02143_02413_20143_20413
Counting sequence:
1, 1, 2, 6, 24, 116, 632, 3722, 23124, 149356, 993572, 6764672, 46926016, 330568120, 2358824588, 17016419094, 123909737376, 909631377000, 6725206460504, 50033428138026, 374303437351996, 2814093967922400, 21251294173395228, 161129936674452594, 1226164907293083120, 9361863513572875968, 71695720444694640496, 550596336903097885232, 4239228696766929307412, 32716653462394703959708, 253048451324675408547760, 1961207350956868078908350, 15228863195721210707995804, 118462453548210861094037372, 923025263993034675080742436, 7203126510170632222454057456, 56293999283096482441799861488, 440554228770036710218595854120, 3452221420131586533745782405580, 27084980787517338715982648964658, 212745409039297721463645112805264, 1672888762449740158195810791588848, 13168144926275150140304710622532336, 103755254824321109193858287022246108, 818281132925383935680928438601083252, 6459254148935125761963448324069097940, 51030689543251241863111241644250808936, 403490022943704978328326430257196564622, 3192792291804846408182520886051452201892, 25283096931177431794808224085476514697668, 200353895849241101963535450700263585696268, 1588767254458069394407882636211528441761454, 12606820798994886106139532847372216752179784, 100097277836012779121817456403090939179222404, 795242523253787421110149561366398935422501184, 6321606202127441606159494265304706700539933314, 50280113614665383097328191253456581209529667052, 400126224381749875584315450311958398877448417076, 3185819865270206325294123208054242116441411349196, 25378198489913385979848281713365005849179186906004, 202259115766725652837043099456722305677483485521400, 1612708680937979893910533111031066243127199716247480, 12864632455005257944777313666268027967577921020762060, 102665839384439649671312352222289936710103183799615702, 819663253104155156756293770602714139199889514351739680, 6546663184670979993994686827088332522000099748762385848, 52308702511951419023175732841113455249057954504531417048, 418111361285579436616074938904319541909365333257498279498, 3343250843524533101878737610652859964825119649045521802972, 26742380616526997730664608937651133220524926443989745877968, 213983670329029461497362501617270668479276762916631507486780, 1712798305942938162013171660371231980136613806629636400532546, 13714266951468272523240654309658392381918668497911299376994800, 109843836826253551083406245862216003132061764237708150128495728, 880058665668705940906268310323096055797700589563502968475436752, 7053045128462720336905015534266205369142704243055837606927434076, 56541489016890586879620634305394562353204461568594340500647959060, 453398350666980821341614803733365887999338831351781856173282113012, 3636733359539815999182348302649923156200924678907890430930957161928, 29178210923045426283013291609401854420658308037407079592949848494558, 234163123169282373788140763676779457694518574556023103993651009426052, 1879697977720854280421848325892717710351579031658235541017459614408580, 15092617793942935539639834877677449507457182994540388701235422531652812, 121211912993087362925204978468215136099914137362219807209944934508102586, 973705610919149954774624659676772018769401901116330845671967186962820744, 7823645718099868715975801338859178884364868795262659015617401355244024012, 62876362111962786744747582780933426416606778188400382357405575852883080792, 505428866751083806489418786746405033958170740304171075329025048080067204178, 4063729990752559596031483735043325753682276986445075835534073564103604604020, 32679819649674675450212059634636184431474089270626539410617817563018537146540, 262858713374982232616015075519392239369455487402733640708059714426016704760948, 2114710931363841415151415992646531346173631939203789816083077306832077836947628, 17016240025360657348282708849737338932474884066195813984209730549788421029121296, 136948814073553926631104254552712649783086199597458882497242499899372268503241568, 1102384786355376471457903888088346261756985907368267240215532545294866798972967412, 8875373753858490414223812003580664714740155961514921923931674260308219805743986134, 71468866515995655091298673820495279932554255263519207836073691108926196967069233016, 575602001490949840553149284432408387947106507782771626032079043203885120894704477824, 4636617396526110433791891769966299886110006572333840921471895903614714537497620367216, 37355301465081194459368549588984056222856032137553209160725152060354392491786377097472, 301005031874865949048664213752403099433721908034693279505656730609620264398451750727780
