01243_01342_10243_10342_20143
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3505, 20910, 128672, 810230, 5193634, 33769514, 222155467, 1475842608, 9886416662, 66704415132, 452883985837, 3091788947752, 21210621357180, 146147599738602, 1010958933864072, 7018034754609670, 48876146740495793, 341393867562729336, 2391030257968841536, 16787701256400969542, 118138457010802862454, 833127782595464444778, 5886897624276006211303, 41673213908498900108566, 295508624539483841421249, 2098834159615891228797566, 14929233924777372998321104, 106343007933598201167435422, 758501489305468425624317610, 5416854354612733684747923678, 38730310900709433934992445289, 277230005202190677287019199368, 1986503862167827721770113591772, 14248691712736120866325504572730, 102299895620022742661413010022580, 735139629320262132324713595244744, 5287375846454305401060426339922420, 38060001343931365192164999766626352, 274182313698839802623575180634341448, 1976682556167503600262986725351060032, 14260905411431451796423205023255978510, 102957187658608519131767813597071594470, 743794903778251532836545544821763845589, 5376813785292904659770763890030104101072, 38892071703762707512545968969425693467524, 281482308198667269730184110699163159627994, 2038380840378089456859797307672988666996540, 14769117925822437064533809048799646942172198, 107065637722544285480435681925745091082008017, 776539884821426746224072261820574080951490472, 5634920098126974596285572562536802128860660908, 40908610630372058344300461733868537856066193782, 297123967926189427068154665733933936961495099974, 2158986873097300523265956444308153180838169373322, 15694423887780758582236296655472804959569940326843, 114134732754966099933882251181031974234590041057720, 830350871838545905305029342779620421966958646998278, 6043261795827478143190941514499399782537752515874860, 43998912115346882987126959671407961422892618564853301, 320455920682789201598029893244028594127470787784794200, 2334779008316102605991603884023895371074776846140400164, 17016485844607249080313651708905592640118454654972069034, 124061288309809000571036003109600301986834311515395208288, 904775627200927091087706678676650087497929116735864080746, 6600544373084545540981501965216626114739155392458455663959, 48166944572161184767442761992293557952108162393411174716960, 351597116637872585256427625013707119111485550977245242550516, 2567230751312071686886361280185410297174597558115180226531194, 18750142540725153152311919415819711693239665020729740689019266, 136981245662459709963265779111142485513286077648485129546840478, 1000993942234382268492750131284872147729045451936130473646058025, 7316656009916137584496695130364532943169790377449735184430276248, 53493601524369602936577459117719590391092425357407953527654934852, 391197726985721128553358137928072286362218167545151968995504439738, 2861498108332062791225421625089504949117399892208793757003144377148, 20935856334581812501323346674779111570782551802775361754977779855936, 153209495963362031888140495180969402493001387101408831143944899169088, 1121439829110617870461821307642309133314817219758853155455417217461104, 8210305956322138887873325658890033982538032387510329818949484226860056, 60122023964178988464359923428249795880888847559226896437749970987467248, 440348599510506172414636169420560967317519588562136180030173939667477560, 3225866460959006024343419177010147150007069585491753881557479772378710840, 23636377725324070547888028324913302289944896085960370230678501805305130972, 173220116770265860160677484585458961751208695092808527901277788402643480896, 1269687262506717075050921066714471304517700281184869132701459952046666818880, 9308387428226199948422009620723120530542006180068473654067928987217644743664, 68254245693928083624457863639116713940808011710325545791921172980457041916196, 500565322254018278287325465893020318346612998030632455285992088372048271489030, 3671690821307849748115061909917237338376155851718469304209620837881743758155313, 26936684729301669941265137695631534999258561687182267571603151283557433580731288, 197648428589218126963960816222745285441593760346989837912319411956185887459513984, 1450481874295635856864449028717328879003788415228722926898562987196893681865171110, 10646320678594009553691971816779851910855187395841894555171667245214260742485935466, 78154448045330222397892511240781055108655113412114187159056652854324754187778430894
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25070/
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[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[20,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[160,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[159,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[5,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[14,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[157,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[27,x,k[0]]
F[22,x,k[0]] = F[2,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[29,x,k[0]] = F[30,x,k[0]]+F[35,x,k[0]]
F[30,x,k[0]] = F[2,x]*F[31,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]*F[4,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[23,x,k[0]]*F[4,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x]*F[39,x,k[0]]*F[4,x]
F[37,x] = 1/F[4,x]*F[38,x]
F[38,x] = F[2,x]
F[40,x,k[0]] = F[156,x]*F[39,x,k[0]]*F[4,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[42,x,k[0]] = F[155,x,k[0]]+F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[4,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[152,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[48,x,k[0]] = F[4,x]*F[47,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[4,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[105,x,k[0]]+F[51,x,k[0]]
F[52,x,k[0]] = F[4,x]*F[51,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[54,x,k[0]] = F[103,x,k[0]]+F[53,x,k[0]]
F[54,x,k[0]] = F[15,x,k[0]]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,1,k[0]]
F[56,x,k[0],k[1]] = F[57,x,k[1]]+F[63,x,k[0],k[1]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[4,x]*F[59,x,k[0]]
F[59,x,k[0]] = 1/(-1+k[0])*(F[60,x,k[0]]*k[0]-F[60,x,1])
F[60,x,k[0]] = F[61,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[61,x,k[0]]
F[62,x,k[0]] = F[20,x,k[0]]
F[63,x,k[0],k[1]] = F[64,x,k[0],1,k[1]]
F[64,x,k[0],k[1],k[2]] = (F[65,x,k[0],k[1],k[2]]-F[65,x,k[0],1,k[2]])/(-1+k[1])
F[65,x,k[0],k[1],k[2]] = F[66,x,k[0],k[1],k[2]]
F[66,x,k[0],k[1],k[2]] = F[19,x,k[1]]*F[67,x,k[0],k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = (F[68,x,k[0],k[1],1]*k[1]-F[68,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[68,x,k[0],k[1],k[2]] = F[101,x,k[0],k[1],k[2]]+F[69,x,k[0],k[1]*k[2]]
F[70,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[69,x,k[0],k[1]]
F[71,x,k[0],k[1]] = 1/(-1+k[1])*(F[70,x,k[0],k[1]]*k[1]-F[70,x,k[0],1])
F[72,x,k[0],k[1]] = F[71,x,k[0],k[1]]+F[98,x,k[1]]
F[73,x,k[0],k[1]] = F[4,x]*F[72,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[74,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,k[1]]+F[96,x,k[0],k[1]]
F[10,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[0,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,1,k[0]]
F[80,x,k[0],k[1]] = F[81,x,k[0]*k[1],k[1]]
F[81,x,k[0],k[1]] = F[82,x,k[1]]+F[84,x,k[0],k[1]]
F[82,x,k[0]] = F[21,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[23,x,k[0]]+F[33,x,k[0]]
F[84,x,k[0],k[1]] = F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[19,x,k[0]]*F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = (F[87,x,k[0],1]*k[0]-F[87,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[87,x,k[0],k[1]] = F[88,x,k[0],k[0]*k[1]]
F[88,x,k[0],k[1]] = F[89,x,k[1],k[0]]
F[89,x,k[0],k[1]] = F[90,x,k[0],k[1]]+F[91,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[81,x,k[1],k[0]]
F[91,x,k[0],k[1]] = F[92,x,k[1],k[0]]
F[92,x,k[0],k[1]] = F[93,x,k[1]]+F[94,x,k[0],k[1]]
F[93,x,k[0]] = F[69,x,1,k[0]]
F[94,x,k[0],k[1]] = F[95,x,1,k[0],k[1]]
F[95,x,k[0],k[1],k[2]] = -k[0]*(F[65,x,1,k[1],k[2]]-F[65,x,k[0],k[1],k[2]])/(-1+k[0])
F[96,x,k[0],k[1]] = F[97,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[19,x,k[0]]*F[56,x,k[0],k[1]]
F[99,x,k[0]] = F[4,x]*F[98,x,k[0]]
F[99,x,k[0]] = F[75,x,k[0]]
F[100,x,k[0],k[1]] = -k[0]*(F[96,x,1,k[1]]-F[96,x,k[0],k[1]])/(-1+k[0])
