10243_10342_20143_20341_30142_30241
Counting sequence:
1, 1, 2, 6, 24, 114, 600, 3372, 19832, 120622, 752944, 4798628, 31107880, 204558536, 1361555656, 9157975304, 62162748952, 425359331966, 2931482487712, 20332867150436, 141845200971168, 994718876545548, 7008956389343568, 49601859594298248, 352436269398939440, 2513426424743065324, 17986024235797705104, 129116359341993868728, 929628536998274657592, 6711728704424822570852, 48582427996491600536872, 352512349214797074566144, 2563637275030004890899416, 18683936824011236688308702, 136444862576475084957522016, 998331530083933210843933956, 7317739062414869460958785600, 53730738626727121278767558380, 395161678847296267325130879376, 2910704568150121842882537220040, 21471403839890504047749565068304, 158610439030778515705865553209060, 1173232795548822553303318651007328, 8689438170561952203608380440414456, 64436207714838485535725817917607120, 478383606430058748478047292360665664, 3555570953375768249911687701396240336, 26455086081125849684432952469373028976, 197041184619014456105993195481543192688, 1469045303879234264849074162904728870732, 10962941357193399899434198564443690293248, 81887391557087008838200920898611863494888, 612195632982000382193675268596602767382592, 4580708677897559229486868069055115166749848, 34302923797423363112826702634637273596142464, 257082841241237933071143760222644175839294896, 1928175886421306532375636094461267260104947168, 14472399146580893327883988626143952513703003800, 108703627014872279445194254718979648725224434384, 817046880956707090451170068941145254264787157056, 6145251617892154178087294256708472182817941718360, 46250122980778828707485049068935499834642520146652, 348303511632407801220741177378833802137239701884904, 2624618409899730991256877767494872797000209459694192, 19789273213186914765450470277015936118472939601953624, 149293614538660328265150436651474601479939933876432798, 1126919859844375612852434501138833624487860770892641632, 8510954302315835394720324696463920361078920942366712004, 64311735005401896478265365954653683554550101514002909184, 486208484513567200452921603050827401316464598593231589420, 3677638566745490582137929919725779587146462226938211735760, 27830683994252448162504803195669604234807309513688280357256, 210708179609449019251776640088944797918601814373642563798096, 1596012076352303965467300802954973290391356422104504195127988, 12094363342394001925299185058768450098713611802197594123371168, 91688931358285821471924728418061794446080861730549914669538584, 695397402649249291839357793352887721102079221805478121443160112, 5276268004970534878456799106410306136368148658265835897102805648, 40049196689486562007507463568052844186393797587619235601916215408, 304109274781976836055073823878032184423235228022300513702041356848, 2310097378687965691845484353851009154775738260758920212629132144848, 17554630629702227783388278522450154553648608696176133847046639814340, 133447380898078247882740935355547710134383597390176751532861365044160, 1014802813245437373604501174477508563957746866046749359905492472685496, 7719744879364847996887777915322698141225587860551400870004570130311104, 58744939787819112928373647458231190020974214287784052091895640096370152, 447178460681484532242001105115998626161321237457584288818200069129901024, 3405108626443587543350817931898329471988497330263172395210059927445949040, 25936874167425086004594974008861967300338833877029428180979849911595152544, 197623169876290424827193230977583811149800372113723517611436431423117109608, 1506221141912248862856860450417426822330364302498759990718627405799513077152, 11483319641068941375803312399260892378514858873613281411778888339612376046928, 87573211932390760251271535578375510601959032527067349203963116303870106312240, 668032473888233175283075076254857509880226869834015536053989973119198213501576, 5097342134100932620228723934587950298959367942254766639936342610719435139564816, 38905180136100959481232536529490964850772520578249342489344305290888328450392768, 297020285280210947797902141321097999098066079704638449324248443108223345860794864, 2268179895545048729789165285230565621129146917246047615162846845057703947580043148, 17325242770469509415352498328753708816187032022230894865993391974977286345239554496, 132369953339730848617319895736153468145521547427022300602065402219291465040474780008, 1011592568225730598417918561880795760279915010021901602982638106051867090460548969856
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24569/
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[65,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[65,x]*F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = F[4,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[295,x]*F[65,x]
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[16,x,k[0],1]
F[16,x,k[0],k[1]] = F[17,x,k[0]]+F[294,x,k[0],k[1]]
F[18,x,k[0]] = F[17,x,k[0]]*F[65,x]
F[18,x,k[0]] = F[19,x,k[0]]
F[20,x,k[0]] = F[19,x,k[0]]+F[292,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]+F[288,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[65,x]
F[25,x,k[0]] = F[26,x,k[0]]+F[283,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[34,x,k[0]]
F[27,x,k[0]] = F[23,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[32,x,k[0]] = F[28,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[65,x]
F[36,x,k[0]] = F[270,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[26,x,1]-F[26,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[63,x]*F[65,x]
F[41,x,k[0]] = -k[0]*(F[42,x,1]-F[42,x,k[0]])/(-1+k[0])
F[43,x,k[0]] = F[184,x]+F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[4,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[17,x,k[0]]*F[33,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0],1]
F[49,x,k[0],k[1]] = F[48,x,k[0],k[1]]*F[59,x,k[0]]
F[50,x,k[0],k[1]] = F[179,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[50,x,k[0],k[1]]*F[65,x]
F[51,x,k[0],k[1]] = F[52,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[52,x,k[0],k[1]]+F[68,x,k[0]]
F[54,x,k[0],k[1]] = F[53,x,k[0],k[1]]*F[87,x]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[175,x,k[0],k[1]]+F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[57,x,k[0]]+F[90,x,k[0],k[1]]
F[57,x,k[0]] = F[58,x,k[0]]+F[66,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]*F[62,x]
F[59,x,k[0]] = F[1,x]+F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]*F[59,x,k[0]]
F[62,x] = F[63,x]
F[63,x] = 1/F[65,x]*F[64,x]
F[64,x] = F[2,x]
F[65,x] = x
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[87,x]
F[68,x,k[0]] = F[69,x,k[0]]+F[71,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[44,x,k[0]]*F[59,x,k[0]]*F[65,x]
F[71,x,k[0]] = F[72,x,k[0]]*F[81,x]
F[72,x,k[0]] = F[73,x]+F[76,x,k[0]]
F[73,x] = F[74,x]
F[74,x] = F[65,x]*F[75,x]
F[75,x] = F[1,x]+F[73,x]
F[76,x,k[0]] = F[77,x]+F[78,x,k[0]]+F[79,x,k[0]]
F[77,x] = 0
F[78,x,k[0]] = F[33,x,k[0]]*F[72,x,k[0]]
F[79,x,k[0]] = F[65,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[60,x,k[0]]+F[76,x,k[0]]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[65,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[1,x]+F[82,x]
F[86,x] = F[82,x]