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25542/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[40,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[40,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[40,x]*F[85,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]+F[183,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[70,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[41,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[32,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]+F[25,x,k[0]]
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[20,x,k[0]]*F[22,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[27,x,k[0]]
F[26,x,k[0]] = F[23,x,k[0]]
F[27,x,k[0]] = F[28,x]+F[29,x,k[0]]+F[31,x,k[0]]
F[28,x] = 0
F[29,x,k[0]] = F[20,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]
F[31,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[32,x,k[0]] = F[2,x]+F[33,x,k[0]]
F[33,x,k[0]] = F[28,x]+F[34,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[20,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[32,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[33,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[40,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[13,x,k[0]]*F[20,x,k[0]]
F[40,x] = x
F[41,x,k[0]] = F[1,x]+F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = F[20,x,k[0]]*F[41,x,k[0]]
F[43,x,k[0]] = F[40,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[45,x,k[0]]+F[46,x,k[0]]+F[69,x,k[0]]
F[45,x,k[0]] = F[20,x,k[0]]*F[44,x,k[0]]
F[46,x,k[0]] = F[40,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[44,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[40,x]*F[50,x,k[0]]*F[68,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[66,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0],1]
F[53,x,k[0],k[1]] = F[44,x,k[0]]+F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[28,x]+F[56,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[20,x,k[0]]*F[55,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[20,x,k[1]]*F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[41,x,k[0]]+F[55,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[40,x]*F[54,x,k[0],k[1]]
F[60,x,k[0],k[1]] = F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[40,x]*F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]+F[65,x,k[0],k[1]]
F[63,x,k[0],k[1]] = F[41,x,k[0]]*F[64,x,k[0],k[1]]
F[64,x,k[0],k[1]] = -k[1]*(F[54,x,k[0],1]-F[54,x,k[0],k[1]])/(-1+k[1])
F[65,x,k[0],k[1]] = F[53,x,k[0],k[1]]*F[55,x,k[0],k[1]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[52,x,k[0]]^2*F[40,x]
F[68,x,k[0]] = F[41,x,k[0]]
F[69,x,k[0]] = F[40,x]*F[52,x,k[0]]
F[71,x,k[0]] = F[164,x,k[0]]+F[70,x,k[0]]
F[72,x,k[0]] = F[20,x,k[0]]*F[71,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[33,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[40,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[158,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[12,x]*F[40,x]*F[81,x,k[0]]
F[81,x,k[0]] = F[155,x,k[0]]+F[157,x,k[0]]+F[28,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[20,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[154,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[81,x,k[0]]+F[85,x]
F[85,x] = F[1,x]+F[153,x]+F[86,x]
F[86,x] = F[40,x]*F[87,x]
F[87,x] = 1/F[40,x]*F[88,x]
F[88,x] = -F[1,x]-F[89,x]+F[4,x]
F[89,x] = F[40,x]*F[90,x]
F[90,x] = F[85,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[40,x]*F[85,x]*F[93,x]
F[93,x] = F[94,x,1]
F[94,x,k[0]] = F[101,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[41,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[28,x]+F[97,x,k[0]]+F[98,x,k[0]]+F[99,x,k[0]]
F[97,x,k[0]] = F[20,x,k[0]]*F[96,x,k[0]]
F[98,x,k[0]] = F[20,x,k[0]]*F[95,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[40,x]
F[94,x,k[0]] = F[100,x,k[0]]+F[44,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[40,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[152,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[41,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]*F[20,x,k[0]]