F[101,x,k[0],k[1],k[2]] = -k[0]*(F[102,x,1,k[1],k[2]]-F[102,x,k[0],k[1],k[2]])/(-1+k[0])
F[102,x,k[0],k[1],k[2]] = F[65,x,k[0],k[1],k[1]*k[2]]
F[103,x,k[0]] = F[104,x,k[0]]+F[82,x,k[0]]
F[104,x,k[0]] = F[84,x,1,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]*F[4,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,1,k[0]]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1]]
F[110,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[4,x]
F[111,x,k[0],k[1]] = 1/(-1+k[1])*(F[112,x,k[0],k[1]]*k[1]-F[112,x,k[0],1])
F[112,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[151,x,k[0],k[1]]
F[114,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[140,x,k[0],k[1]]
F[115,x,k[0],k[1]] = F[114,x,k[0],k[1]]*F[19,x,k[1]]
F[115,x,k[0],k[1]] = F[116,x,k[0],k[1]]
F[116,x,k[0],k[1]] = F[117,x,k[1]]+F[119,x,k[0],k[1]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[119,x,k[0],k[1]] = F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]*F[19,x,k[0]]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[122,x,k[0],k[1]] = -k[1]*(F[116,x,k[0],1]-F[116,x,k[0],k[1]])/(-1+k[1])
F[123,x,k[0],k[1]] = F[124,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[125,x,k[0],k[1]]*F[4,x]
F[125,x,k[0],k[1]] = -k[1]*(F[126,x,k[0],1]-F[126,x,k[0],k[1]])/(-1+k[1])
F[126,x,k[0],k[1]] = F[127,x,k[1]]+F[137,x,k[0],k[1]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[19,x,k[0]]
F[130,x,k[0]] = F[129,x,k[0]]*F[4,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[21,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[19,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0],1]
F[135,x,k[0],k[1]] = (F[136,x,k[0],k[1]]*k[1]-F[136,x,k[0],1])/(-1+k[1])
F[136,x,k[0],k[1]] = F[92,x,k[0],k[0]*k[1]]
F[137,x,k[0],k[1]] = -k[1]*(F[138,x,k[0],1]-F[138,x,k[0],k[1]])/(-1+k[1])
F[138,x,k[0],k[1]] = F[139,x,k[0],k[1]]
F[139,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[19,x,k[0]]
F[140,x,k[0],k[1]] = (F[141,x,k[0],k[1]]*k[0]-F[141,x,1,k[1]])/(-1+k[0])
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]*F[19,x,k[1]]
F[143,x,k[0],k[1]] = F[144,x,k[0],k[1],1]
F[144,x,k[0],k[1],k[2]] = (F[145,x,k[0],k[1],k[2]]*k[2]-F[145,x,k[0],k[1],1])/(-1+k[2])
F[145,x,k[0],k[1],k[2]] = F[113,x,k[0],k[1]*k[2]]+F[146,x,k[0],k[1],k[2]]
F[146,x,k[0],k[1],k[2]] = (F[147,x,k[0],k[1],k[2]]*k[0]-F[147,x,1,k[1],k[2]])/(-1+k[0])
F[147,x,k[0],k[1],k[2]] = F[148,x,k[0],k[1],k[1]*k[2]]
F[148,x,k[0],k[1],k[2]] = F[149,x,k[0],k[1],k[2]]
F[149,x,k[0],k[1],k[2]] = F[150,x,k[0],k[1],k[2]]*F[19,x,k[1]]
F[150,x,k[0],k[1],k[2]] = (F[145,x,k[0],k[1],1]*k[1]-F[145,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[151,x,k[0],k[1]] = (F[109,x,k[0],k[1]]*k[0]-F[109,x,1,k[1]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[154,x]*F[39,x,k[0]]
F[154,x] = (1+F[154,x])*x+F[154,x]^2
F[55,x,k[0]] = F[104,x,k[0]]+F[155,x,k[0]]
F[156,x] = 2+F[156,x]^2+(-2+x)*F[156,x]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[4,x]*F[55,x,k[0]]
F[61,x,k[0]] = F[159,x,k[0]]+F[54,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,1,k[0]]
F[163,x,k[0],k[1]] = F[162,x,k[0],k[1]]*F[4,x]
F[163,x,k[0],k[1]] = F[141,x,k[0],k[1]]
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)+F_{160}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{159}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = y_{0} x
F_{20}\! \left(x , y_{0}\right) = F_{157}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right) F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x \right) F_{39}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x , y_{0}\right) = F_{156}\! \left(x \right) F_{39}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{44}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{47}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{51}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , 1, y_{0}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = -\frac{-F_{60}\! \left(x , y_{0}\right) y_{0}+F_{60}\! \left(x , 1\right)}{-1+y_{0}}
F_{60}\! \left(x , y_{0}\right) = F_{61}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{64}\! \left(x , y_{0}, 1, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{65}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{1}\right) F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{68}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{68}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{101}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{69}\! \left(x , y_{0}, y_{1} y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{69}\! \left(x , y_{0}, y_{1}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{70}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{70}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{71}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{4}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{74}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , y_{1}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}\right) = F_{75}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , 1, y_{0}\right)
F_{80}\! \left(x , y_{0}, y_{1}\right) = F_{81}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{82}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{85}\! \left(x , y_{0}, y_{1}\right)
F_{85}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)
F_{86}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{87}\! \left(x , y_{0}, 1\right) y_{0}-F_{87}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{87}\! \left(x , y_{0}, y_{1}\right) = F_{88}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{88}\! \left(x , y_{0}, y_{1}\right) = F_{89}\! \left(x , y_{1}, y_{0}\right)
F_{89}\! \left(x , y_{0}, y_{1}\right) = F_{90}\! \left(x , y_{0}, y_{1}\right)+F_{91}\! \left(x , y_{0}, y_{1}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = F_{81}\! \left(x , y_{1}, y_{0}\right)
F_{91}\! \left(x , y_{0}, y_{1}\right) = F_{92}\! \left(x , y_{1}, y_{0}\right)
F_{92}\! \left(x , y_{0}, y_{1}\right) = F_{93}\! \left(x , y_{1}\right)+F_{94}\! \left(x , y_{0}, y_{1}\right)
F_{93}\! \left(x , y_{0}\right) = F_{69}\! \left(x , 1, y_{0}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{95}\! \left(x , 1, y_{0}, y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{65}\! \left(x , 1, y_{1}, y_{2}\right)-F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{96}\! \left(x , y_{0}, y_{1}\right) = F_{97}\! \left(x , y_{0}, y_{1}\right)
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{99}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{98}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{75}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{96}\! \left(x , 1, y_{1}\right)-F_{96}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{101}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{102}\! \left(x , 1, y_{1}, y_{2}\right)-F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{65}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{103}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{84}\! \left(x , 1, y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , 1, y_{0}\right)
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0}, y_{1}\right)
F_{110}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{112}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{112}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{112}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{140}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{1}\right)+F_{119}\! \left(x , y_{0}, y_{1}\right)
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{120}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{116}\! \left(x , y_{0}, 1\right)-F_{116}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{123}\! \left(x , y_{0}, y_{1}\right) = F_{124}\! \left(x , y_{0}, y_{1}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{126}\! \left(x , y_{0}, 1\right)-F_{126}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)
F_{127}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{132}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{132}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)
