eq(F_128(x, k_0), F_121(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_3(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_132(x, k_0))
Eq(F_131(x, k_0), F_110(x, k_0) + F_94(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_142(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_137(x, k_0) + F_138(x, k_0) + F_17(x))
Eq(F_134(x, k_0), F_135(x, k_0)*F_3(x))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_133(x, k_0) + F_62(x, k_0))
Eq(F_137(x, k_0), 0)
Eq(F_138(x, k_0), F_139(x, k_0)*F_3(x))
Eq(F_139(x, k_0), F_140(x, k_0) + F_141(x, k_0))
Eq(F_140(x, k_0), F_94(x, k_0))
Eq(F_141(x, k_0), F_133(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_146(x, k_0) + F_147(x, k_0) + F_151(x, k_0) + F_17(x))
Eq(F_143(x, k_0), F_144(x, k_0)*F_3(x))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_142(x, k_0) + F_70(x, k_0))
Eq(F_146(x, k_0), 0)
Eq(F_147(x, k_0), F_148(x, k_0)*F_3(x))
Eq(F_148(x, k_0), F_149(x, k_0) + F_150(x, k_0))
Eq(F_149(x, k_0), F_110(x, k_0))
Eq(F_150(x, k_0), F_142(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0)*F_3(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_133(x, k_0) + F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_158(x, k_0) + F_159(x, k_0) + 2*F_17(x))
Eq(F_155(x, k_0), F_156(x, k_0)*F_3(x))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_154(x, k_0) + F_81(x, k_0))
Eq(F_158(x, k_0), 0)
Eq(F_159(x, k_0), F_160(x, k_0)*F_3(x))
Eq(F_160(x, k_0), F_161(x, k_0) + F_162(x, k_0))
Eq(F_161(x, k_0), F_121(x, k_0))
Eq(F_162(x, k_0), F_154(x, k_0))
Eq(F_163(x, k_0), F_164(x, 1, k_0))
Eq(F_164(x, k_0, k_1), -F_89(x, k_0) + (-k_0*F_89(x, k_0) + k_1*F_89(x, k_1))/(-k_0 + k_1))
Eq(F_165(x, k_0), F_12(x, k_0)*F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0) + F_257(x, k_0))
Eq(F_167(x, k_0), F_168(x) + F_89(x, k_0))
Eq(F_168(x), F_169(x) + F_17(x) + F_5(x))
Eq(F_169(x), F_170(x, 1))
Eq(F_170(x, k_0), F_171(x, k_0)*F_3(x))
Eq(F_171(x, k_0), F_17(x) + F_172(x, k_0) + F_193(x, k_0) + F_238(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0)*F_3(x))
Eq(F_173(x, k_0), F_174(x, k_0) + F_6(x))
Eq(F_174(x, k_0), F_17(x) + F_175(x, k_0) + F_224(x, k_0) + F_225(x, k_0) + F_235(x, k_0))
Eq(F_175(x, k_0), F_176(x, 1, k_0))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1)*F_3(x))
Eq(F_177(x, k_0, k_1), F_178(x, 1, k_0, k_1))
Eq(F_178(x, k_0, k_1, k_2), (-k_0*F_179(x, k_0, k_2) + k_1*F_179(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_179(x, k_0, k_1), F_17(x) + F_176(x, k_0, k_1) + F_180(x, k_0, k_1) + F_182(x, k_1, k_0) + F_222(x, k_0, k_1))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1))
Eq(F_181(x, k_0, k_1), F_12(x, k_0)*F_179(x, k_0, k_1))
Eq(F_182(x, k_0, k_1), F_12(x, k_0)*F_183(x, k_1, k_0))
Eq(F_183(x, k_0, k_1), (-k_0*F_184(x, k_0/k_1, k_1) + k_1*F_184(x, 1, k_1))/(-k_0 + k_1))
Eq(F_184(x, k_0, k_1), F_185(x, k_0, k_1) + F_188(x, k_0, k_1))
Eq(F_185(x, k_0, k_1), F_186(x, k_1) + F_187(x, k_0, k_1))
Eq(F_186(x, k_0), F_24(x) + F_60(x, k_0))
Eq(F_187(x, k_0, k_1), F_60(x, k_0*k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1, 1))
Eq(F_189(x, k_0, k_1, k_2), F_171(x, k_0*k_1) + F_190(x, k_0, k_1, k_2))
Eq(F_190(x, k_0, k_1, k_2), F_191(x, k_1*k_2))
Eq(F_191(x, k_0), F_17(x) + F_192(x, k_0) + F_193(x, k_0) + F_197(x, k_0))
Eq(F_192(x, k_0), F_181(x, 1, k_0))