F[87,x] = F[1,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[65,x]*F[87,x]
F[90,x,k[0],k[1]] = F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[87,x]*F[92,x,k[0],k[1]]
F[92,x,k[0],k[1]] = F[157,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[154,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[95,x,k[0],k[1]]
F[95,x,k[0],k[1]] = F[33,x,k[1]]*F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[97,x,k[1],k[0]]
F[97,x,k[0],k[1]] = F[104,x,k[0],k[1]]+F[98,x,k[1]]
F[98,x,k[0]] = F[101,x,k[0]]+F[99,x,k[0]]
F[100,x,k[0]] = F[65,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[69,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[65,x]
F[103,x,k[0]] = F[96,x,k[0],1]
F[104,x,k[0],k[1]] = F[105,x,k[1],k[0]]
F[105,x,k[0],k[1]] = F[106,x,k[0],k[1]]+F[141,x,k[0],k[1]]
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]+F[94,x,k[0],k[1]]
F[107,x,k[0],k[1]] = F[108,x,k[1],k[0]]
F[108,x,k[0],k[1]] = F[109,x,k[0],k[1]]*F[65,x]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1],1]
F[110,x,k[0],k[1],k[2]] = (F[111,x,k[0],k[1],k[2]]*k[2]-F[111,x,k[0],k[1],1])/(-1+k[2])
F[111,x,k[0],k[1],k[2]] = F[112,x,k[1],k[0],k[2]]
F[112,x,k[0],k[1],k[2]] = F[113,x,k[0],k[1]]+F[138,x,k[0],k[1],k[2]]
F[113,x,k[0],k[1]] = F[114,x,k[1],k[0]]
F[114,x,k[0],k[1]] = F[115,x,k[0],k[1]]+F[121,x,k[0],k[1]]
F[115,x,k[0],k[1]] = F[116,x,k[1],k[0]]
F[116,x,k[0],k[1]] = F[117,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[117,x,k[0],k[1]] = F[118,x,k[0],k[1]]
F[118,x,k[0],k[1]] = F[119,x,k[0],k[1]]*F[65,x]
F[119,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = -k[1]*(F[117,x,k[0],1]-F[117,x,k[0],k[1]])/(-1+k[1])
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]
F[122,x,k[0],k[1]] = F[123,x,k[0],k[1]]*F[65,x]
F[123,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[125,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[115,x,k[0],k[1]]*F[43,x,k[1]]
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[128,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[127,x,k[1],k[0]]
F[127,x,k[0],k[1]] = -k[1]*(F[48,x,k[0],1]-F[48,x,k[0],k[1]])/(-1+k[1])
F[128,x,k[0],k[1]] = F[129,x,k[0]]+F[133,x,k[0],k[1]]
F[129,x,k[0]] = F[1,x]+F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[129,x,k[0]]*F[132,x,k[0]]
F[132,x,k[0]] = k[0]*x
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]+F[60,x,k[1]]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]+F[137,x,k[0],k[1]]+F[77,x]
F[135,x,k[0],k[1]] = F[136,x,k[0],k[1]]*F[33,x,k[1]]
F[136,x,k[0],k[1]] = F[130,x,k[0]]+F[134,x,k[0],k[1]]
F[137,x,k[0],k[1]] = F[132,x,k[0]]*F[133,x,k[0],k[1]]
F[138,x,k[0],k[1],k[2]] = F[139,x,k[0],k[1],k[2]]
F[139,x,k[0],k[1],k[2]] = F[140,x,k[0],k[1],k[2]]*F[33,x,k[2]]
F[140,x,k[0],k[1],k[2]] = -k[1]*(F[112,x,k[0],1,k[2]]-F[112,x,k[0],k[1],k[2]])/(-1+k[1])
F[142,x,k[0],k[1]] = F[141,x,k[0],k[1]]+F[146,x,k[0]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]
F[143,x,k[0],k[1]] = F[144,x,k[0],k[1]]*F[33,x,k[0]]
F[145,x,k[0],k[1]] = F[144,x,k[0],k[1]]*F[33,x,k[1]]
F[145,x,k[0],k[1]] = F[106,x,k[0],k[1]]
F[146,x,k[0]] = F[147,x,k[0]]+F[150,x,k[0]]
F[99,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]+F[19,x,k[0]]
F[149,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[65,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[142,x,k[0],1]
F[154,x,k[0],k[1]] = F[155,x,k[0],k[1]]
F[155,x,k[0],k[1]] = F[156,x,k[0],k[1]]*F[65,x]
F[156,x,k[0],k[1]] = -k[1]*(F[94,x,k[0],1]-F[94,x,k[0],k[1]])/(-1+k[1])
F[157,x,k[0],k[1]] = F[158,x,k[0],k[1]]*F[81,x]
F[158,x,k[0],k[1]] = F[159,x,k[1]]+F[165,x,k[0],k[1]]
F[159,x,k[0]] = F[160,x,k[0]]+F[163,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]*F[33,x,k[0]]
F[162,x,k[0]] = F[1,x]+F[160,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[159,x,k[0]]*F[65,x]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[166,x,k[0],k[1]] = F[167,x,k[0],k[1]]+F[169,x,k[0],k[1]]+F[77,x]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]*F[33,x,k[0]]
F[168,x,k[0],k[1]] = F[160,x,k[1]]+F[166,x,k[0],k[1]]
F[169,x,k[0],k[1]] = F[170,x,k[0],k[1]]*F[33,x,k[1]]
F[170,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[60,x,k[0]]
F[171,x,k[0],k[1]] = 2*F[77,x]+F[172,x,k[0],k[1]]+F[174,x,k[0],k[1]]
F[172,x,k[0],k[1]] = F[173,x,k[0],k[1]]*F[33,x,k[0]]
F[173,x,k[0],k[1]] = F[163,x,k[1]]+F[171,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[165,x,k[0],k[1]]*F[65,x]
F[175,x,k[0],k[1]] = F[176,x,k[0],k[1]]+F[58,x,k[0]]
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[168,x,k[0],k[1]]*F[178,x]*F[87,x]
F[178,x] = F[1,x]+F[81,x]
F[179,x,k[0],k[1]] = F[168,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[182,x,k[0]]
F[181,x,k[0],k[1]] = F[44,x,k[0]]+F[48,x,k[0],k[1]]
F[182,x,k[0]] = F[183,x,k[0]]*F[81,x]
F[183,x,k[0]] = F[75,x]+F[80,x,k[0]]
F[184,x] = F[185,x]+F[4,x]
F[185,x] = F[186,x]
F[186,x] = F[187,x]*F[65,x]
F[187,x] = F[188,x]+F[192,x]
F[188,x] = F[189,x]
F[189,x] = 1/F[65,x]*F[190,x]
F[190,x] = F[191,x]
F[191,x] = -F[0,x]+F[63,x]
F[192,x] = F[193,x]
F[193,x] = F[194,x,1]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[65,x]
F[196,x,k[0]] = F[197,x,k[0]]+F[259,x]
F[197,x,k[0]] = F[198,x,k[0]]+F[255,x,k[0]]
F[198,x,k[0]] = F[194,x,k[0]]+F[199,x,k[0]]
F[199,x,k[0]] = F[200,x]+F[254,x,k[0]]
F[200,x] = F[201,x]+F[210,x]
F[201,x] = F[0,x]+F[202,x]
F[202,x] = F[2,x]+F[203,x]
F[203,x] = F[204,x]
F[204,x] = F[205,x]*F[65,x]
F[205,x] = F[206,x]+F[208,x]
F[206,x] = F[207,x]
F[207,x] = F[184,x]*F[62,x]*F[65,x]
F[208,x] = F[209,x]
F[209,x] = F[187,x]*F[65,x]
F[210,x] = F[211,x]+F[252,x]
F[211,x] = F[212,x,1]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]*F[33,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0],1]
F[215,x,k[0],k[1]] = F[216,x,k[0],k[0]*k[1]]
F[216,x,k[0],k[1]] = F[217,x,k[0],k[1]]+F[230,x,k[0],k[1]]
F[217,x,k[0],k[1]] = F[218,x,k[0]]+F[226,x,k[0],k[1]]
F[218,x,k[0]] = F[219,x,k[0]]+F[59,x,k[0]]
F[219,x,k[0]] = F[2,x]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]*F[33,x,k[0]]
F[222,x,k[0]] = F[219,x,k[0]]+F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]
F[224,x,k[0]] = F[218,x,k[0]]*F[225,x]*F[65,x]
F[225,x] = F[184,x]
F[226,x,k[0],k[1]] = F[227,x,k[0],k[1]]
F[227,x,k[0],k[1]] = F[228,x,k[0],k[1]]*F[33,x,k[1]]
F[228,x,k[0],k[1]] = (-F[229,x,1,k[1]]*k[1]+F[229,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[229,x,k[0],k[1]] = F[216,x,k[0]*k[1],k[1]]
F[230,x,k[0],k[1]] = F[231,x,k[1]]+F[247,x,k[0],k[1]]
F[231,x,k[0]] = F[202,x]+F[232,x,k[0]]
F[232,x,k[0]] = F[233,x,k[0],1]
F[233,x,k[0],k[1]] = F[234,x,k[0],k[1]]
F[234,x,k[0],k[1]] = F[235,x,k[0],k[1]]*F[33,x,k[1]]
F[235,x,k[0],k[1]] = F[236,x,k[0]]+F[246,x,k[0],k[1]]
F[236,x,k[0]] = F[212,x,k[0]]+F[237,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]*F[33,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[244,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]+F[242,x,k[0]]
F[241,x,k[0]] = F[191,x]+F[237,x,k[0]]
F[242,x,k[0]] = F[243,x,k[0]]
F[243,x,k[0]] = F[225,x]*F[241,x,k[0]]*F[65,x]
F[244,x,k[0]] = F[241,x,k[0]]+F[245,x,k[0]]
F[245,x,k[0]] = (F[232,x,k[0]]-F[232,x,1])/(-1+k[0])
F[246,x,k[0],k[1]] = -k[0]*(F[233,x,1,k[1]]-F[233,x,k[0],k[1]])/(-1+k[0])
