02413_03412_03421_13420

Counting sequence:
1, 1, 2, 6, 24, 116, 634, 3762, 23639, 154842, 1046412, 7244248, 51118497, 366321049, 2658572316, 19499383727, 144298804765, 1075982364686, 8075880480167, 60959734933626, 462440945774911, 3523485480616598, 26951041358186869, 206862720710080729, 1592707476533199129, 12297088948602265317, 95184152689978091888, 738450947450799813665, 5740961475831983234689, 44717303168280248354883, 348919853046773934508246, 2726928533028600546464539, 21343488611700278823866253, 167283066527246378847099511, 1312773602076432959858383963, 10314298298258485881174119949, 81127122772088925593218096031, 638758779122771419000345640711, 5034112955540717627397793346321, 39709804834057902253421771906732, 313499641640051739517690867409252, 2476958248707555449747055238650336, 19584944740504326784517687936707170, 154963485991128431590000695768359061, 1226937908388013301264412612603580395, 9720444479463815345793799556606964450, 77055802730578810422626095283792123251, 611176577690039022972389761773641127263, 4850177268029056366062082287891435176390, 38509368893445185777095871500421404027992, 305901924468073229944618023898066504234847, 2431055742675061615655702949462019626606019, 19328363530093325134636325462841669878308309, 153735404679521270013326156912581495539098093, 1223272178591888742365037573134847434224588107, 9737219691906236959096816212741352961526854822, 77535798017299043750130961770431936708891080928, 617615481805312425275806138195631159983024260727, 4921260044869736158874119654549788705761260387833, 39225696765684802321163738170247403482810713592788, 312748737646539993609138687331771920125976003372021, 2494282663815724239854784692260445249616740509100366, 19898298115841295831584191169185291564153263918811575, 158782120368635236185745995056050752366397917268214224, 1267354632249638202519432564941624262858586978395231883, 10118155484029242985870897833663558705601802624445157126, 80799214136053220744215745444020048170965623230029805764, 645374338515944726597396549984467336241580168423446303198, 5155981921538109420237848222005835266991778423362921553580, 41200526677473113639309399004656655300866446062483272871532, 329293048047730424411586020222666496473604788933438528600855, 2632374367376566696264800299888397982065584596798077393195370, 21047236266285991467824002952991322660543154073791810871629845, 168314684677855197140312617899686466610420091152588807270722633, 1346250127252317541077669919840538833628469773095145007701519598, 10769703808689909977320053098846180070492959617973423942861710711, 86169498612145133848179876982876484624775019358211965643746216997, 689561236785407624226174694011356427175507390267930819025383630397, 5518986713615978403565937391389486344144867174030849955454929508800, 44178499124738776587906925792710360735396311971325308270268016321736, 353692316538160513136755084545772074558133188044727748141242861215892, 2832053145746187805666260770733348657663214881472957942575835209908008, 22679653101779108621465679050007414821641869862420712345320012360491257, 181647263264222326739491149559408364146198821584602588223786526086378057, 1455047047875210214782079427699866286143725320863323649102657837727688225, 11656798559717360054333334630912729913964377303211005834101380107997383010, 93397240501451066564078808376696710755510658281127881645120834242754617049, 748410339887719388600737247472720171018645987194306636536186280420626075942, 5997842221256594400991520683128809914319567370123551411353362255554115922457, 48072689396951766646662163010434419454088985067118790288073701715578935345578, 385343980859580835938509286429794038398806244670590682047646071165206354996568, 3089187183934940432903081575183178094351604555862816455590836922432787657912903, 24767610459144498036821557131998566569246987772590183878413419633947259453329971, 198594416315448815330536902858857711643002158749908913376094167534240659822592210, 1592545488312014744899690984006704438705631378997722365134145076737664524939242366, 12771956601999824672956614874649652240867285033362103246690478823261155010289478921, 102438385958840456902207498256026523642805443564709956262742360940560583582570719292, 821687522310119584999446233177854829359810146025674581993896574485523166799048787762, 6591561881992323185471065927542198428519644710457614664442480555437848482232088003469, 52881856221741514996788160587785911066273898892112739557062793393501797149842844032346, 424288086317115004387677458742122480720349485891516029655099698198427560056471342001050

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24900/
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[82,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 16*x+(1+x)^3*F[5,x]^2+(8*x^2-20*x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[82,x]*F[9,x]
F[9,x] = F[10,x]+F[157,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x,1]
F[13,x,k[0]] = F[12,x,k[0]]+F[6,x]
F[14,x,k[0]] = F[13,x,k[0]]+F[80,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[4,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[25,x,k[0]]