Eq(F_193(x, k_0), F_12(x, k_0)*F_194(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, 1))
Eq(F_196(x, k_0, k_1), F_188(x, k_1, k_0))
Eq(F_197(x, k_0), F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0)*F_3(x))
Eq(F_199(x, k_0), 2*F_17(x) + F_200(x, k_0) + F_218(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0)*F_3(x))
Eq(F_201(x, k_0), 2*F_17(x) + F_202(x, k_0) + F_216(x, k_0) + F_217(x, k_0))
Eq(F_202(x, k_0), F_203(x, k_0)*F_3(x))
Eq(F_203(x, k_0), F_204(x, 1, k_0))
Eq(F_204(x, k_0, k_1), (k_0*F_205(x, k_0, k_1) - F_205(x, 1, k_1))/(k_0 - 1))
Eq(F_205(x, k_0, k_1), 2*F_17(x) + F_206(x, k_0, k_1) + F_207(x, k_0, k_1) + F_209(x, k_1, k_0))
Eq(F_206(x, k_0, k_1), F_204(x, k_0, k_1)*F_3(x))
Eq(F_207(x, k_0, k_1), F_208(x, k_0, k_1))
Eq(F_208(x, k_0, k_1), F_12(x, k_0)*F_205(x, k_0, k_1))
Eq(F_209(x, k_0, k_1), F_12(x, k_0)*F_210(x, k_1, k_0))
Eq(F_210(x, k_0, k_1), F_211(x, k_0, k_1) + F_214(x, k_0, k_1))
Eq(F_211(x, k_0, k_1), F_212(x, k_0) + F_213(x, k_0, k_1))
Eq(F_212(x, k_0), F_171(x, k_0) + F_186(x, k_0))
Eq(F_213(x, k_0, k_1), F_205(x, k_0, k_1))
Eq(F_214(x, k_0, k_1), F_215(x, k_1))
Eq(F_215(x, k_0), F_199(x, k_0) + F_52(x, k_0))
Eq(F_216(x, k_0), F_200(x, k_0))
Eq(F_217(x, k_0), F_209(x, k_0, 1))
Eq(F_218(x, k_0), F_12(x, k_0)*F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0) + F_221(x, k_0))
Eq(F_220(x, k_0), F_168(x) + F_199(x, k_0))
Eq(F_221(x, k_0), F_199(x, k_0))
Eq(F_222(x, k_0, k_1), F_223(x, k_0, k_1))
Eq(F_223(x, k_0, k_1), F_213(x, k_0, k_1)*F_3(x))
Eq(F_224(x, k_0), F_192(x, k_0))
Eq(F_225(x, k_0), F_12(x, k_0)*F_226(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_233(x, k_0))
Eq(F_227(x, k_0), F_228(x, k_0) + F_230(x, k_0))
Eq(F_228(x, k_0), F_186(x, k_0) + F_229(x, k_0))
Eq(F_229(x, k_0), F_60(x, k_0))
Eq(F_230(x, k_0), F_231(x, k_0) + F_232(x, k_0))
Eq(F_231(x, k_0), F_25(x))
Eq(F_232(x, k_0), F_131(x, k_0))
Eq(F_233(x, k_0), F_234(x, 1, k_0))
Eq(F_234(x, k_0, k_1), (-k_0*F_188(x, k_0/k_1, k_1) + k_1*F_188(x, 1, k_1))/(-k_0 + k_1))
Eq(F_235(x, k_0), F_236(x, k_0))
Eq(F_236(x, k_0), F_237(x, k_0)*F_3(x))
Eq(F_237(x, k_0), F_201(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0)*F_3(x))
Eq(F_239(x, k_0), F_17(x) + F_218(x, k_0) + F_240(x, k_0) + F_247(x) + F_248(x))
Eq(F_240(x, k_0), F_241(x, k_0)*F_3(x))
Eq(F_241(x, k_0), F_242(x, k_0) + F_244(x, k_0))
Eq(F_242(x, k_0), F_243(x, 1, k_0))
Eq(F_243(x, k_0, k_1), F_205(x, k_0, k_1) + F_7(x, k_0))
Eq(F_244(x, k_0), F_245(x))
Eq(F_245(x), F_246(x, 1))
Eq(F_246(x, k_0), F_174(x, k_0))
Eq(F_247(x), F_193(x, 1))
Eq(F_248(x), F_249(x)*F_3(x))
Eq(F_249(x), F_250(x))
Eq(F_250(x), F_251(x, 1))
Eq(F_251(x, k_0), F_252(x, k_0))
Eq(F_252(x, k_0), F_253(x) + F_256(x, k_0))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_255(x, 1))
Eq(F_255(x, k_0), F_220(x, k_0))
Eq(F_256(x, k_0), F_191(x, k_0))
Eq(F_257(x, k_0), F_191(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0)*F_3(x))
Eq(F_259(x, k_0), F_260(x, k_0, 1))
Eq(F_260(x, k_0, k_1), -F_191(x, k_1) + (-k_0*F_191(x, k_0) + k_1*F_191(x, k_1))/(-k_0 + k_1))
Eq(F_261(x), F_262(x, 1))
Eq(F_262(x, k_0), F_212(x, k_0)*F_3(x))
Pack JSON:
{"name": "point_and_col_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": [], "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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 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