F[247,x,k[0],k[1]] = F[248,x,k[0],k[1]]
F[248,x,k[0],k[1]] = F[249,x,k[0],k[1]]*F[33,x,k[0]]
F[249,x,k[0],k[1]] = F[230,x,k[0],k[1]]+F[250,x,k[0],k[1]]
F[250,x,k[0],k[1]] = F[251,x,k[0],k[1]]
F[251,x,k[0],k[1]] = F[225,x]*F[230,x,k[0],k[1]]*F[65,x]
F[252,x] = F[253,x]
F[253,x] = F[211,x]*F[225,x]*F[65,x]
F[254,x,k[0]] = F[212,x,k[0]]+F[232,x,k[0]]
F[255,x,k[0]] = F[256,x,k[0],1]
F[256,x,k[0],k[1]] = (F[257,x,k[0],k[1]]*k[1]-F[257,x,k[0],1])/(-1+k[1])
F[257,x,k[0],k[1]] = F[241,x,k[0]]+F[258,x,k[0],k[1]]
F[258,x,k[0],k[1]] = (F[233,x,k[0],k[1]]-F[233,x,1,k[1]])/(-1+k[0])
F[259,x] = F[260,x]+F[261,x]
F[260,x] = F[240,x,1]
F[261,x] = F[262,x,1]
F[262,x,k[0]] = (F[263,x,k[0]]-F[263,x,1])/(-1+k[0])
F[263,x,k[0]] = F[264,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]*F[65,x]
F[265,x,k[0]] = F[266,x,k[0]]+F[269,x,k[0]]
F[266,x,k[0]] = F[236,x,k[0]]+F[267,x,k[0]]
F[267,x,k[0]] = F[268,x,k[0]]
F[268,x,k[0]] = F[225,x]*F[236,x,k[0]]*F[65,x]
F[269,x,k[0]] = -k[0]*(-F[263,x,k[0]]+F[263,x,1])/(-1+k[0])
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[272,x,k[0]]*F[33,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0],1]
F[273,x,k[0],k[1]] = F[274,x,k[0],k[0]*k[1]]
F[274,x,k[0],k[1]] = F[275,x,k[0],k[1]]
F[275,x,k[0],k[1]] = F[276,x,k[0],k[1]]+F[280,x,k[0],k[1]]
F[276,x,k[0],k[1]] = F[277,x,k[1],k[0]]
F[277,x,k[0],k[1]] = F[278,x,k[0],k[1]]*F[43,x,k[1]]
F[278,x,k[0],k[1]] = F[279,x,k[1],k[0]]
F[279,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[148,x,k[0]]
F[280,x,k[0],k[1]] = F[281,x,k[0],k[1]]
F[281,x,k[0],k[1]] = F[127,x,k[0],k[1]]*F[282,x,k[0],k[1]]
F[282,x,k[0],k[1]] = F[162,x,k[1]]+F[170,x,k[0],k[1]]
F[283,x,k[0]] = F[284,x,k[0]]
F[284,x,k[0]] = F[285,x,k[0]]*F[31,x,k[0]]*F[33,x,k[0]]*F[59,x,k[0]]
F[285,x,k[0]] = F[286,x,k[0]]+F[44,x,k[0]]
F[286,x,k[0]] = F[287,x,k[0],1]
F[287,x,k[0],k[1]] = F[48,x,k[0],k[0]*k[1]]
F[288,x,k[0]] = F[289,x,k[0],1]
F[289,x,k[0],k[1]] = F[290,x,k[0],k[0]*k[1]]
F[290,x,k[0],k[1]] = F[291,x,k[0],k[1]]
F[291,x,k[0],k[1]] = F[181,x,k[0],k[1]]*F[282,x,k[0],k[1]]*F[65,x]
F[292,x,k[0]] = F[293,x,k[0],1]
F[293,x,k[0],k[1]] = F[117,x,k[0],k[0]*k[1]]
F[294,x,k[0],k[1]] = F[119,x,k[0],k[1]]
F[295,x] = F[0,x]+F[2,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_{65}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{65}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{295}\! \left(x \right) F_{65}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}, 1\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}\right)+F_{294}\! \left(x , y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)+F_{292}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{288}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\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_{25}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)+F_{283}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{34}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{23}\! \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_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{28}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = y_{0} x
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{36}\! \left(x , y_{0}\right) = F_{270}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{26}\! \left(x , 1\right)-F_{26}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}\right) = F_{40}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right) F_{63}\! \left(x \right) F_{65}\! \left(x \right)
F_{41}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{42}\! \left(x , 1\right)-F_{42}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{43}\! \left(x , y_{0}\right) = F_{184}\! \left(x \right)+F_{42}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{44}\! \left(x , y_{0}\right)+F_{47}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right)+F_{45}\! \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_{17}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}, 1\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{1}\right) F_{59}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{179}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{50}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{51}\! \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_{52}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right) F_{87}\! \left(x \right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{0}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right) F_{62}\! \left(x \right)
F_{59}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)
F_{65}\! \left(x \right) = x
F_{66}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right) F_{87}\! \left(x \right)
F_{68}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{44}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}\right) F_{81}\! \left(x \right)
F_{72}\! \left(x , y_{0}\right) = F_{73}\! \left(x \right)+F_{76}\! \left(x , y_{0}\right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x , y_{0}\right) = F_{77}\! \left(x \right)+F_{78}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)
F_{77}\! \left(x \right) = 0
F_{78}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right) F_{72}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{65}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{65}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{82}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{65}\! \left(x \right) F_{87}\! \left(x \right)
F_{90}\! \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_{87}\! \left(x \right) F_{92}\! \left(x , y_{0}, y_{1}\right)
F_{92}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{154}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{95}\! \left(x , y_{0}, y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{1}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = F_{97}\! \left(x , y_{1}, y_{0}\right)
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{104}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)
F_{98}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{99}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{65}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\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_{65}\! \left(x \right)
F_{103}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}, 1\right)
F_{104}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , y_{1}, y_{0}\right)
F_{105}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \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_{94}\! \left(x , y_{0}, y_{1}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{1}, y_{0}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = F_{109}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0}, y_{1}, 1\right)
F_{110}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{111}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{112}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{1}, y_{0}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{0}, y_{1}\right)+F_{121}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{1}, y_{0}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{117}\! \left(x , y_{0}, y_{1}\right) = F_{118}\! \left(x , y_{0}, y_{1}\right)