F_{133}\! \left(x , y_{0}\right) = F_{134}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{134}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}, 1\right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{136}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{136}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{92}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{138}\! \left(x , y_{0}, 1\right)-F_{138}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{138}\! \left(x , y_{0}, y_{1}\right) = F_{139}\! \left(x , y_{0}, y_{1}\right)
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{0}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{141}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , y_{0}, y_{1}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{143}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{1}\right)
F_{143}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}, 1\right)
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{145}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{147}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{148}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{148}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{19}\! \left(x , y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{145}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{145}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{151}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{109}\! \left(x , y_{0}, y_{1}\right)+F_{109}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)
F_{153}\! \left(x , y_{0}\right) = F_{154}\! \left(x \right) F_{39}\! \left(x , y_{0}\right)
F_{154}\! \left(x \right) = F_{154}\! \left(x \right) x +F_{154} \left(x \right)^{2}+x
F_{55}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right)+F_{155}\! \left(x , y_{0}\right)
F_{156}\! \left(x \right) = F_{156}\! \left(x \right) x +F_{156} \left(x \right)^{2}-2 F_{156}\! \left(x \right)+2
F_{157}\! \left(x , y_{0}\right) = F_{158}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{55}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)
F_{160}\! \left(x , y_{0}\right) = F_{161}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , 1, y_{0}\right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_20(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_19(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_160(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_159(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_5(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_14(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_157(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_27(x, k_0))
Eq(F_22(x, k_0), F_2(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_4(x))
Eq(F_29(x, k_0), F_30(x, k_0) + F_35(x, k_0))
Eq(F_30(x, k_0), F_2(x)*F_31(x, k_0))
Eq(F_32(x, k_0), F_31(x, k_0)*F_4(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_23(x, k_0)*F_4(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x)*F_39(x, k_0)*F_4(x))
Eq(F_37(x), F_38(x)/F_4(x))
Eq(F_38(x), F_2(x))
Eq(F_40(x, k_0), F_156(x)*F_39(x, k_0)*F_4(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_42(x, k_0), F_155(x, k_0) + F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_4(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_152(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_48(x, k_0), F_4(x)*F_47(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_4(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_105(x, k_0) + F_51(x, k_0))
Eq(F_52(x, k_0), F_4(x)*F_51(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_54(x, k_0), F_103(x, k_0) + F_53(x, k_0))
Eq(F_54(x, k_0), F_15(x, k_0) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, 1, k_0))
Eq(F_56(x, k_0, k_1), F_57(x, k_1) + F_63(x, k_0, k_1))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_4(x)*F_59(x, k_0))
Eq(F_59(x, k_0), (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_61(x, k_0))
Eq(F_62(x, k_0), F_20(x, k_0))
Eq(F_63(x, k_0, k_1), F_64(x, k_0, 1, k_1))
Eq(F_64(x, k_0, k_1, k_2), -F_65(x, k_0, k_1, k_2) + (-k_1*F_65(x, k_0, k_1, k_2) + F_65(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_65(x, k_0, k_1, k_2), F_66(x, k_0, k_1, k_2))
Eq(F_66(x, k_0, k_1, k_2), F_19(x, k_1)*F_67(x, k_0, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), (-k_1*F_68(x, k_0, k_1, 1) + k_2*F_68(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_68(x, k_0, k_1, k_2), F_101(x, k_0, k_1, k_2) + F_69(x, k_0, k_1*k_2))
Eq(F_70(x, k_0, k_1), F_100(x, k_0, k_1) + F_69(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), (k_1*F_70(x, k_0, k_1) - F_70(x, k_0, 1))/(k_1 - 1))
Eq(F_72(x, k_0, k_1), F_71(x, k_0, k_1) + F_98(x, k_1))
Eq(F_73(x, k_0, k_1), F_4(x)*F_72(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_74(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, k_1) + F_96(x, k_0, k_1))
Eq(F_10(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_0(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, 1, k_0))
Eq(F_80(x, k_0, k_1), F_81(x, k_0*k_1, k_1))
Eq(F_81(x, k_0, k_1), F_82(x, k_1) + F_84(x, k_0, k_1))
Eq(F_82(x, k_0), F_21(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_23(x, k_0) + F_33(x, k_0))
Eq(F_84(x, k_0, k_1), F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_19(x, k_0)*F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), (-k_0*F_87(x, k_0, 1) + k_1*F_87(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_87(x, k_0, k_1), F_88(x, k_0, k_0*k_1))
Eq(F_88(x, k_0, k_1), F_89(x, k_1, k_0))
Eq(F_89(x, k_0, k_1), F_90(x, k_0, k_1) + F_91(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_81(x, k_1, k_0))
Eq(F_91(x, k_0, k_1), F_92(x, k_1, k_0))
Eq(F_92(x, k_0, k_1), F_93(x, k_1) + F_94(x, k_0, k_1))
Eq(F_93(x, k_0), F_69(x, 1, k_0))
Eq(F_94(x, k_0, k_1), F_95(x, 1, k_0, k_1))
Eq(F_95(x, k_0, k_1, k_2), -F_65(x, 1, k_1, k_2) + (-k_0*F_65(x, k_0, k_1, k_2) + F_65(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_96(x, k_0, k_1), F_97(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_19(x, k_0)*F_56(x, k_0, k_1))
Eq(F_99(x, k_0), F_4(x)*F_98(x, k_0))
Eq(F_99(x, k_0), F_75(x, k_0))
Eq(F_100(x, k_0, k_1), -F_96(x, 1, k_1) + (-k_0*F_96(x, k_0, k_1) + F_96(x, 1, k_1))/(1 - k_0))
Eq(F_101(x, k_0, k_1, k_2), -F_102(x, 1, k_1, k_2) + (-k_0*F_102(x, k_0, k_1, k_2) + F_102(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_102(x, k_0, k_1, k_2), F_65(x, k_0, k_1, k_1*k_2))
Eq(F_103(x, k_0), F_104(x, k_0) + F_82(x, k_0))
Eq(F_104(x, k_0), F_84(x, 1, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0)*F_4(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, 1, k_0))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1))
Eq(F_110(x, k_0, k_1), F_111(x, k_0, k_1)*F_4(x))
Eq(F_111(x, k_0, k_1), (k_1*F_112(x, k_0, k_1) - F_112(x, k_0, 1))/(k_1 - 1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0, k_1) + F_151(x, k_0, k_1))
Eq(F_114(x, k_0, k_1), F_113(x, k_0, k_1) + F_140(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), F_114(x, k_0, k_1)*F_19(x, k_1))
Eq(F_115(x, k_0, k_1), F_116(x, k_0, k_1))
Eq(F_116(x, k_0, k_1), F_117(x, k_1) + F_119(x, k_0, k_1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_119(x, k_0, k_1), F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1)*F_19(x, k_0))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_122(x, k_0, k_1), -F_116(x, k_0, 1) + (k_1*F_116(x, k_0, k_1) - F_116(x, k_0, 1))/(k_1 - 1))
Eq(F_123(x, k_0, k_1), F_124(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_125(x, k_0, k_1)*F_4(x))
Eq(F_125(x, k_0, k_1), -F_126(x, k_0, 1) + (k_1*F_126(x, k_0, k_1) - F_126(x, k_0, 1))/(k_1 - 1))
Eq(F_126(x, k_0, k_1), F_127(x, k_1) + F_137(x, k_0, k_1))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_19(x, k_0))
Eq(F_130(x, k_0), F_129(x, k_0)*F_4(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_21(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_19(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0, 1))
Eq(F_135(x, k_0, k_1), (-k_1*F_136(x, k_0, k_1) + F_136(x, k_0, 1))/(1 - k_1))
Eq(F_136(x, k_0, k_1), F_92(x, k_0, k_0*k_1))
Eq(F_137(x, k_0, k_1), -F_138(x, k_0, 1) + (k_1*F_138(x, k_0, k_1) - F_138(x, k_0, 1))/(k_1 - 1))
Eq(F_138(x, k_0, k_1), F_139(x, k_0, k_1))
Eq(F_139(x, k_0, k_1), F_126(x, k_0, k_1)*F_19(x, k_0))