F[107,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[109,x,k[0]]+F[111,x,k[0]]+F[146,x,k[0]]
F[107,x,k[0]] = (F[108,x,k[0]]*k[0]-F[108,x,1])/(-1+k[0])
F[108,x,k[0]] = F[38,x,k[0]]+F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]*F[40,x]
F[110,x,k[0]] = (F[52,x,k[0]]*k[0]-F[52,x,1])/(-1+k[0])
F[111,x,k[0]] = F[112,x,k[0]]*F[40,x]
F[112,x,k[0]] = (F[113,x,k[0]]*k[0]-F[113,x,1])/(-1+k[0])
F[113,x,k[0]] = F[114,x,k[0]]+F[90,x]
F[114,x,k[0]] = F[115,x,k[0]]+F[81,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[40,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = F[81,x,k[0]]*F[93,x]
F[119,x,k[0]] = F[120,x,k[0]]*F[41,x,k[0]]
F[120,x,k[0]] = -k[0]*(F[121,x,1]-F[121,x,k[0]])/(-1+k[0])
F[52,x,k[0]] = F[121,x,k[0]]+F[122,x]
F[122,x] = F[123,x,1]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x]+F[130,x,k[0]]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = (-1+x^3*F[126,x]^2+6*x^2*F[126,x]+(-11*F[126,x]+9)*x)*(x*F[126,x]-1)
F[127,x] = F[128,x]
F[128,x] = F[126,x]*F[129,x]*F[40,x]
F[129,x] = F[122,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[140,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[139,x,k[0]]+F[28,x]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[137,x,k[0]]
F[135,x,k[0]] = F[126,x]+F[136,x,k[0]]
F[136,x,k[0]] = F[132,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = k[0]*x
F[139,x,k[0]] = F[131,x,k[0]]*F[40,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]*F[40,x]
F[142,x,k[0]] = F[143,x,k[0]]+F[145,x,k[0]]
F[143,x,k[0]] = F[126,x]*F[144,x,k[0]]
F[144,x,k[0]] = -k[0]*(F[131,x,1]-F[131,x,k[0]])/(-1+k[0])
F[145,x,k[0]] = F[123,x,k[0]]*F[132,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[40,x]
F[147,x,k[0]] = (F[148,x,k[0]]*k[0]-F[148,x,1])/(-1+k[0])
F[149,x,k[0]] = F[148,x,k[0]]*F[40,x]
F[108,x,k[0]] = F[1,x]+F[149,x,k[0]]+F[150,x,k[0]]+F[151,x,k[0]]
F[150,x,k[0]] = F[20,x,k[0]]*F[94,x,k[0]]
F[151,x,k[0]] = F[113,x,k[0]]*F[40,x]
F[152,x,k[0]] = F[94,x,k[0]]*F[96,x,k[0]]
F[153,x] = F[40,x]*F[90,x]
F[154,x,k[0]] = F[81,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[40,x]
F[148,x,k[0]] = F[156,x,k[0]]+F[87,x]
F[157,x,k[0]] = F[114,x,k[0]]*F[40,x]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[13,x,k[0]]*F[160,x,k[0]]*F[20,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[162,x,k[0]]+F[163,x,k[0]]+F[28,x]
F[161,x,k[0]] = F[160,x,k[0]]*F[20,x,k[0]]
F[162,x,k[0]] = F[160,x,k[0]]*F[20,x,k[0]]
F[163,x,k[0]] = F[40,x]*F[94,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]*F[169,x,k[0]]*F[40,x]
F[166,x,k[0]] = F[16,x,k[0]]+F[167,x,k[0]]+F[168,x,k[0]]
F[167,x,k[0]] = F[166,x,k[0]]*F[20,x,k[0]]
F[168,x,k[0]] = F[13,x,k[0]]*F[40,x]
F[169,x,k[0]] = F[1,x]+F[170,x,k[0]]+F[171,x,k[0]]+F[182,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[20,x,k[0]]
F[171,x,k[0]] = F[172,x,k[0]]*F[40,x]
F[173,x,k[0]] = F[172,x,k[0]]*F[40,x]
F[44,x,k[0]] = F[1,x]+F[173,x,k[0]]+F[174,x,k[0]]+F[175,x,k[0]]
F[174,x,k[0]] = F[20,x,k[0]]*F[44,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]*F[40,x]
F[176,x,k[0]] = F[169,x,k[0]]+F[177,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[173,x,k[0]]+F[179,x,k[0]]+F[180,x,k[0]]+F[28,x]
F[179,x,k[0]] = F[178,x,k[0]]*F[20,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[178,x,k[0]]*F[40,x]
F[182,x,k[0]] = F[176,x,k[0]]*F[40,x]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[40,x]*F[41,x,k[0]]
F[186,x,k[0]] = F[185,x,k[0]]*F[20,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = -k[0]*(F[38,x,1]-F[38,x,k[0]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{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_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right) F_{85}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{22}\! \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_{23}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{40}\! \left(x \right) = x
F_{41}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{50}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y , 1\right)
F_{53}\! \left(x , y , z\right) = F_{44}\! \left(x , y\right)+F_{54}\! \left(x , y , z\right)
F_{54}\! \left(x , y , z\right) = F_{55}\! \left(x , y , z\right)+F_{60}\! \left(x , y , z\right)