F[17,x,k[0]] = F[18,x,1,k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]+F[205,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[14,x,k[0]]*F[22,x,k[1]]
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x,k[0]]^2*F[25,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0]]*F[35,x,k[1]]*F[82,x]
F[28,x,k[0]] = F[29,x,1,k[0]]
F[29,x,k[0],k[1]] = (F[30,x,k[0],k[1]]*k[0]-F[30,x,1,k[1]])/(-1+k[0])
F[30,x,k[0],k[1]] = F[31,x,k[0]]+F[32,x,k[0],k[1]]
F[31,x,k[0]] = (x*k[0]+1)^3*F[31,x,k[0]]^2+(8*x^2*k[0]^2-20*x*k[0])*F[31,x,k[0]]+16*k[0]*x
F[33,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[33,x,k[0],k[1]] = F[34,k[0]*x,k[1]]
F[15,x,k[0]] = F[12,x,k[0]]+F[34,x,k[0]]
F[35,x,k[0]] = F[186,x,k[0]]+F[36,x,k[0]]
F[37,x,k[0]] = F[36,x,k[0]]*F[82,x]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[2,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[25,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = F[22,x,k[0]]*F[38,x,k[0]]
F[44,x,k[0]] = F[184,x,k[0]]+F[43,x,k[0]]
F[45,x,k[0]] = F[25,x,k[0]]*F[44,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[25,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[83,x,k[0]]
F[49,x,k[0]] = F[50,x,1,k[0]]
F[50,x,k[0],k[1]] = (F[51,x,k[0],k[1]]*k[0]-F[51,x,1,k[1]])/(-1+k[0])
F[51,x,k[0],k[1]] = F[0,x]+F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*k[1]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1]]*F[82,x]
F[55,x,k[0],k[1]] = F[56,x,k[0],1,k[1]]
F[56,x,k[0],k[1],k[2]] = F[57,x,k[0],k[1]*k[2],k[2]]
F[57,x,k[0],k[1],k[2]] = F[58,x,k[0],k[1],k[2]]+F[59,x,k[0],k[1],k[2]]
F[58,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[51,x,k[0],k[1]]
F[59,x,k[0],k[1],k[2]] = F[60,x,k[0],k[1],k[2]]
F[60,x,k[0],k[1],k[2]] = F[35,x,k[2]]*F[61,x,k[0],k[1]]*F[82,x]
F[61,x,k[0],k[1]] = F[5,x]+F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]
F[63,x,k[0],k[1]] = k[0]*k[1]*F[64,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[65,x,k[0],k[1]]*F[82,x]
F[65,x,k[0],k[1]] = F[66,x,k[0],1,k[1]]
F[66,x,k[0],k[1],k[2]] = F[67,x,k[0],k[1]*k[2],k[2]]
F[67,x,k[0],k[1],k[2]] = F[68,x,k[0],k[1],k[2]]+F[69,x,k[0],k[1],k[2]]
F[68,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[61,x,k[0],k[1]]
F[69,x,k[0],k[1],k[2]] = F[70,x,k[0],k[1],k[2]]
F[70,x,k[0],k[1],k[2]] = F[61,x,k[0],k[1]]*F[71,x,k[2]]*F[82,x]
F[72,x,k[0]] = F[71,x,k[0]]*F[80,x,k[0]]*F[82,x]
F[72,x,k[0]] = F[73,x,k[0]]
F[74,x,k[0]] = F[73,x,k[0]]+F[77,x,k[0]]
F[75,x,k[0]] = F[25,x,k[0]]*F[74,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[34,x,k[0]] = F[23,x,k[0]]+F[76,x,k[0]]
F[77,x,k[0]] = F[22,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[76,x,k[0]]+F[79,x]
F[79,x] = (1+F[79,x])^2*x^3+(3*F[79,x]^2+14*F[79,x]+11)*x^2+(3*F[79,x]^2-14*F[79,x]-1)*x+F[79,x]^2+2*F[79,x]
F[81,x,k[0]] = F[35,x,k[0]]*F[80,x,k[0]]*F[82,x]
F[81,x,k[0]] = F[43,x,k[0]]
F[82,x] = x
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[82,x]*F[85,x,k[0]]
F[86,x,k[0]] = F[25,x,k[0]]*F[85,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[25,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,1,k[0]]
F[89,x,k[0],k[1]] = F[182,x,k[0],k[1]]+F[90,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[126,x,k[0],k[1]]+F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[92,x,k[0]]
F[92,x,k[0]] = F[0,x]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]+F[95,x,k[0]]
F[94,x,k[0]] = (x*F[94,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[94,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[94,x,k[0]]+x^2*k[0]^2)*(1+F[94,x,k[0]])
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[82,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[15,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[25,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]*F[82,x]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[2,x]+F[95,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0],1]
F[105,x,k[0],k[1]] = F[106,x,k[0],k[1]]
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]*F[25,x,k[1]]
F[107,x,k[0],k[1]] = F[108,x,k[0],k[1]]+F[124,x,k[0],k[1]]
F[108,x,k[0],k[1]] = F[109,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[109,x,k[0],k[1]] = F[103,x,k[0]]*F[110,x,k[0],k[1]]
F[110,x,k[0],k[1]] = F[111,x,k[0],k[0]*k[1]]
F[111,x,k[0],k[1]] = F[112,x,1,k[0],k[1]]
F[112,x,k[0],k[1],k[2]] = F[113,x,k[1]]+F[114,x,k[0],k[1],k[2]]
F[113,x,k[0]] = 1+F[113,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[113,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[113,x,k[0]]+k[0]*x*F[113,x,k[0]]^4
F[114,x,k[0],k[1],k[2]] = F[115,x,k[0],k[1],k[2]]
F[115,x,k[0],k[1],k[2]] = F[113,x,k[1]]*F[116,x,k[0],k[2],k[1]]*F[118,x,k[0],k[2]]
F[116,x,k[0],k[1],k[2]] = k[0]*k[1]*F[117,x,k[2],k[1]]
F[117,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[82,x]
F[118,x,k[0],k[1]] = F[1,x]+F[119,x,k[0],k[1]]
F[119,x,k[0],k[1]] = F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[118,x,k[0],k[1]]*F[121,x,k[0],k[1]]
F[121,x,k[0],k[1]] = k[0]*k[1]*F[122,x,k[1]]
F[122,x,k[0]] = F[22,x,k[0]]*F[82,x]