Eq(F_140(x, k_0, k_1), (-k_0*F_141(x, k_0, k_1) + F_141(x, 1, k_1))/(1 - k_0))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1)*F_19(x, k_1))
Eq(F_143(x, k_0, k_1), F_144(x, k_0, k_1, 1))
Eq(F_144(x, k_0, k_1, k_2), (-k_2*F_145(x, k_0, k_1, k_2) + F_145(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_145(x, k_0, k_1, k_2), F_113(x, k_0, k_1*k_2) + F_146(x, k_0, k_1, k_2))
Eq(F_146(x, k_0, k_1, k_2), (-k_0*F_147(x, k_0, k_1, k_2) + F_147(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_147(x, k_0, k_1, k_2), F_148(x, k_0, k_1, k_1*k_2))
Eq(F_148(x, k_0, k_1, k_2), F_149(x, k_0, k_1, k_2))
Eq(F_149(x, k_0, k_1, k_2), F_150(x, k_0, k_1, k_2)*F_19(x, k_1))
Eq(F_150(x, k_0, k_1, k_2), (-k_1*F_145(x, k_0, k_1, 1) + k_2*F_145(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_151(x, k_0, k_1), (-k_0*F_109(x, k_0, k_1) + F_109(x, 1, k_1))/(1 - k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_154(x)*F_39(x, k_0))
Eq(F_154(x), (x - 3)*(F_154(x) + 1) + (F_154(x) + 1)**2 + F_154(x) + 2)
Eq(F_55(x, k_0), F_104(x, k_0) + F_155(x, k_0))
Eq(F_156(x), (x - 2)*F_156(x) + F_156(x)**2 + 2)
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_4(x)*F_55(x, k_0))
Eq(F_61(x, k_0), F_159(x, k_0) + F_54(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, 1, k_0))
Eq(F_163(x, k_0, k_1), F_162(x, k_0, k_1)*F_4(x))
Eq(F_163(x, k_0, k_1), F_141(x, k_0, k_1))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 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"pos": [[1, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25653/
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[5,x]+F[95,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[7,x]+F[92,x]+F[93,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[86,x,k[0]]+F[88,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[15,x,1,k[0]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[58,x,k[0],k[1]]+F[60,x,k[0],k[1]]+F[78,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[3,x]
F[17,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[18,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[43,x,k[1],k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[3,x]
F[20,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0]]*F[23,x,k[0],k[1]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1]] = (F[24,x,k[0],1]*k[0]-F[24,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[25,x,k[0],k[0]*k[1]]
F[25,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[53,x,k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[3,x]
F[27,x,k[0],k[1]] = F[1,x]+F[28,x,k[0],k[1]]+F[44,x,k[0],k[1]]+F[46,x,k[0],k[1]]+F[50,x,k[0],k[1]]+F[52,x,k[1]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[3,x]
F[29,x,k[0],k[1]] = F[30,x,1,k[0],k[1]]
F[30,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[31,x,k[0],k[1],k[2]]*k[0]-F[31,x,1,k[1],k[2]])
F[31,x,k[0],k[1],k[2]] = F[1,x]+F[32,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[36,x,k[0],k[1],k[2]]+F[40,x,k[1],k[0],k[2]]+F[43,x,k[2],k[0]]
F[32,x,k[0],k[1],k[2]] = F[3,x]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[31,x,k[0],k[1],k[2]]*k[0]-F[31,x,1,k[1],k[2]])
F[34,x,k[0],k[1],k[2]] = F[3,x]*F[35,x,k[0],k[1],k[2]]
F[35,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[2]]*k[0]-F[20,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[36,x,k[0],k[1],k[2]] = F[22,x,k[0]]*F[37,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = (F[38,x,k[0],1,k[2]]*k[0]-F[38,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[38,x,k[0],k[1],k[2]] = F[39,x,k[0],k[0]*k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = (F[25,x,k[0],k[1]]*k[1]-F[25,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[40,x,k[0],k[1],k[2]] = F[22,x,k[0]]*F[41,x,k[1],k[0],k[2]]
F[41,x,k[0],k[1],k[2]] = (-F[42,x,1,k[1],k[2]]*k[1]+F[42,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[42,x,k[0],k[1],k[2]] = F[39,x,k[0]*k[1],k[1],k[2]]
F[43,x,k[0],k[1]] = F[22,x,k[0]]*F[25,x,k[1],k[0]]
F[44,x,k[0],k[1]] = F[3,x]*F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = 1/(-1+k[0])*(F[20,x,k[0],k[1]]*k[0]-F[20,x,1,k[1]])
F[46,x,k[0],k[1]] = F[3,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = 1/(-1+k[0])*(F[48,x,k[0],k[1]]*k[0]-F[48,x,1,k[1]])
F[48,x,k[0],k[1]] = (F[49,x,k[0]]*k[0]-F[49,x,k[1]]*k[1])/(-k[1]+k[0])
F[49,x,k[0]] = F[25,x,1,k[0]]
F[50,x,k[0],k[1]] = F[22,x,k[0]]*F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[41,x,1,k[0],k[1]]
F[52,x,k[0]] = F[22,x,k[0]]*F[49,x,k[0]]
F[53,x,k[0]] = F[22,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[55,x,k[0]]+F[57,x,k[0]]
F[55,x,k[0]] = F[3,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[18,x,1,k[0]]
F[57,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[58,x,k[0],k[1]] = F[3,x]*F[59,x,k[0],k[1]]
F[59,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[60,x,k[0],k[1]] = F[22,x,k[0]]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = (F[62,x,k[0],1]*k[0]-F[62,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[62,x,k[0],k[1]] = F[63,x,k[0],k[0]*k[1]]
F[63,x,k[0],k[1]] = F[1,x]+F[26,x,k[0],k[1]]+F[53,x,k[1]]+F[60,x,k[0],k[1]]+F[64,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[3,x]*F[65,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[1,x]+F[28,x,k[0],k[1]]+F[66,x,k[0],k[1]]+F[79,x,k[0],k[1]]+F[83,x,k[0],k[1]]+F[85,x,k[1]]
F[66,x,k[0],k[1]] = F[3,x]*F[67,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[68,x,1,k[0],k[1]]
F[68,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[69,x,k[0],k[1],k[2]]*k[0]-F[69,x,1,k[1],k[2]])
F[69,x,k[0],k[1],k[2]] = F[1,x]+F[32,x,k[0],k[1],k[2]]+F[70,x,k[0],k[1],k[2]]+F[72,x,k[0],k[1],k[2]]+F[74,x,k[1],k[0],k[2]]+F[78,x,k[2],k[0]]
F[70,x,k[0],k[1],k[2]] = F[3,x]*F[71,x,k[0],k[1],k[2]]
F[71,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[69,x,k[0],k[1],k[2]]*k[0]-F[69,x,1,k[1],k[2]])
F[72,x,k[0],k[1],k[2]] = F[22,x,k[0]]*F[73,x,k[0],k[1],k[2]]
F[73,x,k[0],k[1],k[2]] = (F[61,x,k[0],k[1]]*k[1]-F[61,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[74,x,k[0],k[1],k[2]] = F[22,x,k[0]]*F[75,x,k[1],k[0],k[2]]
F[75,x,k[0],k[1],k[2]] = (-F[76,x,1,k[1],k[2]]*k[1]+F[76,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[76,x,k[0],k[1],k[2]] = F[77,x,k[0]*k[1],k[1],k[2]]
F[77,x,k[0],k[1],k[2]] = (F[63,x,k[0],k[1]]*k[1]-F[63,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[78,x,k[0],k[1]] = F[22,x,k[0]]*F[63,x,k[1],k[0]]
F[79,x,k[0],k[1]] = F[3,x]*F[80,x,k[0],k[1]]
F[80,x,k[0],k[1]] = 1/(-1+k[0])*(F[81,x,k[0],k[1]]*k[0]-F[81,x,1,k[1]])
F[81,x,k[0],k[1]] = (F[82,x,k[0]]*k[0]-F[82,x,k[1]]*k[1])/(-k[1]+k[0])
F[82,x,k[0]] = F[63,x,1,k[0]]
F[83,x,k[0],k[1]] = F[22,x,k[0]]*F[84,x,k[0],k[1]]
F[84,x,k[0],k[1]] = F[75,x,1,k[0],k[1]]
F[85,x,k[0]] = F[22,x,k[0]]*F[82,x,k[0]]
F[86,x,k[0]] = F[3,x]*F[87,x,k[0]]
F[87,x,k[0]] = 1/(-1+k[0])*(F[49,x,k[0]]*k[0]-F[49,x,1])
F[88,x,k[0]] = F[22,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,1,k[0]]
F[90,x,k[0],k[1]] = (-F[91,x,1,k[1]]*k[1]+F[91,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[91,x,k[0],k[1]] = F[25,x,k[0]*k[1],k[1]]
F[92,x] = F[57,x,1]
F[93,x] = F[3,x]*F[94,x]
F[94,x] = F[49,x,1]
F[95,x] = F[3,x]*F[96,x]
F[96,x] = F[97,x,1]
F[97,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[8,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[3,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[22,x,k[0]]
F[101,x,k[0]] = F[62,x,k[0],1]