F_{118}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \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) = -\frac{y_{1} \left(F_{117}\! \left(x , y_{0}, 1\right)-F_{117}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \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_{65}\! \left(x \right)
F_{123}\! \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_{124}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{0}, y_{1}\right) F_{43}\! \left(x , y_{1}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{128}\! \left(x , y_{0}, y_{1}\right)
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{1}, y_{0}\right)
F_{127}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{48}\! \left(x , y_{0}, 1\right)-F_{48}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{128}\! \left(x , y_{0}, y_{1}\right) = F_{129}\! \left(x , y_{0}\right)+F_{133}\! \left(x , y_{0}, y_{1}\right)
F_{129}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{132}\! \left(x , y_{0}\right)
F_{132}\! \left(x , y_{0}\right) = y_{0} x
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{1}\right)
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{135}\! \left(x , y_{0}, y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)+F_{77}\! \left(x \right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = F_{136}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}\right)+F_{134}\! \left(x , y_{0}, y_{1}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{0}\right) F_{133}\! \left(x , y_{0}, y_{1}\right)
F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{33}\! \left(x , y_{2}\right)
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} \left(F_{112}\! \left(x , y_{0}, 1, y_{2}\right)-F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{1}}
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{146}\! \left(x , y_{0}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{143}\! \left(x , y_{0}, y_{1}\right)
F_{143}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)
F_{146}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{148}\! \left(x , y_{0}\right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{149}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{151}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)
F_{153}\! \left(x , y_{0}\right) = F_{142}\! \left(x , y_{0}, 1\right)
F_{154}\! \left(x , y_{0}, y_{1}\right) = F_{155}\! \left(x , y_{0}, y_{1}\right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{156}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{94}\! \left(x , y_{0}, 1\right)-F_{94}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{157}\! \left(x , y_{0}, y_{1}\right) = F_{158}\! \left(x , y_{0}, y_{1}\right) F_{81}\! \left(x \right)
F_{158}\! \left(x , y_{0}, y_{1}\right) = F_{159}\! \left(x , y_{1}\right)+F_{165}\! \left(x , y_{0}, y_{1}\right)
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{163}\! \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 , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x , y_{0}\right)
F_{163}\! \left(x , y_{0}\right) = F_{164}\! \left(x , y_{0}\right)
F_{164}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = F_{167}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{0}, y_{1}\right)+F_{77}\! \left(x \right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{1}\right)+F_{166}\! \left(x , y_{0}, y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}\right)
F_{171}\! \left(x , y_{0}, y_{1}\right) = 2 F_{77}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \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_{33}\! \left(x , y_{0}\right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{165}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right) F_{178}\! \left(x \right) F_{87}\! \left(x \right)
F_{178}\! \left(x \right) = F_{1}\! \left(x \right)+F_{81}\! \left(x \right)
F_{179}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \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_{182}\! \left(x , y_{0}\right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}\right) = F_{183}\! \left(x , y_{0}\right) F_{81}\! \left(x \right)
F_{183}\! \left(x , y_{0}\right) = F_{75}\! \left(x \right)+F_{80}\! \left(x , y_{0}\right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{4}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{65}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{192}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = \frac{F_{190}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{63}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{194}\! \left(x , y_{0}\right) = F_{195}\! \left(x , y_{0}\right)
F_{195}\! \left(x , y_{0}\right) = F_{196}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{196}\! \left(x , y_{0}\right) = F_{197}\! \left(x , y_{0}\right)+F_{259}\! \left(x \right)
F_{197}\! \left(x , y_{0}\right) = F_{198}\! \left(x , y_{0}\right)+F_{255}\! \left(x , y_{0}\right)
F_{198}\! \left(x , y_{0}\right) = F_{194}\! \left(x , y_{0}\right)+F_{199}\! \left(x , y_{0}\right)
F_{199}\! \left(x , y_{0}\right) = F_{200}\! \left(x \right)+F_{254}\! \left(x , y_{0}\right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{210}\! \left(x \right)
F_{201}\! \left(x \right) = F_{0}\! \left(x \right)+F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{2}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{65}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{208}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{184}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{187}\! \left(x \right) F_{65}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{252}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x , 1\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_{33}\! \left(x , y_{0}\right)
F_{214}\! \left(x , y_{0}\right) = F_{215}\! \left(x , y_{0}, 1\right)
F_{215}\! \left(x , y_{0}, y_{1}\right) = F_{216}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{216}\! \left(x , y_{0}, y_{1}\right) = F_{217}\! \left(x , y_{0}, y_{1}\right)+F_{230}\! \left(x , y_{0}, y_{1}\right)
F_{217}\! \left(x , y_{0}, y_{1}\right) = F_{218}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}, y_{1}\right)
F_{218}\! \left(x , y_{0}\right) = F_{219}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{219}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{220}\! \left(x , y_{0}\right)
F_{220}\! \left(x , y_{0}\right) = F_{221}\! \left(x , y_{0}\right)
F_{221}\! \left(x , y_{0}\right) = F_{222}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{222}\! \left(x , y_{0}\right) = F_{219}\! \left(x , y_{0}\right)+F_{223}\! \left(x , y_{0}\right)
F_{223}\! \left(x , y_{0}\right) = F_{224}\! \left(x , y_{0}\right)
F_{224}\! \left(x , y_{0}\right) = F_{218}\! \left(x , y_{0}\right) F_{225}\! \left(x \right) F_{65}\! \left(x \right)
F_{225}\! \left(x \right) = F_{184}\! \left(x \right)
F_{226}\! \left(x , y_{0}, y_{1}\right) = F_{227}\! \left(x , y_{0}, y_{1}\right)