F[123,x,k[0],k[1]] = F[105,x,k[0],k[1]]*F[22,x,k[1]]
F[124,x,k[0],k[1]] = F[125,x,k[0],k[0]*k[1]]
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]+F[179,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[127,x,k[0],k[1]]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[80,x,k[0]]*F[82,x]
F[129,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[178,x]*F[82,x]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[172,x,k[0],k[1]]
F[132,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[132,x,k[0],k[1]] = F[133,x,k[0],k[1]]+F[136,x,k[0],k[1]]
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]+F[92,x,k[0]]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]
F[135,x,k[0],k[1]] = F[25,x,k[1]]*F[89,x,k[0],k[1]]
F[136,x,k[0],k[1]] = F[137,x,k[0],k[1]]
F[137,x,k[0],k[1]] = F[138,x,k[0],k[1]]*F[82,x]
F[138,x,k[0],k[1]] = 1/(-1+k[0])*(F[139,x,k[0],k[1]]*k[0]-F[139,x,1,k[1]])
F[139,x,k[0],k[1]] = F[130,x,k[0],k[1]]+F[140,x,k[0],k[1]]
F[140,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[141,x]
F[141,x] = F[0,x]+F[142,x]
F[142,x] = F[143,x]+F[2,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[82,x]
F[145,x] = F[146,x]+F[150,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[82,x]
F[148,x] = F[149,x,1]
F[149,x,k[0]] = F[90,x,1,k[0]]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[82,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[17,x,1]
F[154,x] = F[155,x,1]
F[155,x,k[0]] = F[156,x,k[0]]+F[160,x,k[0]]
F[156,x,k[0]] = F[157,x]*F[22,x,k[0]]
F[157,x] = F[158,x]
F[158,x] = F[159,x]*F[82,x]
F[159,x] = F[85,x,1]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[162,x]*F[35,x,k[0]]*F[82,x]
F[162,x] = F[163,x,1]
F[164,x,k[0]] = F[163,x,k[0]]+F[167,x,k[0]]
F[165,x,k[0]] = F[164,x,k[0]]*F[25,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[33,x,k[0],1]
F[167,x,k[0]] = F[168,k[0]*x]
F[168,x] = F[169,x,1]
F[169,x,k[0]] = (F[170,x,k[0]]*k[0]-F[170,x,1])/(-1+k[0])
F[170,x,k[0]] = F[61,x,k[0],1]
F[171,x,k[0],k[1]] = F[0,x]*F[111,x,k[0],k[1]]
F[172,x,k[0],k[1]] = F[173,x,k[0],k[1]]
F[173,x,k[0],k[1]] = F[128,x,k[0],k[1]]*F[174,x]*F[82,x]
F[174,x] = F[175,x]
F[175,x] = F[176,x]*F[82,x]
F[176,x] = F[177,x,1]
F[177,x,k[0]] = F[65,x,1,k[0]]
F[178,x] = F[174,x]+F[5,x]
F[179,x,k[0],k[1]] = F[180,x,k[0],k[1]]
F[180,x,k[0],k[1]] = F[181,x,k[0],k[1]]*F[35,x,k[1]]*F[82,x]
F[181,x,k[0],k[1]] = k[1]*(F[34,x,k[0]]-F[34,x,k[1]])/(-k[1]+k[0])
F[182,x,k[0],k[1]] = F[179,x,k[0],k[1]]+F[183,x,k[0],k[1]]
F[183,x,k[0],k[1]] = F[134,x,k[0],k[1]]*F[22,x,k[1]]
F[184,x,k[0]] = F[185,x,k[0]]*F[22,x,k[0]]
F[185,x,k[0]] = F[0,x]+F[46,x,k[0]]
F[187,x,k[0]] = F[186,x,k[0]]+F[204,x,k[0]]
F[188,x,k[0]] = F[187,x,k[0]]*F[82,x]
F[188,x,k[0]] = F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[191,x,k[0]]*F[82,x]
F[191,x,k[0]] = F[192,x,k[0]]+F[195,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]
F[193,x,k[0]] = F[194,x]*F[35,x,k[0]]*F[82,x]
F[194,x] = F[80,x,1]
F[88,x,k[0]] = F[195,x,k[0]]+F[196,x,k[0]]
F[196,x,k[0]] = F[197,x,1,k[0]]
F[197,x,k[0],k[1]] = F[198,x,k[0],k[1]]+F[203,x,k[0],k[1]]
F[198,x,k[0],k[1]] = F[199,x,k[0],k[1]]+F[200,x,k[0],k[1]]
F[199,x,k[0],k[1]] = F[22,x,k[1]]*F[92,x,k[0]]
F[200,x,k[0],k[1]] = F[201,x,k[0],k[0]*k[1]]
F[201,x,k[0],k[1]] = F[202,x,k[0],k[1]]
F[202,x,k[0],k[1]] = F[35,x,k[1]]*F[80,x,k[0]]*F[82,x]
F[203,x,k[0],k[1]] = F[182,x,k[0],k[0]*k[1]]
F[204,x,k[0]] = F[35,x,k[0]]*F[79,x]
F[205,x,k[0],k[1]] = F[206,x,k[1]]+F[228,x,k[0],k[1]]
F[207,x,k[0]] = F[206,x,k[0]]+F[224,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[212,x,k[0]]
F[208,x,k[0]] = F[14,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = 1/(-1+k[0])*(F[210,x,k[0]]*k[0]-F[210,x,1])
F[210,x,k[0]] = F[189,x,k[0]]+F[211,x,k[0]]
F[211,x,k[0]] = F[2,x]*F[22,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]*F[82,x]
F[214,x,k[0]] = 1/(-1+k[0])*(F[215,x,k[0]]*k[0]-F[215,x,1])
F[215,x,k[0]] = F[216,x,k[0]]+F[218,x,k[0]]
F[216,x,k[0]] = F[155,x,k[0]]+F[217,x,k[0]]
F[217,x,k[0]] = F[20,x,1,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[194,x]*F[220,x,k[0]]*F[82,x]
F[221,x,k[0]] = F[220,x,k[0]]*F[80,x,k[0]]*F[82,x]
F[221,x,k[0]] = F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,1,k[0]]
F[223,x,k[0],k[1]] = F[205,x,k[0]*k[1],k[1]]
F[224,x,k[0]] = F[225,x,k[0]]+F[226,x,k[0]]
F[225,x,k[0]] = F[185,x,k[0]]+F[210,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]
F[227,x,k[0]] = F[216,x,k[0]]*F[82,x]
F[228,x,k[0],k[1]] = F[229,x,k[0],k[1]]
F[229,x,k[0],k[1]] = F[220,x,k[1]]*F[34,x,k[0]]*F[82,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x^{3} F_{5} \left(x \right)^{2}+3 x^{2} F_{5} \left(x \right)^{2}+8 x^{2} F_{5}\! \left(x \right)+3 x F_{5} \left(x \right)^{2}-20 x F_{5}\! \left(x \right)+F_{5} \left(x \right)^{2}+16 x
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{82}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{157}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{13}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)+F_{6}\! \left(x \right)