F_{55}\! \left(x , y , z\right) = F_{28}\! \left(x \right)+F_{56}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)+F_{59}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right) F_{55}\! \left(x , y , z\right)
F_{57}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{58}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{41}\! \left(x , y\right)+F_{55}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = F_{40}\! \left(x \right) F_{54}\! \left(x , y , z\right)
F_{60}\! \left(x , y , z\right) = F_{61}\! \left(x , y , z\right)
F_{61}\! \left(x , y , z\right) = F_{40}\! \left(x \right) F_{62}\! \left(x , y , z\right)
F_{62}\! \left(x , y , z\right) = F_{63}\! \left(x , y , z\right)+F_{65}\! \left(x , y , z\right)
F_{63}\! \left(x , y , z\right) = F_{41}\! \left(x , y\right) F_{64}\! \left(x , y , z\right)
F_{64}\! \left(x , y , z\right) = -\frac{z \left(F_{54}\! \left(x , y , 1\right)-F_{54}\! \left(x , y , z\right)\right)}{-1+z}
F_{65}\! \left(x , y , z\right) = F_{53}\! \left(x , y , z\right) F_{55}\! \left(x , y , z\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{52}\! \left(x , y\right)^{2} F_{40}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{164}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{28}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{153}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{40}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{40}\! \left(x \right)}
F_{88}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{89}\! \left(x \right)+F_{4}\! \left(x \right)
F_{89}\! \left(x \right) = F_{40}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{40}\! \left(x \right) F_{85}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x , 1\right)
F_{94}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{94}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = -\frac{-F_{108}\! \left(x , y\right) y +F_{108}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{110}\! \left(x , y\right) = -\frac{-F_{52}\! \left(x , y\right) y +F_{52}\! \left(x , 1\right)}{-1+y}
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{112}\! \left(x , y\right) = -\frac{-F_{113}\! \left(x , y\right) y +F_{113}\! \left(x , 1\right)}{-1+y}
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{90}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{93}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = -\frac{y \left(F_{121}\! \left(x , 1\right)-F_{121}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x \right)+F_{130}\! \left(x , y\right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = x^{4} F_{126} \left(x \right)^{3}+5 x^{3} F_{126} \left(x \right)^{2}-11 x^{2} F_{126} \left(x \right)^{2}+3 x^{2} F_{126}\! \left(x \right)+10 x F_{126}\! \left(x \right)-9 x +1
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{126}\! \left(x \right) F_{129}\! \left(x \right) F_{40}\! \left(x \right)
F_{129}\! \left(x \right) = F_{122}\! \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_{140}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{139}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{137}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{126}\! \left(x \right)+F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{132}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = y x
F_{139}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{126}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = -\frac{y \left(F_{131}\! \left(x , 1\right)-F_{131}\! \left(x , y\right)\right)}{-1+y}
F_{145}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{132}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{147}\! \left(x , y\right) = -\frac{-y F_{148}\! \left(x , y\right)+F_{148}\! \left(x , 1\right)}{-1+y}
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{150}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{94}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{153}\! \left(x \right) = F_{40}\! \left(x \right) F_{90}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{160}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{162}\! \left(x , y\right)+F_{163}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{169}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{170}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{172}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{173}\! \left(x , y\right)+F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{40}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{40}\! \left(x \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_{40}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = -\frac{y \left(F_{38}\! \left(x , 1\right)-F_{38}\! \left(x , y\right)\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_40(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_40(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_40(x)*F_85(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0) + F_183(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_70(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_41(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_32(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0) + F_25(x, k_0))
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_20(x, k_0)*F_22(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_23(x, k_0))
Eq(F_27(x, k_0), F_28(x) + F_29(x, k_0) + F_31(x, k_0))
Eq(F_28(x), 0)
Eq(F_29(x, k_0), F_20(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), F_23(x, k_0) + F_27(x, k_0))
Eq(F_31(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_32(x, k_0), F_2(x) + F_33(x, k_0))
Eq(F_33(x, k_0), F_28(x) + F_34(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_20(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_32(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_33(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_40(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_13(x, k_0)*F_20(x, k_0))
Eq(F_40(x), x)
Eq(F_41(x, k_0), F_1(x) + F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), F_20(x, k_0)*F_41(x, k_0))
Eq(F_43(x, k_0), F_40(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_45(x, k_0) + F_46(x, k_0) + F_69(x, k_0))
Eq(F_45(x, k_0), F_20(x, k_0)*F_44(x, k_0))
Eq(F_46(x, k_0), F_40(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_44(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_40(x)*F_50(x, k_0)*F_68(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_66(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0, 1))
Eq(F_53(x, k_0, k_1), F_44(x, k_0) + F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_28(x) + F_56(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_20(x, k_0)*F_55(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_20(x, k_1)*F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_41(x, k_0) + F_55(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_40(x)*F_54(x, k_0, k_1))
Eq(F_60(x, k_0, k_1), F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_40(x)*F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1) + F_65(x, k_0, k_1))
Eq(F_63(x, k_0, k_1), F_41(x, k_0)*F_64(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), -F_54(x, k_0, 1) + (-k_1*F_54(x, k_0, k_1) + F_54(x, k_0, 1))/(1 - k_1))
Eq(F_65(x, k_0, k_1), F_53(x, k_0, k_1)*F_55(x, k_0, k_1))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_40(x)*F_52(x, k_0)**2)
Eq(F_68(x, k_0), F_41(x, k_0))
Eq(F_69(x, k_0), F_40(x)*F_52(x, k_0))
Eq(F_71(x, k_0), F_164(x, k_0) + F_70(x, k_0))
Eq(F_72(x, k_0), F_20(x, k_0)*F_71(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_33(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_40(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_158(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_12(x)*F_40(x)*F_81(x, k_0))
Eq(F_81(x, k_0), F_155(x, k_0) + F_157(x, k_0) + F_28(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_20(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_154(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_81(x, k_0) + F_85(x))
Eq(F_85(x), F_1(x) + F_153(x) + F_86(x))
Eq(F_86(x), F_40(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_40(x))
Eq(F_88(x), -F_1(x) + F_4(x) - F_89(x))
Eq(F_89(x), F_40(x)*F_90(x))
Eq(F_90(x), F_85(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_40(x)*F_85(x)*F_93(x))
Eq(F_93(x), F_94(x, 1))
Eq(F_94(x, k_0), F_101(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_41(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_28(x) + F_97(x, k_0) + F_98(x, k_0) + F_99(x, k_0))
Eq(F_97(x, k_0), F_20(x, k_0)*F_96(x, k_0))
Eq(F_98(x, k_0), F_20(x, k_0)*F_95(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_40(x))