F_{227}\! \left(x , y_{0}, y_{1}\right) = F_{228}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{228}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{229}\! \left(x , 1, y_{1}\right) y_{1}-F_{229}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{229}\! \left(x , y_{0}, y_{1}\right) = F_{216}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{230}\! \left(x , y_{0}, y_{1}\right) = F_{231}\! \left(x , y_{1}\right)+F_{247}\! \left(x , y_{0}, y_{1}\right)
F_{231}\! \left(x , y_{0}\right) = F_{202}\! \left(x \right)+F_{232}\! \left(x , y_{0}\right)
F_{232}\! \left(x , y_{0}\right) = F_{233}\! \left(x , y_{0}, 1\right)
F_{233}\! \left(x , y_{0}, y_{1}\right) = F_{234}\! \left(x , y_{0}, y_{1}\right)
F_{234}\! \left(x , y_{0}, y_{1}\right) = F_{235}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{235}\! \left(x , y_{0}, y_{1}\right) = F_{236}\! \left(x , y_{0}\right)+F_{246}\! \left(x , y_{0}, y_{1}\right)
F_{236}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)+F_{237}\! \left(x , y_{0}\right)
F_{237}\! \left(x , y_{0}\right) = F_{238}\! \left(x , y_{0}\right)
F_{238}\! \left(x , y_{0}\right) = F_{239}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{239}\! \left(x , y_{0}\right) = F_{240}\! \left(x , y_{0}\right)+F_{244}\! \left(x , y_{0}\right)
F_{240}\! \left(x , y_{0}\right) = F_{241}\! \left(x , y_{0}\right)+F_{242}\! \left(x , y_{0}\right)
F_{241}\! \left(x , y_{0}\right) = F_{191}\! \left(x \right)+F_{237}\! \left(x , y_{0}\right)
F_{242}\! \left(x , y_{0}\right) = F_{243}\! \left(x , y_{0}\right)
F_{243}\! \left(x , y_{0}\right) = F_{225}\! \left(x \right) F_{241}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{244}\! \left(x , y_{0}\right) = F_{241}\! \left(x , y_{0}\right)+F_{245}\! \left(x , y_{0}\right)
F_{245}\! \left(x , y_{0}\right) = -\frac{-F_{232}\! \left(x , y_{0}\right)+F_{232}\! \left(x , 1\right)}{-1+y_{0}}
F_{246}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{233}\! \left(x , 1, y_{1}\right)-F_{233}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{247}\! \left(x , y_{0}, y_{1}\right) = F_{248}\! \left(x , y_{0}, y_{1}\right)
F_{248}\! \left(x , y_{0}, y_{1}\right) = F_{249}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{249}\! \left(x , y_{0}, y_{1}\right) = F_{230}\! \left(x , y_{0}, y_{1}\right)+F_{250}\! \left(x , y_{0}, y_{1}\right)
F_{250}\! \left(x , y_{0}, y_{1}\right) = F_{251}\! \left(x , y_{0}, y_{1}\right)
F_{251}\! \left(x , y_{0}, y_{1}\right) = F_{225}\! \left(x \right) F_{230}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{211}\! \left(x \right) F_{225}\! \left(x \right) F_{65}\! \left(x \right)
F_{254}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)+F_{232}\! \left(x , y_{0}\right)
F_{255}\! \left(x , y_{0}\right) = F_{256}\! \left(x , y_{0}, 1\right)
F_{256}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{257}\! \left(x , y_{0}, y_{1}\right)+F_{257}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{257}\! \left(x , y_{0}, y_{1}\right) = F_{241}\! \left(x , y_{0}\right)+F_{258}\! \left(x , y_{0}, y_{1}\right)
F_{258}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{233}\! \left(x , 1, y_{1}\right)-F_{233}\! \left(x , y_{0}, y_{1}\right)}{-1+y_{0}}
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{261}\! \left(x \right)
F_{260}\! \left(x \right) = F_{240}\! \left(x , 1\right)
F_{261}\! \left(x \right) = F_{262}\! \left(x , 1\right)
F_{262}\! \left(x , y_{0}\right) = -\frac{-F_{263}\! \left(x , y_{0}\right)+F_{263}\! \left(x , 1\right)}{-1+y_{0}}
F_{263}\! \left(x , y_{0}\right) = F_{264}\! \left(x , y_{0}\right)
F_{264}\! \left(x , y_{0}\right) = F_{265}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{265}\! \left(x , y_{0}\right) = F_{266}\! \left(x , y_{0}\right)+F_{269}\! \left(x , y_{0}\right)
F_{266}\! \left(x , y_{0}\right) = F_{236}\! \left(x , y_{0}\right)+F_{267}\! \left(x , y_{0}\right)
F_{267}\! \left(x , y_{0}\right) = F_{268}\! \left(x , y_{0}\right)
F_{268}\! \left(x , y_{0}\right) = F_{225}\! \left(x \right) F_{236}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{269}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(-F_{263}\! \left(x , y_{0}\right)+F_{263}\! \left(x , 1\right)\right)}{-1+y_{0}}
F_{270}\! \left(x , y_{0}\right) = F_{271}\! \left(x , y_{0}\right)
F_{271}\! \left(x , y_{0}\right) = F_{272}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{272}\! \left(x , y_{0}\right) = F_{273}\! \left(x , y_{0}, 1\right)
F_{273}\! \left(x , y_{0}, y_{1}\right) = F_{274}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{274}\! \left(x , y_{0}, y_{1}\right) = F_{275}\! \left(x , y_{0}, y_{1}\right)
F_{275}\! \left(x , y_{0}, y_{1}\right) = F_{276}\! \left(x , y_{0}, y_{1}\right)+F_{280}\! \left(x , y_{0}, y_{1}\right)
F_{276}\! \left(x , y_{0}, y_{1}\right) = F_{277}\! \left(x , y_{1}, y_{0}\right)
F_{277}\! \left(x , y_{0}, y_{1}\right) = F_{278}\! \left(x , y_{0}, y_{1}\right) F_{43}\! \left(x , y_{1}\right)
F_{278}\! \left(x , y_{0}, y_{1}\right) = F_{279}\! \left(x , y_{1}, y_{0}\right)
F_{279}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)+F_{148}\! \left(x , y_{0}\right)
F_{280}\! \left(x , y_{0}, y_{1}\right) = F_{281}\! \left(x , y_{0}, y_{1}\right)
F_{281}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{0}, y_{1}\right) F_{282}\! \left(x , y_{0}, y_{1}\right)
F_{282}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{1}\right)+F_{170}\! \left(x , y_{0}, y_{1}\right)
F_{283}\! \left(x , y_{0}\right) = F_{284}\! \left(x , y_{0}\right)
F_{284}\! \left(x , y_{0}\right) = F_{285}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right)
F_{285}\! \left(x , y_{0}\right) = F_{286}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{286}\! \left(x , y_{0}\right) = F_{287}\! \left(x , y_{0}, 1\right)
F_{287}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{288}\! \left(x , y_{0}\right) = F_{289}\! \left(x , y_{0}, 1\right)
F_{289}\! \left(x , y_{0}, y_{1}\right) = F_{290}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{290}\! \left(x , y_{0}, y_{1}\right) = F_{291}\! \left(x , y_{0}, y_{1}\right)
F_{291}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right) F_{282}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{292}\! \left(x , y_{0}\right) = F_{293}\! \left(x , y_{0}, 1\right)
F_{293}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{294}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right)
F_{295}\! \left(x \right) = F_{0}\! \left(x \right)+F_{2}\! \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_65(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_65(x)*F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_4(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_295(x)*F_65(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_16(x, k_0, 1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0) + F_294(x, k_0, k_1))
Eq(F_18(x, k_0), F_17(x, k_0)*F_65(x))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_20(x, k_0), F_19(x, k_0) + F_292(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0) + F_288(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_65(x))
Eq(F_25(x, k_0), F_26(x, k_0) + F_283(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_34(x, k_0))