F_{14}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , 1, y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{205}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \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_{21}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}\right)
F_{22}\! \left(x , y_{0}\right) = F_{1}\! \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_{22}\! \left(x , y_{0}\right)^{2} F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = y_{0} x
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{1}\right) F_{82}\! \left(x \right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , 1, y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{30}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{30}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}\right) = x^{3} F_{31}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{31}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{31}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{31}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{31}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{31}\! \left(x , y_{0}\right)^{2}
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(y_{0} x , y_{1}\right)
F_{15}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)+F_{34}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{186}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{40}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{41}\! \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_{42}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{184}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}\right)
F_{45}\! \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_{47}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{50}\! \left(x , 1, y_{0}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{51}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{51}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{0}\! \left(x \right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = y_{0} y_{1} F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0}, 1, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{35}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{5}\! \left(x \right)+F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = y_{0} y_{1} F_{64}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{65}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{66}\! \left(x , y_{0}, 1, y_{1}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{67}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{61}\! \left(x , y_{0}, y_{1}\right) F_{71}\! \left(x , y_{2}\right) F_{82}\! \left(x \right)
F_{72}\! \left(x , y_{0}\right) = F_{71}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{72}\! \left(x , y_{0}\right) = F_{73}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{73}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{74}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = x^{3} F_{79} \left(x \right)^{2}+2 x^{3} F_{79}\! \left(x \right)+3 x^{2} F_{79} \left(x \right)^{2}+x^{3}+14 x^{2} F_{79}\! \left(x \right)+3 x F_{79} \left(x \right)^{2}+11 x^{2}-14 x F_{79}\! \left(x \right)+F_{79} \left(x \right)^{2}-x +2 F_{79}\! \left(x \right)
F_{81}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{81}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}\right)
F_{82}\! \left(x \right) = x
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{82}\! \left(x \right) F_{85}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{85}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{89}\! \left(x , 1, y_{0}\right)
F_{89}\! \left(x , y_{0}, y_{1}\right) = F_{182}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{91}\! \left(x , y_{0}, y_{1}\right)
F_{91}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right) F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = x^{2} F_{94}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+x F_{94}\! \left(x , y_{0}\right)^{4} y_{0}+2 x^{2} F_{94}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{94}\! \left(x , y_{0}\right)^{3} y_{0}+x^{2} y_{0}^{2}+x F_{94}\! \left(x , y_{0}\right)^{2} y_{0}-x F_{94}\! \left(x , y_{0}\right) y_{0}-F_{94}\! \left(x , y_{0}\right)^{3}+F_{94}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{82}\! \left(x \right) F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{95}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}, 1\right)
F_{105}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)
F_{106}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}, y_{1}\right) F_{25}\! \left(x , y_{1}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , y_{0}, y_{1}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = F_{109}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{103}\! \left(x , y_{0}\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_{0} y_{1}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x , 1, y_{0}, y_{1}\right)