Eq(F_94(x, k_0), F_100(x, k_0) + F_44(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_40(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_152(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_41(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_20(x, k_0))
Eq(F_107(x, k_0), F_1(x) + F_106(x, k_0) + F_109(x, k_0) + F_111(x, k_0) + F_146(x, k_0))
Eq(F_107(x, k_0), (-k_0*F_108(x, k_0) + F_108(x, 1))/(1 - k_0))
Eq(F_108(x, k_0), F_38(x, k_0) + F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0)*F_40(x))
Eq(F_110(x, k_0), (-k_0*F_52(x, k_0) + F_52(x, 1))/(1 - k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_40(x))
Eq(F_112(x, k_0), (-k_0*F_113(x, k_0) + F_113(x, 1))/(1 - k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_90(x))
Eq(F_114(x, k_0), F_115(x, k_0) + F_81(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0)*F_40(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), F_81(x, k_0)*F_93(x))
Eq(F_119(x, k_0), F_120(x, k_0)*F_41(x, k_0))
Eq(F_120(x, k_0), -F_121(x, 1) + (-k_0*F_121(x, k_0) + F_121(x, 1))/(1 - k_0))
Eq(F_52(x, k_0), F_121(x, k_0) + F_122(x))
Eq(F_122(x), F_123(x, 1))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x) + F_130(x, k_0))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), x**4*F_126(x)**3 + x**2*(5*x - 11)*F_126(x)**2 - 9*x + (3*x**2 + 10*x)*F_126(x) + 1)
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_126(x)*F_129(x)*F_40(x))
Eq(F_129(x), F_122(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_140(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_139(x, k_0) + F_28(x))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_137(x, k_0))
Eq(F_135(x, k_0), F_126(x) + F_136(x, k_0))
Eq(F_136(x, k_0), F_132(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), k_0*x)
Eq(F_139(x, k_0), F_131(x, k_0)*F_40(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0)*F_40(x))
Eq(F_142(x, k_0), F_143(x, k_0) + F_145(x, k_0))
Eq(F_143(x, k_0), F_126(x)*F_144(x, k_0))
Eq(F_144(x, k_0), -F_131(x, 1) + (-k_0*F_131(x, k_0) + F_131(x, 1))/(1 - k_0))
Eq(F_145(x, k_0), F_123(x, k_0)*F_132(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_40(x))
Eq(F_147(x, k_0), (-k_0*F_148(x, k_0) + F_148(x, 1))/(1 - k_0))
Eq(F_149(x, k_0), F_148(x, k_0)*F_40(x))
Eq(F_108(x, k_0), F_1(x) + F_149(x, k_0) + F_150(x, k_0) + F_151(x, k_0))
Eq(F_150(x, k_0), F_20(x, k_0)*F_94(x, k_0))
Eq(F_151(x, k_0), F_113(x, k_0)*F_40(x))
Eq(F_152(x, k_0), F_94(x, k_0)*F_96(x, k_0))
Eq(F_153(x), F_40(x)*F_90(x))
Eq(F_154(x, k_0), F_81(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_40(x))
Eq(F_148(x, k_0), F_156(x, k_0) + F_87(x))
Eq(F_157(x, k_0), F_114(x, k_0)*F_40(x))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_13(x, k_0)*F_160(x, k_0)*F_20(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_162(x, k_0) + F_163(x, k_0) + F_28(x))
Eq(F_161(x, k_0), F_160(x, k_0)*F_20(x, k_0))
Eq(F_162(x, k_0), F_160(x, k_0)*F_20(x, k_0))
Eq(F_163(x, k_0), F_40(x)*F_94(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0)*F_169(x, k_0)*F_40(x))
Eq(F_166(x, k_0), F_16(x, k_0) + F_167(x, k_0) + F_168(x, k_0))
Eq(F_167(x, k_0), F_166(x, k_0)*F_20(x, k_0))
Eq(F_168(x, k_0), F_13(x, k_0)*F_40(x))
Eq(F_169(x, k_0), F_1(x) + F_170(x, k_0) + F_171(x, k_0) + F_182(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_20(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0)*F_40(x))
Eq(F_173(x, k_0), F_172(x, k_0)*F_40(x))
Eq(F_44(x, k_0), F_1(x) + F_173(x, k_0) + F_174(x, k_0) + F_175(x, k_0))
Eq(F_174(x, k_0), F_20(x, k_0)*F_44(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0)*F_40(x))
Eq(F_176(x, k_0), F_169(x, k_0) + F_177(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_173(x, k_0) + F_179(x, k_0) + F_180(x, k_0) + F_28(x))
Eq(F_179(x, k_0), F_178(x, k_0)*F_20(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_178(x, k_0)*F_40(x))
Eq(F_182(x, k_0), F_176(x, k_0)*F_40(x))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_40(x)*F_41(x, k_0))
Eq(F_186(x, k_0), F_185(x, k_0)*F_20(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), -F_38(x, 1) + (-k_0*F_38(x, k_0) + F_38(x, 1))/(1 - k_0))
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, 1, 4, 3], "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": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": 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