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_{5}\! \left(x \right)+F_{95}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)+F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{12}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = -\frac{-F_{9}\! \left(x , y_{0}\right) y_{0}+F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y_{0}\right) = -\frac{-F_{14}\! \left(x , y_{0}\right) y_{0}+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, y_{0}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)+F_{78}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{1}, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{14}\! \left(x , y_{0}\right) y_{0}-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{24}\! \left(x , y_{0}, 1\right) y_{0}-F_{24}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , 1, y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{43}\! \left(x , y_{2}, y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}\right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{38}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{38}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{25}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{25}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{42}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{42}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{1}, y_{0}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{20}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{20}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{48}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{48}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{49}\! \left(x , y_{0}\right) y_{0}-F_{49}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{49}\! \left(x , y_{0}\right) = F_{25}\! \left(x , 1, y_{0}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , 1, y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{18}\! \left(x , 1, y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{59}\! \left(x , y_{0}, y_{1}\right)
F_{59}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{62}\! \left(x , y_{0}, 1\right) y_{0}-F_{62}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)+F_{64}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{65}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{66}\! \left(x , y_{0}, y_{1}\right)+F_{79}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{1}\right)
F_{66}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{67}\! \left(x , y_{0}, y_{1}\right)
F_{67}\! \left(x , y_{0}, y_{1}\right) = F_{68}\! \left(x , 1, y_{0}, y_{1}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{69}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{78}\! \left(x , y_{2}, y_{0}\right)
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{69}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}\right) F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{61}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{61}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{76}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{76}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{77}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{63}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{63}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{78}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{63}\! \left(x , y_{1}, y_{0}\right)
F_{79}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{80}\! \left(x , y_{0}, y_{1}\right)
F_{80}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{81}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{81}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{81}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{82}\! \left(x , y_{0}\right) y_{0}-F_{82}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{82}\! \left(x , y_{0}\right) = F_{63}\! \left(x , 1, y_{0}\right)
F_{83}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , 1, y_{0}, y_{1}\right)
F_{85}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = -\frac{-F_{49}\! \left(x , y_{0}\right) y_{0}+F_{49}\! \left(x , 1\right)}{-1+y_{0}}
F_{88}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{90}\! \left(x , 1, y_{0}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{91}\! \left(x , 1, y_{1}\right) y_{1}-y_{0} F_{91}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{91}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{92}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{93}\! \left(x \right) = F_{3}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{95}\! \left(x \right) = F_{3}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x , 1\right)
F_{97}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{97}\! \left(x , y_{0}\right)+F_{97}\! \left(x , 1\right)}{-1+y_{0}}
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}, 1\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_5(x) + F_95(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_7(x) + F_92(x) + F_93(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_15(x, 1, k_0))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_58(x, k_0, k_1) + F_60(x, k_0, k_1) + F_78(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_3(x))
Eq(F_17(x, k_0, k_1), (k_0*F_18(x, k_0, k_1) - F_18(x, 1, k_1))/(k_0 - 1))
Eq(F_18(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_43(x, k_1, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_3(x))
Eq(F_20(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0)*F_23(x, k_0, k_1))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0, 1) + k_1*F_24(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_0*k_1))
Eq(F_25(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_26(x, k_0, k_1) + F_53(x, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_3(x))
Eq(F_27(x, k_0, k_1), F_1(x) + F_28(x, k_0, k_1) + F_44(x, k_0, k_1) + F_46(x, k_0, k_1) + F_50(x, k_0, k_1) + F_52(x, k_1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_3(x))
Eq(F_29(x, k_0, k_1), F_30(x, 1, k_0, k_1))
Eq(F_30(x, k_0, k_1, k_2), (-k_0*F_31(x, k_0, k_1, k_2) + F_31(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_31(x, k_0, k_1, k_2), F_1(x) + F_32(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_36(x, k_0, k_1, k_2) + F_40(x, k_1, k_0, k_2) + F_43(x, k_2, k_0))
Eq(F_32(x, k_0, k_1, k_2), F_3(x)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), (k_0*F_31(x, k_0, k_1, k_2) - F_31(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_34(x, k_0, k_1, k_2), F_3(x)*F_35(x, k_0, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, k_2) + k_1*F_20(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1, k_2), F_22(x, k_0)*F_37(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), (-k_0*F_38(x, k_0, 1, k_2) + k_1*F_38(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_38(x, k_0, k_1, k_2), F_39(x, k_0, k_0*k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), (-k_1*F_25(x, k_0, k_1) + k_2*F_25(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_40(x, k_0, k_1, k_2), F_22(x, k_0)*F_41(x, k_1, k_0, k_2))
Eq(F_41(x, k_0, k_1, k_2), (-k_0*F_42(x, k_0/k_1, k_1, k_2) + k_1*F_42(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1, k_2), F_39(x, k_0*k_1, k_1, k_2))
Eq(F_43(x, k_0, k_1), F_22(x, k_0)*F_25(x, k_1, k_0))
Eq(F_44(x, k_0, k_1), F_3(x)*F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), (k_0*F_20(x, k_0, k_1) - F_20(x, 1, k_1))/(k_0 - 1))
Eq(F_46(x, k_0, k_1), F_3(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (k_0*F_48(x, k_0, k_1) - F_48(x, 1, k_1))/(k_0 - 1))
Eq(F_48(x, k_0, k_1), (-k_0*F_49(x, k_0) + k_1*F_49(x, k_1))/(-k_0 + k_1))
Eq(F_49(x, k_0), F_25(x, 1, k_0))
Eq(F_50(x, k_0, k_1), F_22(x, k_0)*F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_41(x, 1, k_0, k_1))
Eq(F_52(x, k_0), F_22(x, k_0)*F_49(x, k_0))
Eq(F_53(x, k_0), F_22(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_53(x, k_0) + F_55(x, k_0) + F_57(x, k_0))
Eq(F_55(x, k_0), F_3(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_18(x, 1, k_0))
Eq(F_57(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_58(x, k_0, k_1), F_3(x)*F_59(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_60(x, k_0, k_1), F_22(x, k_0)*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), (-k_0*F_62(x, k_0, 1) + k_1*F_62(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_0*k_1))
Eq(F_63(x, k_0, k_1), F_1(x) + F_26(x, k_0, k_1) + F_53(x, k_1) + F_60(x, k_0, k_1) + F_64(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_3(x)*F_65(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_1(x) + F_28(x, k_0, k_1) + F_66(x, k_0, k_1) + F_79(x, k_0, k_1) + F_83(x, k_0, k_1) + F_85(x, k_1))
Eq(F_66(x, k_0, k_1), F_3(x)*F_67(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_68(x, 1, k_0, k_1))
Eq(F_68(x, k_0, k_1, k_2), (-k_0*F_69(x, k_0, k_1, k_2) + F_69(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_69(x, k_0, k_1, k_2), F_1(x) + F_32(x, k_0, k_1, k_2) + F_70(x, k_0, k_1, k_2) + F_72(x, k_0, k_1, k_2) + F_74(x, k_1, k_0, k_2) + F_78(x, k_2, k_0))
Eq(F_70(x, k_0, k_1, k_2), F_3(x)*F_71(x, k_0, k_1, k_2))