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{1}\right)+F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{113}\! \left(x , y_{0}\right) = x^{2} F_{113}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+y_{0} x F_{113}\! \left(x , y_{0}\right)^{4}-x F_{113}\! \left(x , y_{0}\right)^{3} y_{0}-2 x F_{113}\! \left(x , y_{0}\right)^{2} y_{0}+2 x F_{113}\! \left(x , y_{0}\right) y_{0}-F_{113}\! \left(x , y_{0}\right)^{3}+3 F_{113}\! \left(x , y_{0}\right)^{2}-2 F_{113}\! \left(x , y_{0}\right)+1
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{1}\right) F_{116}\! \left(x , y_{0}, y_{2}, y_{1}\right) F_{118}\! \left(x , y_{0}, y_{2}\right)
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} y_{1} F_{117}\! \left(x , y_{2}, y_{1}\right)
F_{117}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)
F_{118}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{119}\! \left(x , y_{0}, y_{1}\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_{118}\! \left(x , y_{0}, y_{1}\right) F_{121}\! \left(x , y_{0}, y_{1}\right)
F_{121}\! \left(x , y_{0}, y_{1}\right) = y_{0} y_{1} F_{122}\! \left(x , y_{1}\right)
F_{122}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{123}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{179}\! \left(x , y_{0}, y_{1}\right)
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{0}, y_{1}\right)
F_{127}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right) F_{178}\! \left(x \right) F_{82}\! \left(x \right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right)
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{172}\! \left(x , y_{0}, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}\right) = F_{133}\! \left(x , y_{0}, y_{1}\right)+F_{136}\! \left(x , y_{0}, y_{1}\right)
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{0}\right)
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{135}\! \left(x , y_{0}, y_{1}\right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}\right) F_{89}\! \left(x , y_{0}, y_{1}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{137}\! \left(x , y_{0}, y_{1}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = F_{138}\! \left(x , y_{0}, y_{1}\right) F_{82}\! \left(x \right)
F_{138}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{139}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{139}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right)+F_{140}\! \left(x , y_{0}, y_{1}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{0}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{2}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{82}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{150}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{82}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x , 1\right)
F_{149}\! \left(x , y_{0}\right) = F_{90}\! \left(x , 1, y_{0}\right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{82}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{154}\! \left(x \right) = F_{155}\! \left(x , 1\right)
F_{155}\! \left(x , y_{0}\right) = F_{156}\! \left(x , y_{0}\right)+F_{160}\! \left(x , y_{0}\right)
F_{156}\! \left(x , y_{0}\right) = F_{157}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{82}\! \left(x \right)
F_{159}\! \left(x \right) = F_{85}\! \left(x , 1\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 \right) F_{35}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x , 1\right)
F_{164}\! \left(x , y_{0}\right) = F_{163}\! \left(x , y_{0}\right)+F_{167}\! \left(x , y_{0}\right)
F_{165}\! \left(x , y_{0}\right) = F_{164}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{165}\! \left(x , y_{0}\right) = F_{166}\! \left(x , y_{0}\right)
F_{166}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}, 1\right)
F_{167}\! \left(x , y_{0}\right) = F_{168}\! \left(y_{0} x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x , 1\right)
F_{169}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{170}\! \left(x , y_{0}\right)+F_{170}\! \left(x , 1\right)}{-1+y_{0}}
F_{170}\! \left(x , y_{0}\right) = F_{61}\! \left(x , y_{0}, 1\right)
F_{171}\! \left(x , y_{0}, y_{1}\right) = F_{0}\! \left(x \right) F_{111}\! \left(x , y_{0}, y_{1}\right)
F_{172}\! \left(x , y_{0}, y_{1}\right) = F_{173}\! \left(x , y_{0}, y_{1}\right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right) F_{174}\! \left(x \right) F_{82}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{82}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x , 1\right)
F_{177}\! \left(x , y_{0}\right) = F_{65}\! \left(x , 1, y_{0}\right)
F_{178}\! \left(x \right) = F_{174}\! \left(x \right)+F_{5}\! \left(x \right)
F_{179}\! \left(x , y_{0}, y_{1}\right) = F_{180}\! \left(x , y_{0}, y_{1}\right)
F_{180}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right) F_{82}\! \left(x \right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{34}\! \left(x , y_{0}\right)-F_{34}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{182}\! \left(x , y_{0}, y_{1}\right) = F_{179}\! \left(x , y_{0}, y_{1}\right)+F_{183}\! \left(x , y_{0}, y_{1}\right)
F_{183}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)