Eq(F_27(x, k_0), F_23(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_33(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_32(x, k_0), F_28(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_65(x))
Eq(F_36(x, k_0), F_270(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), -F_26(x, 1) + (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_63(x)*F_65(x))
Eq(F_41(x, k_0), -F_42(x, 1) + (-k_0*F_42(x, k_0) + F_42(x, 1))/(1 - k_0))
Eq(F_43(x, k_0), F_184(x) + F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_4(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_17(x, k_0)*F_33(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0, 1))
Eq(F_49(x, k_0, k_1), F_48(x, k_0, k_1)*F_59(x, k_0))
Eq(F_50(x, k_0, k_1), F_179(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_50(x, k_0, k_1)*F_65(x))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_52(x, k_0, k_1) + F_68(x, k_0))
Eq(F_54(x, k_0, k_1), F_53(x, k_0, k_1)*F_87(x))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_175(x, k_0, k_1) + F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0) + F_90(x, k_0, k_1))
Eq(F_57(x, k_0), F_58(x, k_0) + F_66(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0)*F_62(x))
Eq(F_59(x, k_0), F_1(x) + F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0)*F_59(x, k_0))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)/F_65(x))
Eq(F_64(x), F_2(x))
Eq(F_65(x), x)
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_87(x))
Eq(F_68(x, k_0), F_69(x, k_0) + F_71(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_44(x, k_0)*F_59(x, k_0)*F_65(x))
Eq(F_71(x, k_0), F_72(x, k_0)*F_81(x))
Eq(F_72(x, k_0), F_73(x) + F_76(x, k_0))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_65(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_73(x))
Eq(F_76(x, k_0), F_77(x) + F_78(x, k_0) + F_79(x, k_0))
Eq(F_77(x), 0)
Eq(F_78(x, k_0), F_33(x, k_0)*F_72(x, k_0))
Eq(F_79(x, k_0), F_65(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_60(x, k_0) + F_76(x, k_0))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_65(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_1(x) + F_82(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_1(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_65(x)*F_87(x))
Eq(F_90(x, k_0, k_1), F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_87(x)*F_92(x, k_0, k_1))
Eq(F_92(x, k_0, k_1), F_157(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_154(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_95(x, k_0, k_1))
Eq(F_95(x, k_0, k_1), F_33(x, k_1)*F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_97(x, k_1, k_0))
Eq(F_97(x, k_0, k_1), F_104(x, k_0, k_1) + F_98(x, k_1))
Eq(F_98(x, k_0), F_101(x, k_0) + F_99(x, k_0))
Eq(F_100(x, k_0), F_65(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_69(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_65(x))
Eq(F_103(x, k_0), F_96(x, k_0, 1))
Eq(F_104(x, k_0, k_1), F_105(x, k_1, k_0))
Eq(F_105(x, k_0, k_1), F_106(x, k_0, k_1) + F_141(x, k_0, k_1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1) + F_94(x, k_0, k_1))
Eq(F_107(x, k_0, k_1), F_108(x, k_1, k_0))
Eq(F_108(x, k_0, k_1), F_109(x, k_0, k_1)*F_65(x))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1, 1))
Eq(F_110(x, k_0, k_1, k_2), (-k_2*F_111(x, k_0, k_1, k_2) + F_111(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_111(x, k_0, k_1, k_2), F_112(x, k_1, k_0, k_2))
Eq(F_112(x, k_0, k_1, k_2), F_113(x, k_0, k_1) + F_138(x, k_0, k_1, k_2))
Eq(F_113(x, k_0, k_1), F_114(x, k_1, k_0))
Eq(F_114(x, k_0, k_1), F_115(x, k_0, k_1) + F_121(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), F_116(x, k_1, k_0))
Eq(F_116(x, k_0, k_1), F_117(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_117(x, k_0, k_1), F_118(x, k_0, k_1))
Eq(F_118(x, k_0, k_1), F_119(x, k_0, k_1)*F_65(x))
Eq(F_119(x, k_0, k_1), F_113(x, k_0, k_1) + F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), -F_117(x, k_0, 1) + (-k_1*F_117(x, k_0, k_1) + F_117(x, k_0, 1))/(1 - k_1))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1))
Eq(F_122(x, k_0, k_1), F_123(x, k_0, k_1)*F_65(x))
Eq(F_123(x, k_0, k_1), F_124(x, k_0, k_1) + F_125(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_115(x, k_0, k_1)*F_43(x, k_1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1)*F_128(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_127(x, k_1, k_0))
Eq(F_127(x, k_0, k_1), -F_48(x, k_0, 1) + (-k_1*F_48(x, k_0, k_1) + F_48(x, k_0, 1))/(1 - k_1))
Eq(F_128(x, k_0, k_1), F_129(x, k_0) + F_133(x, k_0, k_1))
Eq(F_129(x, k_0), F_1(x) + F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_129(x, k_0)*F_132(x, k_0))
Eq(F_132(x, k_0), k_0*x)
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1) + F_60(x, k_1))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1) + F_137(x, k_0, k_1) + F_77(x))
Eq(F_135(x, k_0, k_1), F_136(x, k_0, k_1)*F_33(x, k_1))
Eq(F_136(x, k_0, k_1), F_130(x, k_0) + F_134(x, k_0, k_1))
Eq(F_137(x, k_0, k_1), F_132(x, k_0)*F_133(x, k_0, k_1))
Eq(F_138(x, k_0, k_1, k_2), F_139(x, k_0, k_1, k_2))
Eq(F_139(x, k_0, k_1, k_2), F_140(x, k_0, k_1, k_2)*F_33(x, k_2))
Eq(F_140(x, k_0, k_1, k_2), -F_112(x, k_0, 1, k_2) + (-k_1*F_112(x, k_0, k_1, k_2) + F_112(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_142(x, k_0, k_1), F_141(x, k_0, k_1) + F_146(x, k_0))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1))
Eq(F_143(x, k_0, k_1), F_144(x, k_0, k_1)*F_33(x, k_0))
Eq(F_145(x, k_0, k_1), F_144(x, k_0, k_1)*F_33(x, k_1))
Eq(F_145(x, k_0, k_1), F_106(x, k_0, k_1))
Eq(F_146(x, k_0), F_147(x, k_0) + F_150(x, k_0))
Eq(F_99(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0) + F_19(x, k_0))
Eq(F_149(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0)*F_65(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_142(x, k_0, 1))
Eq(F_154(x, k_0, k_1), F_155(x, k_0, k_1))
Eq(F_155(x, k_0, k_1), F_156(x, k_0, k_1)*F_65(x))
Eq(F_156(x, k_0, k_1), -F_94(x, k_0, 1) + (-k_1*F_94(x, k_0, k_1) + F_94(x, k_0, 1))/(1 - k_1))
Eq(F_157(x, k_0, k_1), F_158(x, k_0, k_1)*F_81(x))
Eq(F_158(x, k_0, k_1), F_159(x, k_1) + F_165(x, k_0, k_1))
Eq(F_159(x, k_0), F_160(x, k_0) + F_163(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0)*F_33(x, k_0))
Eq(F_162(x, k_0), F_1(x) + F_160(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_159(x, k_0)*F_65(x))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_166(x, k_0, k_1), F_167(x, k_0, k_1) + F_169(x, k_0, k_1) + F_77(x))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1)*F_33(x, k_0))
Eq(F_168(x, k_0, k_1), F_160(x, k_1) + F_166(x, k_0, k_1))
Eq(F_169(x, k_0, k_1), F_170(x, k_0, k_1)*F_33(x, k_1))
Eq(F_170(x, k_0, k_1), F_166(x, k_0, k_1) + F_60(x, k_0))
Eq(F_171(x, k_0, k_1), F_172(x, k_0, k_1) + F_174(x, k_0, k_1) + 2*F_77(x))
Eq(F_172(x, k_0, k_1), F_173(x, k_0, k_1)*F_33(x, k_0))
Eq(F_173(x, k_0, k_1), F_163(x, k_1) + F_171(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_165(x, k_0, k_1)*F_65(x))
Eq(F_175(x, k_0, k_1), F_176(x, k_0, k_1) + F_58(x, k_0))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1))
Eq(F_177(x, k_0, k_1), F_168(x, k_0, k_1)*F_178(x)*F_87(x))
Eq(F_178(x), F_1(x) + F_81(x))
Eq(F_179(x, k_0, k_1), F_168(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_182(x, k_0))