Eq(F_71(x, k_0, k_1, k_2), (k_0*F_69(x, k_0, k_1, k_2) - F_69(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_72(x, k_0, k_1, k_2), F_22(x, k_0)*F_73(x, k_0, k_1, k_2))
Eq(F_73(x, k_0, k_1, k_2), (-k_1*F_61(x, k_0, k_1) + k_2*F_61(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_74(x, k_0, k_1, k_2), F_22(x, k_0)*F_75(x, k_1, k_0, k_2))
Eq(F_75(x, k_0, k_1, k_2), (-k_0*F_76(x, k_0/k_1, k_1, k_2) + k_1*F_76(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_76(x, k_0, k_1, k_2), F_77(x, k_0*k_1, k_1, k_2))
Eq(F_77(x, k_0, k_1, k_2), (-k_1*F_63(x, k_0, k_1) + k_2*F_63(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_78(x, k_0, k_1), F_22(x, k_0)*F_63(x, k_1, k_0))
Eq(F_79(x, k_0, k_1), F_3(x)*F_80(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), (k_0*F_81(x, k_0, k_1) - F_81(x, 1, k_1))/(k_0 - 1))
Eq(F_81(x, k_0, k_1), (-k_0*F_82(x, k_0) + k_1*F_82(x, k_1))/(-k_0 + k_1))
Eq(F_82(x, k_0), F_63(x, 1, k_0))
Eq(F_83(x, k_0, k_1), F_22(x, k_0)*F_84(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), F_75(x, 1, k_0, k_1))
Eq(F_85(x, k_0), F_22(x, k_0)*F_82(x, k_0))
Eq(F_86(x, k_0), F_3(x)*F_87(x, k_0))
Eq(F_87(x, k_0), (k_0*F_49(x, k_0) - F_49(x, 1))/(k_0 - 1))
Eq(F_88(x, k_0), F_22(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, 1, k_0))
Eq(F_90(x, k_0, k_1), (-k_0*F_91(x, k_0/k_1, k_1) + k_1*F_91(x, 1, k_1))/(-k_0 + k_1))
Eq(F_91(x, k_0, k_1), F_25(x, k_0*k_1, k_1))
Eq(F_92(x), F_57(x, 1))
Eq(F_93(x), F_3(x)*F_94(x))
Eq(F_94(x), F_49(x, 1))
Eq(F_95(x), F_3(x)*F_96(x))
Eq(F_96(x), F_97(x, 1))
Eq(F_97(x, k_0), F_1(x) + F_100(x, k_0) + F_8(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_3(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_22(x, k_0))
Eq(F_101(x, k_0), F_62(x, k_0, 1))
Pack JSON:
{"name": "col_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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[[0, 4], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 4], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 4], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 4], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 4], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 3], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 3], [0, 4], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 4], [0, 4], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 4], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 4], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 4], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 4], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 4], [0, 0]]}, {"patt": [2, 0, 1, 4, 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, 1], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25854/
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[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[20,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[160,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[159,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[5,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[14,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[157,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[27,x,k[0]]
F[22,x,k[0]] = F[2,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[29,x,k[0]] = F[30,x,k[0]]+F[35,x,k[0]]
F[30,x,k[0]] = F[2,x]*F[31,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]*F[4,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[23,x,k[0]]*F[4,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x]*F[39,x,k[0]]*F[4,x]
F[37,x] = 1/F[4,x]*F[38,x]
F[38,x] = F[2,x]
F[40,x,k[0]] = F[156,x]*F[39,x,k[0]]*F[4,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[42,x,k[0]] = F[155,x,k[0]]+F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[4,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[152,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[48,x,k[0]] = F[4,x]*F[47,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[4,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[105,x,k[0]]+F[51,x,k[0]]
F[52,x,k[0]] = F[4,x]*F[51,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[54,x,k[0]] = F[103,x,k[0]]+F[53,x,k[0]]
F[54,x,k[0]] = F[15,x,k[0]]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,1,k[0]]
F[56,x,k[0],k[1]] = F[57,x,k[1]]+F[63,x,k[0],k[1]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[4,x]*F[59,x,k[0]]
F[59,x,k[0]] = 1/(-1+k[0])*(F[60,x,k[0]]*k[0]-F[60,x,1])
F[60,x,k[0]] = F[61,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[61,x,k[0]]
F[62,x,k[0]] = F[20,x,k[0]]
F[63,x,k[0],k[1]] = F[64,x,k[0],1,k[1]]
F[64,x,k[0],k[1],k[2]] = (F[65,x,k[0],k[1],k[2]]-F[65,x,k[0],1,k[2]])/(-1+k[1])
F[65,x,k[0],k[1],k[2]] = F[66,x,k[0],k[1],k[2]]
F[66,x,k[0],k[1],k[2]] = F[19,x,k[1]]*F[67,x,k[0],k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = (F[68,x,k[0],k[1],1]*k[1]-F[68,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[68,x,k[0],k[1],k[2]] = F[101,x,k[0],k[1],k[2]]+F[69,x,k[0],k[1]*k[2]]
F[70,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[69,x,k[0],k[1]]
F[71,x,k[0],k[1]] = 1/(-1+k[1])*(F[70,x,k[0],k[1]]*k[1]-F[70,x,k[0],1])
F[72,x,k[0],k[1]] = F[71,x,k[0],k[1]]+F[98,x,k[1]]
F[73,x,k[0],k[1]] = F[4,x]*F[72,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[74,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,k[1]]+F[96,x,k[0],k[1]]
F[10,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[0,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,1,k[0]]
F[80,x,k[0],k[1]] = F[81,x,k[0]*k[1],k[1]]
F[81,x,k[0],k[1]] = F[82,x,k[1]]+F[84,x,k[0],k[1]]
F[82,x,k[0]] = F[21,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[23,x,k[0]]+F[33,x,k[0]]
F[84,x,k[0],k[1]] = F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[19,x,k[0]]*F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = (F[87,x,k[0],1]*k[0]-F[87,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[87,x,k[0],k[1]] = F[88,x,k[0],k[0]*k[1]]
F[88,x,k[0],k[1]] = F[89,x,k[1],k[0]]
F[89,x,k[0],k[1]] = F[90,x,k[0],k[1]]+F[91,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[81,x,k[1],k[0]]
F[91,x,k[0],k[1]] = F[92,x,k[1],k[0]]
F[92,x,k[0],k[1]] = F[93,x,k[1]]+F[94,x,k[0],k[1]]
F[93,x,k[0]] = F[69,x,1,k[0]]
F[94,x,k[0],k[1]] = F[95,x,1,k[0],k[1]]
F[95,x,k[0],k[1],k[2]] = -k[0]*(F[65,x,1,k[1],k[2]]-F[65,x,k[0],k[1],k[2]])/(-1+k[0])
F[96,x,k[0],k[1]] = F[97,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[19,x,k[0]]*F[56,x,k[0],k[1]]
F[99,x,k[0]] = F[4,x]*F[98,x,k[0]]
F[99,x,k[0]] = F[75,x,k[0]]
F[100,x,k[0],k[1]] = -k[0]*(F[96,x,1,k[1]]-F[96,x,k[0],k[1]])/(-1+k[0])
F[101,x,k[0],k[1],k[2]] = -k[0]*(F[102,x,1,k[1],k[2]]-F[102,x,k[0],k[1],k[2]])/(-1+k[0])
F[102,x,k[0],k[1],k[2]] = F[65,x,k[0],k[1],k[1]*k[2]]
F[103,x,k[0]] = F[104,x,k[0]]+F[82,x,k[0]]
F[104,x,k[0]] = F[84,x,1,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]*F[4,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,1,k[0]]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1]]
F[110,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[4,x]
F[111,x,k[0],k[1]] = 1/(-1+k[1])*(F[112,x,k[0],k[1]]*k[1]-F[112,x,k[0],1])
F[112,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[151,x,k[0],k[1]]
F[114,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[140,x,k[0],k[1]]
F[115,x,k[0],k[1]] = F[114,x,k[0],k[1]]*F[19,x,k[1]]
F[115,x,k[0],k[1]] = F[116,x,k[0],k[1]]
F[116,x,k[0],k[1]] = F[117,x,k[1]]+F[119,x,k[0],k[1]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[119,x,k[0],k[1]] = F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]*F[19,x,k[0]]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[122,x,k[0],k[1]] = -k[1]*(F[116,x,k[0],1]-F[116,x,k[0],k[1]])/(-1+k[1])
F[123,x,k[0],k[1]] = F[124,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[125,x,k[0],k[1]]*F[4,x]
F[125,x,k[0],k[1]] = -k[1]*(F[126,x,k[0],1]-F[126,x,k[0],k[1]])/(-1+k[1])
F[126,x,k[0],k[1]] = F[127,x,k[1]]+F[137,x,k[0],k[1]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[19,x,k[0]]
F[130,x,k[0]] = F[129,x,k[0]]*F[4,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[21,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[19,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0],1]
F[135,x,k[0],k[1]] = (F[136,x,k[0],k[1]]*k[1]-F[136,x,k[0],1])/(-1+k[1])
F[136,x,k[0],k[1]] = F[92,x,k[0],k[0]*k[1]]