F_{184}\! \left(x , y_{0}\right) = F_{185}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{185}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)
F_{187}\! \left(x , y_{0}\right) = F_{186}\! \left(x , y_{0}\right)+F_{204}\! \left(x , y_{0}\right)
F_{188}\! \left(x , y_{0}\right) = F_{187}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{188}\! \left(x , y_{0}\right) = F_{189}\! \left(x , y_{0}\right)
F_{189}\! \left(x , y_{0}\right) = F_{190}\! \left(x , y_{0}\right)
F_{190}\! \left(x , y_{0}\right) = F_{191}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{191}\! \left(x , y_{0}\right) = F_{192}\! \left(x , y_{0}\right)+F_{195}\! \left(x , y_{0}\right)
F_{192}\! \left(x , y_{0}\right) = F_{193}\! \left(x , y_{0}\right)
F_{193}\! \left(x , y_{0}\right) = F_{194}\! \left(x \right) F_{35}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{194}\! \left(x \right) = F_{80}\! \left(x , 1\right)
F_{88}\! \left(x , y_{0}\right) = F_{195}\! \left(x , y_{0}\right)+F_{196}\! \left(x , y_{0}\right)
F_{196}\! \left(x , y_{0}\right) = F_{197}\! \left(x , 1, y_{0}\right)
F_{197}\! \left(x , y_{0}, y_{1}\right) = F_{198}\! \left(x , y_{0}, y_{1}\right)+F_{203}\! \left(x , y_{0}, y_{1}\right)
F_{198}\! \left(x , y_{0}, y_{1}\right) = F_{199}\! \left(x , y_{0}, y_{1}\right)+F_{200}\! \left(x , y_{0}, y_{1}\right)
F_{199}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{92}\! \left(x , y_{0}\right)
F_{200}\! \left(x , y_{0}, y_{1}\right) = F_{201}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{201}\! \left(x , y_{0}, y_{1}\right) = F_{202}\! \left(x , y_{0}, y_{1}\right)
F_{202}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{203}\! \left(x , y_{0}, y_{1}\right) = F_{182}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{204}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right) F_{79}\! \left(x \right)
F_{205}\! \left(x , y_{0}, y_{1}\right) = F_{206}\! \left(x , y_{1}\right)+F_{228}\! \left(x , y_{0}, y_{1}\right)
F_{207}\! \left(x , y_{0}\right) = F_{206}\! \left(x , y_{0}\right)+F_{224}\! \left(x , y_{0}\right)
F_{207}\! \left(x , y_{0}\right) = F_{208}\! \left(x , y_{0}\right)+F_{212}\! \left(x , y_{0}\right)
F_{208}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)+F_{209}\! \left(x , y_{0}\right)
F_{209}\! \left(x , y_{0}\right) = -\frac{-F_{210}\! \left(x , y_{0}\right) y_{0}+F_{210}\! \left(x , 1\right)}{-1+y_{0}}
F_{210}\! \left(x , y_{0}\right) = F_{189}\! \left(x , y_{0}\right)+F_{211}\! \left(x , y_{0}\right)
F_{211}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)
F_{212}\! \left(x , y_{0}\right) = F_{213}\! \left(x , y_{0}\right)
F_{213}\! \left(x , y_{0}\right) = F_{214}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{214}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{215}\! \left(x , y_{0}\right)+F_{215}\! \left(x , 1\right)}{-1+y_{0}}
F_{215}\! \left(x , y_{0}\right) = F_{216}\! \left(x , y_{0}\right)+F_{218}\! \left(x , y_{0}\right)
F_{216}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)+F_{217}\! \left(x , y_{0}\right)
F_{217}\! \left(x , y_{0}\right) = F_{20}\! \left(x , 1, y_{0}\right)
F_{218}\! \left(x , y_{0}\right) = F_{219}\! \left(x , y_{0}\right)
F_{219}\! \left(x , y_{0}\right) = F_{194}\! \left(x \right) F_{220}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{221}\! \left(x , y_{0}\right) = F_{220}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{221}\! \left(x , y_{0}\right) = F_{222}\! \left(x , y_{0}\right)
F_{222}\! \left(x , y_{0}\right) = F_{223}\! \left(x , 1, y_{0}\right)
F_{223}\! \left(x , y_{0}, y_{1}\right) = F_{205}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{224}\! \left(x , y_{0}\right) = F_{225}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}\right)
F_{225}\! \left(x , y_{0}\right) = F_{185}\! \left(x , y_{0}\right)+F_{210}\! \left(x , y_{0}\right)
F_{226}\! \left(x , y_{0}\right) = F_{227}\! \left(x , y_{0}\right)
F_{227}\! \left(x , y_{0}\right) = F_{216}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
F_{228}\! \left(x , y_{0}, y_{1}\right) = F_{229}\! \left(x , y_{0}, y_{1}\right)
F_{229}\! \left(x , y_{0}, y_{1}\right) = F_{220}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}\right) F_{82}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_82(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), 16*x + (x + 1)**3*F_5(x)**2 + (8*x**2 - 20*x)*F_5(x))
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_82(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_157(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_13(x, k_0), F_12(x, k_0) + F_6(x))
Eq(F_14(x, k_0), F_13(x, k_0) + F_80(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_4(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_25(x, k_0))
Eq(F_17(x, k_0), F_18(x, 1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1) + F_205(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_14(x, k_0)*F_22(x, k_1))
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x, k_0)**2*F_25(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0)*F_35(x, k_1)*F_82(x))