Eq(F_181(x, k_0, k_1), F_44(x, k_0) + F_48(x, k_0, k_1))
Eq(F_182(x, k_0), F_183(x, k_0)*F_81(x))
Eq(F_183(x, k_0), F_75(x) + F_80(x, k_0))
Eq(F_184(x), F_185(x) + F_4(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_187(x)*F_65(x))
Eq(F_187(x), F_188(x) + F_192(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)/F_65(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), -F_0(x) + F_63(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_194(x, 1))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_65(x))
Eq(F_196(x, k_0), F_197(x, k_0) + F_259(x))
Eq(F_197(x, k_0), F_198(x, k_0) + F_255(x, k_0))
Eq(F_198(x, k_0), F_194(x, k_0) + F_199(x, k_0))
Eq(F_199(x, k_0), F_200(x) + F_254(x, k_0))
Eq(F_200(x), F_201(x) + F_210(x))
Eq(F_201(x), F_0(x) + F_202(x))
Eq(F_202(x), F_2(x) + F_203(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_205(x)*F_65(x))
Eq(F_205(x), F_206(x) + F_208(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_184(x)*F_62(x)*F_65(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_187(x)*F_65(x))
Eq(F_210(x), F_211(x) + F_252(x))
Eq(F_211(x), F_212(x, 1))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0)*F_33(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0, 1))
Eq(F_215(x, k_0, k_1), F_216(x, k_0, k_0*k_1))
Eq(F_216(x, k_0, k_1), F_217(x, k_0, k_1) + F_230(x, k_0, k_1))
Eq(F_217(x, k_0, k_1), F_218(x, k_0) + F_226(x, k_0, k_1))
Eq(F_218(x, k_0), F_219(x, k_0) + F_59(x, k_0))
Eq(F_219(x, k_0), F_2(x) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0)*F_33(x, k_0))
Eq(F_222(x, k_0), F_219(x, k_0) + F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_224(x, k_0), F_218(x, k_0)*F_225(x)*F_65(x))
Eq(F_225(x), F_184(x))
Eq(F_226(x, k_0, k_1), F_227(x, k_0, k_1))
Eq(F_227(x, k_0, k_1), F_228(x, k_0, k_1)*F_33(x, k_1))
Eq(F_228(x, k_0, k_1), (-k_0*F_229(x, k_0/k_1, k_1) + k_1*F_229(x, 1, k_1))/(-k_0 + k_1))
Eq(F_229(x, k_0, k_1), F_216(x, k_0*k_1, k_1))
Eq(F_230(x, k_0, k_1), F_231(x, k_1) + F_247(x, k_0, k_1))
Eq(F_231(x, k_0), F_202(x) + F_232(x, k_0))
Eq(F_232(x, k_0), F_233(x, k_0, 1))
Eq(F_233(x, k_0, k_1), F_234(x, k_0, k_1))
Eq(F_234(x, k_0, k_1), F_235(x, k_0, k_1)*F_33(x, k_1))
Eq(F_235(x, k_0, k_1), F_236(x, k_0) + F_246(x, k_0, k_1))
Eq(F_236(x, k_0), F_212(x, k_0) + F_237(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0)*F_33(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_244(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0) + F_242(x, k_0))
Eq(F_241(x, k_0), F_191(x) + F_237(x, k_0))
Eq(F_242(x, k_0), F_243(x, k_0))
Eq(F_243(x, k_0), F_225(x)*F_241(x, k_0)*F_65(x))
Eq(F_244(x, k_0), F_241(x, k_0) + F_245(x, k_0))
Eq(F_245(x, k_0), -F_232(x, k_0) + (-k_0*F_232(x, k_0) + F_232(x, 1))/(1 - k_0))
Eq(F_246(x, k_0, k_1), -F_233(x, 1, k_1) + (-k_0*F_233(x, k_0, k_1) + F_233(x, 1, k_1))/(1 - k_0))
Eq(F_247(x, k_0, k_1), F_248(x, k_0, k_1))
Eq(F_248(x, k_0, k_1), F_249(x, k_0, k_1)*F_33(x, k_0))
Eq(F_249(x, k_0, k_1), F_230(x, k_0, k_1) + F_250(x, k_0, k_1))
Eq(F_250(x, k_0, k_1), F_251(x, k_0, k_1))
Eq(F_251(x, k_0, k_1), F_225(x)*F_230(x, k_0, k_1)*F_65(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_211(x)*F_225(x)*F_65(x))
Eq(F_254(x, k_0), F_212(x, k_0) + F_232(x, k_0))
Eq(F_255(x, k_0), F_256(x, k_0, 1))
Eq(F_256(x, k_0, k_1), (-k_1*F_257(x, k_0, k_1) + F_257(x, k_0, 1))/(1 - k_1))
Eq(F_257(x, k_0, k_1), F_241(x, k_0) + F_258(x, k_0, k_1))
Eq(F_258(x, k_0, k_1), -F_233(x, k_0, k_1) + (-k_0*F_233(x, k_0, k_1) + F_233(x, 1, k_1))/(1 - k_0))
Eq(F_259(x), F_260(x) + F_261(x))
Eq(F_260(x), F_240(x, 1))
Eq(F_261(x), F_262(x, 1))
Eq(F_262(x, k_0), -F_263(x, k_0) + (-k_0*F_263(x, k_0) + F_263(x, 1))/(1 - k_0))
Eq(F_263(x, k_0), F_264(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0)*F_65(x))
Eq(F_265(x, k_0), F_266(x, k_0) + F_269(x, k_0))
Eq(F_266(x, k_0), F_236(x, k_0) + F_267(x, k_0))
Eq(F_267(x, k_0), F_268(x, k_0))
Eq(F_268(x, k_0), F_225(x)*F_236(x, k_0)*F_65(x))
Eq(F_269(x, k_0), -F_263(x, 1) + (-k_0*F_263(x, k_0) + F_263(x, 1))/(1 - k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_272(x, k_0)*F_33(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0, 1))
Eq(F_273(x, k_0, k_1), F_274(x, k_0, k_0*k_1))
Eq(F_274(x, k_0, k_1), F_275(x, k_0, k_1))
Eq(F_275(x, k_0, k_1), F_276(x, k_0, k_1) + F_280(x, k_0, k_1))
Eq(F_276(x, k_0, k_1), F_277(x, k_1, k_0))
Eq(F_277(x, k_0, k_1), F_278(x, k_0, k_1)*F_43(x, k_1))
Eq(F_278(x, k_0, k_1), F_279(x, k_1, k_0))
Eq(F_279(x, k_0, k_1), F_116(x, k_0, k_1) + F_148(x, k_0))
Eq(F_280(x, k_0, k_1), F_281(x, k_0, k_1))
Eq(F_281(x, k_0, k_1), F_127(x, k_0, k_1)*F_282(x, k_0, k_1))
Eq(F_282(x, k_0, k_1), F_162(x, k_1) + F_170(x, k_0, k_1))
Eq(F_283(x, k_0), F_284(x, k_0))
Eq(F_284(x, k_0), F_285(x, k_0)*F_31(x, k_0)*F_33(x, k_0)*F_59(x, k_0))
Eq(F_285(x, k_0), F_286(x, k_0) + F_44(x, k_0))
Eq(F_286(x, k_0), F_287(x, k_0, 1))
Eq(F_287(x, k_0, k_1), F_48(x, k_0, k_0*k_1))
Eq(F_288(x, k_0), F_289(x, k_0, 1))
Eq(F_289(x, k_0, k_1), F_290(x, k_0, k_0*k_1))
Eq(F_290(x, k_0, k_1), F_291(x, k_0, k_1))
Eq(F_291(x, k_0, k_1), F_181(x, k_0, k_1)*F_282(x, k_0, k_1)*F_65(x))
Eq(F_292(x, k_0), F_293(x, k_0, 1))
Eq(F_293(x, k_0, k_1), F_117(x, k_0, k_0*k_1))
Eq(F_294(x, k_0, k_1), F_119(x, k_0, k_1))
Eq(F_295(x), F_0(x) + F_2(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]]}}, "idx": 0}, {"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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 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[1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 1], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 1], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 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], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 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], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 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], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24868/
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[43,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[137,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[43,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[4,x]*F[43,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0],1]
F[13,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])/(-1+k[1])
F[14,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[43,x]
F[15,x,k[0],k[1]] = F[1,x]+F[136,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[15,x,k[0],k[0]*k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[134,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[20,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[0]*k[1]]
F[18,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0],k[1]] = F[21,x,k[0],k[0]*k[1]]
F[21,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[19,x,k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[43,x]
F[23,x,k[0],k[1]] = F[132,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0]]+F[96,x,k[0],k[1]]
F[25,x,k[0]] = F[26,x,k[0]]+F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[19,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[46,x,k[0]]