F[137,x,k[0],k[1]] = -k[1]*(F[138,x,k[0],1]-F[138,x,k[0],k[1]])/(-1+k[1])
F[138,x,k[0],k[1]] = F[139,x,k[0],k[1]]
F[139,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[19,x,k[0]]
F[140,x,k[0],k[1]] = (F[141,x,k[0],k[1]]*k[0]-F[141,x,1,k[1]])/(-1+k[0])
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]*F[19,x,k[1]]
F[143,x,k[0],k[1]] = F[144,x,k[0],k[1],1]
F[144,x,k[0],k[1],k[2]] = (F[145,x,k[0],k[1],k[2]]*k[2]-F[145,x,k[0],k[1],1])/(-1+k[2])
F[145,x,k[0],k[1],k[2]] = F[113,x,k[0],k[1]*k[2]]+F[146,x,k[0],k[1],k[2]]
F[146,x,k[0],k[1],k[2]] = (F[147,x,k[0],k[1],k[2]]*k[0]-F[147,x,1,k[1],k[2]])/(-1+k[0])
F[147,x,k[0],k[1],k[2]] = F[148,x,k[0],k[1],k[1]*k[2]]
F[148,x,k[0],k[1],k[2]] = F[149,x,k[0],k[1],k[2]]
F[149,x,k[0],k[1],k[2]] = F[150,x,k[0],k[1],k[2]]*F[19,x,k[1]]
F[150,x,k[0],k[1],k[2]] = (F[145,x,k[0],k[1],1]*k[1]-F[145,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[151,x,k[0],k[1]] = (F[109,x,k[0],k[1]]*k[0]-F[109,x,1,k[1]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[154,x]*F[39,x,k[0]]
F[154,x] = (1+F[154,x])*x+F[154,x]^2
F[55,x,k[0]] = F[104,x,k[0]]+F[155,x,k[0]]
F[156,x] = 2+F[156,x]^2+(-2+x)*F[156,x]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[4,x]*F[55,x,k[0]]
F[61,x,k[0]] = F[159,x,k[0]]+F[54,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,1,k[0]]
F[163,x,k[0],k[1]] = F[162,x,k[0],k[1]]*F[4,x]
F[163,x,k[0],k[1]] = F[141,x,k[0],k[1]]
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)+F_{160}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{159}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = y_{0} x
F_{20}\! \left(x , y_{0}\right) = F_{157}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right) F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x \right) F_{39}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x , y_{0}\right) = F_{156}\! \left(x \right) F_{39}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{44}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{47}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{51}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , 1, y_{0}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = -\frac{-F_{60}\! \left(x , y_{0}\right) y_{0}+F_{60}\! \left(x , 1\right)}{-1+y_{0}}
F_{60}\! \left(x , y_{0}\right) = F_{61}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{64}\! \left(x , y_{0}, 1, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{65}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{1}\right) F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{68}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{68}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{101}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{69}\! \left(x , y_{0}, y_{1} y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{69}\! \left(x , y_{0}, y_{1}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{70}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{70}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{71}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{4}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{74}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , y_{1}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}\right) = F_{75}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , 1, y_{0}\right)
F_{80}\! \left(x , y_{0}, y_{1}\right) = F_{81}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{1}\right)+F_{84}\! \left(x , y_{0}, y_{1}\right)
F_{82}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{85}\! \left(x , y_{0}, y_{1}\right)
F_{85}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)
F_{86}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{87}\! \left(x , y_{0}, 1\right) y_{0}-F_{87}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{87}\! \left(x , y_{0}, y_{1}\right) = F_{88}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{88}\! \left(x , y_{0}, y_{1}\right) = F_{89}\! \left(x , y_{1}, y_{0}\right)
F_{89}\! \left(x , y_{0}, y_{1}\right) = F_{90}\! \left(x , y_{0}, y_{1}\right)+F_{91}\! \left(x , y_{0}, y_{1}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = F_{81}\! \left(x , y_{1}, y_{0}\right)
F_{91}\! \left(x , y_{0}, y_{1}\right) = F_{92}\! \left(x , y_{1}, y_{0}\right)
F_{92}\! \left(x , y_{0}, y_{1}\right) = F_{93}\! \left(x , y_{1}\right)+F_{94}\! \left(x , y_{0}, y_{1}\right)
F_{93}\! \left(x , y_{0}\right) = F_{69}\! \left(x , 1, y_{0}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{95}\! \left(x , 1, y_{0}, y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{65}\! \left(x , 1, y_{1}, y_{2}\right)-F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{96}\! \left(x , y_{0}, y_{1}\right) = F_{97}\! \left(x , y_{0}, y_{1}\right)
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{99}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{98}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{75}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{96}\! \left(x , 1, y_{1}\right)-F_{96}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{101}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{102}\! \left(x , 1, y_{1}, y_{2}\right)-F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{65}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{103}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{84}\! \left(x , 1, y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , 1, y_{0}\right)
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0}, y_{1}\right)
F_{110}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{112}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{112}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{112}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{140}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{1}\right)+F_{119}\! \left(x , y_{0}, y_{1}\right)
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)
F_{118}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{120}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{0}\right)
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{116}\! \left(x , y_{0}, 1\right)-F_{116}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{123}\! \left(x , y_{0}, y_{1}\right) = F_{124}\! \left(x , y_{0}, y_{1}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{126}\! \left(x , y_{0}, 1\right)-F_{126}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)
F_{127}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{132}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{132}\! \left(x , y_{0}\right) = F_{133}\! \left(x , y_{0}\right)
F_{133}\! \left(x , y_{0}\right) = F_{134}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{134}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}, 1\right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{136}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{136}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{92}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{138}\! \left(x , y_{0}, 1\right)-F_{138}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{138}\! \left(x , y_{0}, y_{1}\right) = F_{139}\! \left(x , y_{0}, y_{1}\right)
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{0}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{141}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , y_{0}, y_{1}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{143}\! \left(x , y_{0}, y_{1}\right) F_{19}\! \left(x , y_{1}\right)
F_{143}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}, 1\right)
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{145}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{147}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{148}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{148}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{19}\! \left(x , y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{145}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{145}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{151}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{109}\! \left(x , y_{0}, y_{1}\right)+F_{109}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)
F_{153}\! \left(x , y_{0}\right) = F_{154}\! \left(x \right) F_{39}\! \left(x , y_{0}\right)