Eq(F_28(x, k_0), F_29(x, 1, k_0))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0, k_1) + F_30(x, 1, k_1))/(1 - k_0))
Eq(F_30(x, k_0, k_1), F_31(x, k_0) + F_32(x, k_0, k_1))
Eq(F_31(x, k_0), 16*k_0*x + (k_0*x + 1)**3*F_31(x, k_0)**2 + (8*k_0**2*x**2 - 20*k_0*x)*F_31(x, k_0))
Eq(F_33(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_33(x, k_0, k_1), F_34(k_0*x, k_1))
Eq(F_15(x, k_0), F_12(x, k_0) + F_34(x, k_0))
Eq(F_35(x, k_0), F_186(x, k_0) + F_36(x, k_0))
Eq(F_37(x, k_0), F_36(x, k_0)*F_82(x))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_2(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_25(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), F_22(x, k_0)*F_38(x, k_0))
Eq(F_44(x, k_0), F_184(x, k_0) + F_43(x, k_0))
Eq(F_45(x, k_0), F_25(x, k_0)*F_44(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_25(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_83(x, k_0))
Eq(F_49(x, k_0), F_50(x, 1, k_0))
Eq(F_50(x, k_0, k_1), (-k_0*F_51(x, k_0, k_1) + F_51(x, 1, k_1))/(1 - k_0))
Eq(F_51(x, k_0, k_1), F_0(x) + F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), k_0*k_1*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1)*F_82(x))
Eq(F_55(x, k_0, k_1), F_56(x, k_0, 1, k_1))
Eq(F_56(x, k_0, k_1, k_2), F_57(x, k_0, k_1*k_2, k_2))
Eq(F_57(x, k_0, k_1, k_2), F_58(x, k_0, k_1, k_2) + F_59(x, k_0, k_1, k_2))
Eq(F_58(x, k_0, k_1, k_2), F_22(x, k_2)*F_51(x, k_0, k_1))
Eq(F_59(x, k_0, k_1, k_2), F_60(x, k_0, k_1, k_2))
Eq(F_60(x, k_0, k_1, k_2), F_35(x, k_2)*F_61(x, k_0, k_1)*F_82(x))
Eq(F_61(x, k_0, k_1), F_5(x) + F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1))
Eq(F_63(x, k_0, k_1), k_0*k_1*F_64(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_65(x, k_0, k_1)*F_82(x))
Eq(F_65(x, k_0, k_1), F_66(x, k_0, 1, k_1))
Eq(F_66(x, k_0, k_1, k_2), F_67(x, k_0, k_1*k_2, k_2))
Eq(F_67(x, k_0, k_1, k_2), F_68(x, k_0, k_1, k_2) + F_69(x, k_0, k_1, k_2))
Eq(F_68(x, k_0, k_1, k_2), F_22(x, k_2)*F_61(x, k_0, k_1))
Eq(F_69(x, k_0, k_1, k_2), F_70(x, k_0, k_1, k_2))
Eq(F_70(x, k_0, k_1, k_2), F_61(x, k_0, k_1)*F_71(x, k_2)*F_82(x))
Eq(F_72(x, k_0), F_71(x, k_0)*F_80(x, k_0)*F_82(x))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_74(x, k_0), F_73(x, k_0) + F_77(x, k_0))
Eq(F_75(x, k_0), F_25(x, k_0)*F_74(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_34(x, k_0), F_23(x, k_0) + F_76(x, k_0))
Eq(F_77(x, k_0), F_22(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_76(x, k_0) + F_79(x))
Eq(F_79(x), 16*x + (x + 1)**3*(F_79(x) + 1)**2 + (F_79(x) + 1)*(8*x**2 - 20*x - 1) + F_79(x))
Eq(F_81(x, k_0), F_35(x, k_0)*F_80(x, k_0)*F_82(x))
Eq(F_81(x, k_0), F_43(x, k_0))
Eq(F_82(x), x)
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_82(x)*F_85(x, k_0))
Eq(F_86(x, k_0), F_25(x, k_0)*F_85(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_25(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, 1, k_0))
Eq(F_89(x, k_0, k_1), F_182(x, k_0, k_1) + F_90(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_126(x, k_0, k_1) + F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_111(x, k_0, k_1)*F_92(x, k_0))
Eq(F_92(x, k_0), F_0(x) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0) + F_95(x, k_0))
Eq(F_94(x, k_0), k_0*x*(F_94(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_94(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_94(x, k_0) + 1) + (F_94(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_94(x, k_0) + 1)
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_82(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_15(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_25(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0)*F_82(x))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_2(x) + F_95(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0, 1))
Eq(F_105(x, k_0, k_1), F_106(x, k_0, k_1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1)*F_25(x, k_1))
Eq(F_107(x, k_0, k_1), F_108(x, k_0, k_1) + F_124(x, k_0, k_1))
Eq(F_108(x, k_0, k_1), F_109(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_109(x, k_0, k_1), F_103(x, k_0)*F_110(x, k_0, k_1))
Eq(F_110(x, k_0, k_1), F_111(x, k_0, k_0*k_1))
Eq(F_111(x, k_0, k_1), F_112(x, 1, k_0, k_1))
Eq(F_112(x, k_0, k_1, k_2), F_113(x, k_1) + F_114(x, k_0, k_1, k_2))
Eq(F_113(x, k_0), k_0*x*F_113(x, k_0)**4 + (-k_0*x - 1)*F_113(x, k_0)**3 + (2*k_0*x - 2)*F_113(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_113(x, k_0)**2 + 1)
Eq(F_114(x, k_0, k_1, k_2), F_115(x, k_0, k_1, k_2))
Eq(F_115(x, k_0, k_1, k_2), F_113(x, k_1)*F_116(x, k_0, k_2, k_1)*F_118(x, k_0, k_2))
Eq(F_116(x, k_0, k_1, k_2), k_0*k_1*F_117(x, k_2, k_1))
Eq(F_117(x, k_0, k_1), F_111(x, k_0, k_1)*F_82(x))
Eq(F_118(x, k_0, k_1), F_1(x) + F_119(x, k_0, k_1))
Eq(F_119(x, k_0, k_1), F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_118(x, k_0, k_1)*F_121(x, k_0, k_1))
Eq(F_121(x, k_0, k_1), k_0*k_1*F_122(x, k_1))
Eq(F_122(x, k_0), F_22(x, k_0)*F_82(x))
Eq(F_123(x, k_0, k_1), F_105(x, k_0, k_1)*F_22(x, k_1))
Eq(F_124(x, k_0, k_1), F_125(x, k_0, k_0*k_1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1) + F_179(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_127(x, k_0, k_1))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1)*F_80(x, k_0)*F_82(x))
Eq(F_129(x, k_0, k_1), F_128(x, k_0, k_1)*F_178(x)*F_82(x))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1) + F_172(x, k_0, k_1))
Eq(F_132(x, k_0, k_1), F_131(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_132(x, k_0, k_1), F_133(x, k_0, k_1) + F_136(x, k_0, k_1))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1) + F_92(x, k_0))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1))
Eq(F_135(x, k_0, k_1), F_25(x, k_1)*F_89(x, k_0, k_1))
Eq(F_136(x, k_0, k_1), F_137(x, k_0, k_1))
Eq(F_137(x, k_0, k_1), F_138(x, k_0, k_1)*F_82(x))
Eq(F_138(x, k_0, k_1), (k_0*F_139(x, k_0, k_1) - F_139(x, 1, k_1))/(k_0 - 1))
Eq(F_139(x, k_0, k_1), F_130(x, k_0, k_1) + F_140(x, k_0, k_1))
Eq(F_140(x, k_0, k_1), F_111(x, k_0, k_1)*F_141(x))
Eq(F_141(x), F_0(x) + F_142(x))
Eq(F_142(x), F_143(x) + F_2(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_82(x))
Eq(F_145(x), F_146(x) + F_150(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_82(x))
Eq(F_148(x), F_149(x, 1))
Eq(F_149(x, k_0), F_90(x, 1, k_0))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_82(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_17(x, 1))
Eq(F_154(x), F_155(x, 1))
Eq(F_155(x, k_0), F_156(x, k_0) + F_160(x, k_0))
Eq(F_156(x, k_0), F_157(x)*F_22(x, k_0))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_159(x)*F_82(x))
Eq(F_159(x), F_85(x, 1))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x)*F_35(x, k_0)*F_82(x))
Eq(F_162(x), F_163(x, 1))
Eq(F_164(x, k_0), F_163(x, k_0) + F_167(x, k_0))
Eq(F_165(x, k_0), F_164(x, k_0)*F_25(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_33(x, k_0, 1))
Eq(F_167(x, k_0), F_168(k_0*x))
Eq(F_168(x), F_169(x, 1))
Eq(F_169(x, k_0), (-k_0*F_170(x, k_0) + F_170(x, 1))/(1 - k_0))
Eq(F_170(x, k_0), F_61(x, k_0, 1))
Eq(F_171(x, k_0, k_1), F_0(x)*F_111(x, k_0, k_1))
Eq(F_172(x, k_0, k_1), F_173(x, k_0, k_1))
Eq(F_173(x, k_0, k_1), F_128(x, k_0, k_1)*F_174(x)*F_82(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x)*F_82(x))
Eq(F_176(x), F_177(x, 1))
Eq(F_177(x, k_0), F_65(x, 1, k_0))
Eq(F_178(x), F_174(x) + F_5(x))
Eq(F_179(x, k_0, k_1), F_180(x, k_0, k_1))
Eq(F_180(x, k_0, k_1), F_181(x, k_0, k_1)*F_35(x, k_1)*F_82(x))
Eq(F_181(x, k_0, k_1), -F_34(x, k_0) + (-k_0*F_34(x, k_0) + k_1*F_34(x, k_1))/(-k_0 + k_1))
Eq(F_182(x, k_0, k_1), F_179(x, k_0, k_1) + F_183(x, k_0, k_1))
Eq(F_183(x, k_0, k_1), F_134(x, k_0, k_1)*F_22(x, k_1))
Eq(F_184(x, k_0), F_185(x, k_0)*F_22(x, k_0))
Eq(F_185(x, k_0), F_0(x) + F_46(x, k_0))
Eq(F_187(x, k_0), F_186(x, k_0) + F_204(x, k_0))
Eq(F_188(x, k_0), F_187(x, k_0)*F_82(x))
Eq(F_188(x, k_0), F_189(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_191(x, k_0)*F_82(x))
Eq(F_191(x, k_0), F_192(x, k_0) + F_195(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_193(x, k_0), F_194(x)*F_35(x, k_0)*F_82(x))
Eq(F_194(x), F_80(x, 1))
Eq(F_88(x, k_0), F_195(x, k_0) + F_196(x, k_0))
Eq(F_196(x, k_0), F_197(x, 1, k_0))
Eq(F_197(x, k_0, k_1), F_198(x, k_0, k_1) + F_203(x, k_0, k_1))
Eq(F_198(x, k_0, k_1), F_199(x, k_0, k_1) + F_200(x, k_0, k_1))
Eq(F_199(x, k_0, k_1), F_22(x, k_1)*F_92(x, k_0))
Eq(F_200(x, k_0, k_1), F_201(x, k_0, k_0*k_1))
Eq(F_201(x, k_0, k_1), F_202(x, k_0, k_1))
Eq(F_202(x, k_0, k_1), F_35(x, k_1)*F_80(x, k_0)*F_82(x))
Eq(F_203(x, k_0, k_1), F_182(x, k_0, k_0*k_1))
Eq(F_204(x, k_0), F_35(x, k_0)*F_79(x))
Eq(F_205(x, k_0, k_1), F_206(x, k_1) + F_228(x, k_0, k_1))
Eq(F_207(x, k_0), F_206(x, k_0) + F_224(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_212(x, k_0))
Eq(F_208(x, k_0), F_14(x, k_0) + F_209(x, k_0))
Eq(F_209(x, k_0), (k_0*F_210(x, k_0) - F_210(x, 1))/(k_0 - 1))
Eq(F_210(x, k_0), F_189(x, k_0) + F_211(x, k_0))
Eq(F_211(x, k_0), F_2(x)*F_22(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0)*F_82(x))
Eq(F_214(x, k_0), (k_0*F_215(x, k_0) - F_215(x, 1))/(k_0 - 1))
Eq(F_215(x, k_0), F_216(x, k_0) + F_218(x, k_0))
Eq(F_216(x, k_0), F_155(x, k_0) + F_217(x, k_0))
Eq(F_217(x, k_0), F_20(x, 1, k_0))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_194(x)*F_220(x, k_0)*F_82(x))
Eq(F_221(x, k_0), F_220(x, k_0)*F_80(x, k_0)*F_82(x))
Eq(F_221(x, k_0), F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, 1, k_0))
Eq(F_223(x, k_0, k_1), F_205(x, k_0*k_1, k_1))
Eq(F_224(x, k_0), F_225(x, k_0) + F_226(x, k_0))
Eq(F_225(x, k_0), F_185(x, k_0) + F_210(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0))
Eq(F_227(x, k_0), F_216(x, k_0)*F_82(x))
Eq(F_228(x, k_0, k_1), F_229(x, k_0, k_1))
Eq(F_229(x, k_0, k_1), F_220(x, k_1)*F_34(x, k_0)*F_82(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}], "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, 2, 4, 1, 3], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [1, 3, 4, 2, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], 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