F_{154}\! \left(x \right) = F_{154}\! \left(x \right) x +F_{154} \left(x \right)^{2}+x
F_{55}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right)+F_{155}\! \left(x , y_{0}\right)
F_{156}\! \left(x \right) = F_{156}\! \left(x \right) x +F_{156} \left(x \right)^{2}-2 F_{156}\! \left(x \right)+2
F_{157}\! \left(x , y_{0}\right) = F_{158}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{55}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)
F_{160}\! \left(x , y_{0}\right) = F_{161}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , 1, y_{0}\right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{163}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_20(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_19(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_160(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_159(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_5(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_14(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_157(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_27(x, k_0))
Eq(F_22(x, k_0), F_2(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_4(x))
Eq(F_29(x, k_0), F_30(x, k_0) + F_35(x, k_0))
Eq(F_30(x, k_0), F_2(x)*F_31(x, k_0))
Eq(F_32(x, k_0), F_31(x, k_0)*F_4(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_23(x, k_0)*F_4(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x)*F_39(x, k_0)*F_4(x))
Eq(F_37(x), F_38(x)/F_4(x))
Eq(F_38(x), F_2(x))
Eq(F_40(x, k_0), F_156(x)*F_39(x, k_0)*F_4(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_42(x, k_0), F_155(x, k_0) + F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_4(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_152(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_48(x, k_0), F_4(x)*F_47(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_4(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_105(x, k_0) + F_51(x, k_0))
Eq(F_52(x, k_0), F_4(x)*F_51(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_54(x, k_0), F_103(x, k_0) + F_53(x, k_0))
Eq(F_54(x, k_0), F_15(x, k_0) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, 1, k_0))
Eq(F_56(x, k_0, k_1), F_57(x, k_1) + F_63(x, k_0, k_1))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_4(x)*F_59(x, k_0))
Eq(F_59(x, k_0), (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_61(x, k_0))
Eq(F_62(x, k_0), F_20(x, k_0))
Eq(F_63(x, k_0, k_1), F_64(x, k_0, 1, k_1))
Eq(F_64(x, k_0, k_1, k_2), -F_65(x, k_0, k_1, k_2) + (-k_1*F_65(x, k_0, k_1, k_2) + F_65(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_65(x, k_0, k_1, k_2), F_66(x, k_0, k_1, k_2))
Eq(F_66(x, k_0, k_1, k_2), F_19(x, k_1)*F_67(x, k_0, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), (-k_1*F_68(x, k_0, k_1, 1) + k_2*F_68(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_68(x, k_0, k_1, k_2), F_101(x, k_0, k_1, k_2) + F_69(x, k_0, k_1*k_2))
Eq(F_70(x, k_0, k_1), F_100(x, k_0, k_1) + F_69(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), (k_1*F_70(x, k_0, k_1) - F_70(x, k_0, 1))/(k_1 - 1))
Eq(F_72(x, k_0, k_1), F_71(x, k_0, k_1) + F_98(x, k_1))
Eq(F_73(x, k_0, k_1), F_4(x)*F_72(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_74(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, k_1) + F_96(x, k_0, k_1))
Eq(F_10(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_0(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, 1, k_0))
Eq(F_80(x, k_0, k_1), F_81(x, k_0*k_1, k_1))
Eq(F_81(x, k_0, k_1), F_82(x, k_1) + F_84(x, k_0, k_1))
Eq(F_82(x, k_0), F_21(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_23(x, k_0) + F_33(x, k_0))
Eq(F_84(x, k_0, k_1), F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_19(x, k_0)*F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), (-k_0*F_87(x, k_0, 1) + k_1*F_87(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_87(x, k_0, k_1), F_88(x, k_0, k_0*k_1))
Eq(F_88(x, k_0, k_1), F_89(x, k_1, k_0))
Eq(F_89(x, k_0, k_1), F_90(x, k_0, k_1) + F_91(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_81(x, k_1, k_0))
Eq(F_91(x, k_0, k_1), F_92(x, k_1, k_0))
Eq(F_92(x, k_0, k_1), F_93(x, k_1) + F_94(x, k_0, k_1))
Eq(F_93(x, k_0), F_69(x, 1, k_0))
Eq(F_94(x, k_0, k_1), F_95(x, 1, k_0, k_1))
Eq(F_95(x, k_0, k_1, k_2), -F_65(x, 1, k_1, k_2) + (-k_0*F_65(x, k_0, k_1, k_2) + F_65(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_96(x, k_0, k_1), F_97(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_19(x, k_0)*F_56(x, k_0, k_1))
Eq(F_99(x, k_0), F_4(x)*F_98(x, k_0))
Eq(F_99(x, k_0), F_75(x, k_0))
Eq(F_100(x, k_0, k_1), -F_96(x, 1, k_1) + (-k_0*F_96(x, k_0, k_1) + F_96(x, 1, k_1))/(1 - k_0))
Eq(F_101(x, k_0, k_1, k_2), -F_102(x, 1, k_1, k_2) + (-k_0*F_102(x, k_0, k_1, k_2) + F_102(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_102(x, k_0, k_1, k_2), F_65(x, k_0, k_1, k_1*k_2))
Eq(F_103(x, k_0), F_104(x, k_0) + F_82(x, k_0))
Eq(F_104(x, k_0), F_84(x, 1, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0)*F_4(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, 1, k_0))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1))
Eq(F_110(x, k_0, k_1), F_111(x, k_0, k_1)*F_4(x))
Eq(F_111(x, k_0, k_1), (k_1*F_112(x, k_0, k_1) - F_112(x, k_0, 1))/(k_1 - 1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0, k_1) + F_151(x, k_0, k_1))
Eq(F_114(x, k_0, k_1), F_113(x, k_0, k_1) + F_140(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), F_114(x, k_0, k_1)*F_19(x, k_1))
Eq(F_115(x, k_0, k_1), F_116(x, k_0, k_1))
Eq(F_116(x, k_0, k_1), F_117(x, k_1) + F_119(x, k_0, k_1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_119(x, k_0, k_1), F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1)*F_19(x, k_0))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_122(x, k_0, k_1), -F_116(x, k_0, 1) + (k_1*F_116(x, k_0, k_1) - F_116(x, k_0, 1))/(k_1 - 1))
Eq(F_123(x, k_0, k_1), F_124(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_125(x, k_0, k_1)*F_4(x))
Eq(F_125(x, k_0, k_1), -F_126(x, k_0, 1) + (k_1*F_126(x, k_0, k_1) - F_126(x, k_0, 1))/(k_1 - 1))
Eq(F_126(x, k_0, k_1), F_127(x, k_1) + F_137(x, k_0, k_1))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_19(x, k_0))
Eq(F_130(x, k_0), F_129(x, k_0)*F_4(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_21(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_19(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0, 1))
Eq(F_135(x, k_0, k_1), (-k_1*F_136(x, k_0, k_1) + F_136(x, k_0, 1))/(1 - k_1))
Eq(F_136(x, k_0, k_1), F_92(x, k_0, k_0*k_1))
Eq(F_137(x, k_0, k_1), -F_138(x, k_0, 1) + (k_1*F_138(x, k_0, k_1) - F_138(x, k_0, 1))/(k_1 - 1))
Eq(F_138(x, k_0, k_1), F_139(x, k_0, k_1))
Eq(F_139(x, k_0, k_1), F_126(x, k_0, k_1)*F_19(x, k_0))
Eq(F_140(x, k_0, k_1), (-k_0*F_141(x, k_0, k_1) + F_141(x, 1, k_1))/(1 - k_0))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1)*F_19(x, k_1))
Eq(F_143(x, k_0, k_1), F_144(x, k_0, k_1, 1))
Eq(F_144(x, k_0, k_1, k_2), (-k_2*F_145(x, k_0, k_1, k_2) + F_145(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_145(x, k_0, k_1, k_2), F_113(x, k_0, k_1*k_2) + F_146(x, k_0, k_1, k_2))
Eq(F_146(x, k_0, k_1, k_2), (-k_0*F_147(x, k_0, k_1, k_2) + F_147(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_147(x, k_0, k_1, k_2), F_148(x, k_0, k_1, k_1*k_2))
Eq(F_148(x, k_0, k_1, k_2), F_149(x, k_0, k_1, k_2))
Eq(F_149(x, k_0, k_1, k_2), F_150(x, k_0, k_1, k_2)*F_19(x, k_1))
Eq(F_150(x, k_0, k_1, k_2), (-k_1*F_145(x, k_0, k_1, 1) + k_2*F_145(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_151(x, k_0, k_1), (-k_0*F_109(x, k_0, k_1) + F_109(x, 1, k_1))/(1 - k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_154(x)*F_39(x, k_0))
Eq(F_154(x), (x - 3)*(F_154(x) + 1) + (F_154(x) + 1)**2 + F_154(x) + 2)
Eq(F_55(x, k_0), F_104(x, k_0) + F_155(x, k_0))
Eq(F_156(x), (x - 2)*F_156(x) + F_156(x)**2 + 2)
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_4(x)*F_55(x, k_0))
Eq(F_61(x, k_0), F_159(x, k_0) + F_54(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, 1, k_0))
Eq(F_163(x, k_0, k_1), F_162(x, k_0, k_1)*F_4(x))
Eq(F_163(x, k_0, k_1), F_141(x, k_0, k_1))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 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], [1, 0]]}, {"patt": [2, 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