F[30,x,k[0]] = F[19,x,k[0]]*F[29,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]+F[4,x]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[35,x,k[0]]+F[44,x,k[0]]
F[33,x,k[0]] = F[19,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0],1]
F[35,x,k[0]] = F[36,x,k[0]]*F[43,x]
F[36,x,k[0]] = F[32,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[43,x]
F[39,x,k[0]] = F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[4,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[11,x,k[0]]*k[0]-F[11,x,1])/(-1+k[0])
F[42,x,k[0]] = F[11,x,k[0]]*F[31,x,k[0]]
F[43,x] = x
F[44,x,k[0]] = F[43,x]*F[45,x,k[0]]
F[45,x,k[0]] = (F[32,x,k[0]]*k[0]-F[32,x,1])/(-1+k[0])
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[129,x,k[0]]+F[48,x,k[0]]
F[49,x,k[0]] = F[48,x,k[0]]+F[73,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0],1]
F[50,x,k[0],k[1]] = F[51,x,k[0],k[1]]+F[84,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[52,x,k[0],k[0]*k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[1,x]+F[54,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[19,x,k[0]]*F[53,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[19,x,k[1]]*F[53,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[43,x]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[43,x]*F[59,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[60,x,k[0]]+F[64,x,k[0],k[1]]
F[61,x,k[0]] = F[43,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[28,x,k[0]]*F[43,x]
F[65,x,k[0],k[1]] = F[64,x,k[0],k[0]*k[1]]
F[66,x,k[0],k[1]] = F[60,x,k[0]]+F[65,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[43,x]*F[66,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[68,x,k[0],k[1]]
F[68,x,k[0],k[1]] = F[43,x]*F[69,x,k[0],k[1]]
F[69,x,k[0],k[1]] = F[50,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[71,x,k[0],k[0]*k[1]]
F[71,x,k[0],k[1]] = F[72,x,k[0]]+F[80,x,k[0],k[1]]
F[28,x,k[0]] = F[72,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[78,x,k[0]]
F[74,x,k[0]] = F[62,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[1,x]+F[76,x,k[0]]+F[77,x,k[0]]
F[76,x,k[0]] = F[19,x,k[0]]*F[75,x,k[0]]
F[77,x,k[0]] = F[25,x,k[0]]*F[43,x]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[11,x,k[0]]*F[43,x]*F[74,x,k[0]]
F[80,x,k[0],k[1]] = F[81,x,k[0],k[1]]
F[81,x,k[0],k[1]] = -k[1]*(F[82,x,k[0],1]-F[82,x,k[0],k[1]])/(-1+k[1])
F[82,x,k[0],k[1]] = F[83,x,k[0],k[1]]
F[83,x,k[0],k[1]] = F[43,x]*F[64,x,k[0],k[1]]
F[84,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[86,x,k[0]]+F[88,x,k[0],k[1]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[11,x,k[0]]*F[43,x]*F[75,x,k[0]]
F[88,x,k[0],k[1]] = F[89,x,k[0],k[1]]
F[89,x,k[0],k[1]] = F[43,x]*F[90,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[110,x,k[0],k[1]]+F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[11,x,k[0]]*F[92,x,k[0],k[1]]
F[92,x,k[0],k[1]] = F[6,x]+F[93,x,k[0],k[1]]+F[94,x,k[0],k[1]]+F[95,x,k[0],k[1]]
F[93,x,k[0],k[1]] = F[19,x,k[0]]*F[92,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[55,x,k[0],k[0]*k[1]]
F[95,x,k[0],k[1]] = F[43,x]*F[96,x,k[0],k[1]]
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[1]]*F[98,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[99,x,k[0]]
F[100,x,k[0]] = F[43,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[25,x,k[0]] = F[101,x,k[0]]+F[75,x,k[0]]
F[103,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[106,x,k[0]]
F[104,x,k[0],k[1]] = F[103,x,k[0],k[1]]*F[19,x,k[1]]
F[104,x,k[0],k[1]] = F[105,x,k[0],k[1]]
F[105,x,k[0],k[1]] = F[88,x,k[0],k[1]]+F[92,x,k[0],k[1]]
F[107,x,k[0]] = F[106,x,k[0]]*F[43,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]+F[75,x,k[0]]
F[109,x,k[0]] = F[75,x,k[0]]+F[86,x,k[0]]
F[110,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[112,x,k[0],k[1]]
F[111,x,k[0],k[1]] = k[0]*k[1]*(F[96,x,k[0],k[1]]-F[96,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[112,x,k[0],k[1]] = F[113,x,k[0]*k[1]]+F[116,x,k[0],k[1]]
F[113,x,k[0]] = F[1,x]+F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[113,x,k[0]]*F[19,x,k[0]]
F[116,x,k[0],k[1]] = F[117,x,k[0]]+F[120,x,k[0],k[1]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[19,x,k[0]]
F[119,x,k[0]] = F[1,x]+F[117,x,k[0]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]+F[123,x,k[0],k[1]]+F[6,x]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]*F[19,x,k[0]]
F[122,x,k[0],k[1]] = F[114,x,k[0]*k[1]]+F[120,x,k[0],k[1]]
F[123,x,k[0],k[1]] = F[116,x,k[0],k[1]]*F[19,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[126,x,k[0],k[1]] = F[127,x,k[0],k[1]]*F[43,x]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]
F[128,x,k[0],k[1]] = F[11,x,k[0]]*F[43,x]*F[59,x,k[0],k[1]]
F[129,x,k[0]] = F[130,x,k[0],1]
F[130,x,k[0],k[1]] = k[0]*k[1]*(F[131,x,k[0],k[1]]-F[131,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[131,x,k[0],k[1]] = F[82,x,k[0],k[0]*k[1]]
F[132,x,k[0],k[1]] = F[133,x,k[0],k[1]]
F[133,x,k[0],k[1]] = F[11,x,k[0]]*F[24,x,k[0],k[1]]*F[43,x]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]*F[43,x]
F[135,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]*k[1]-F[24,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[22,x,k[0],k[1]] = F[136,x,k[0],k[0]*k[1]]
F[137,x] = F[138,x]*F[43,x]
F[138,x] = F[32,x,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_{43}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{137}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y , 1\right)
F_{13}\! \left(x , y , z\right) = -\frac{-F_{12}\! \left(x , y , z\right) z +F_{12}\! \left(x , y , 1\right)}{-1+z}
F_{14}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{136}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = F_{15}\! \left(x , y , y z \right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{134}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , y z \right)
F_{18}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , y z \right)
F_{21}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{23}\! \left(x , y , z\right) = F_{132}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y\right)+F_{96}\! \left(x , y , z\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y , 1\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{43}\! \left(x \right) = x
F_{44}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y , 1\right)
F_{50}\! \left(x , y , z\right) = F_{51}\! \left(x , y , z\right)+F_{84}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{52}\! \left(x , y , y z \right)
F_{52}\! \left(x , y , z\right) = F_{53}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)
F_{53}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)+F_{56}\! \left(x , y , z\right)
F_{54}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right) F_{53}\! \left(x , y , z\right)
F_{55}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{53}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{57}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{59}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y\right)+F_{64}\! \left(x , y , z\right)
F_{61}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{65}\! \left(x , y , z\right) = F_{64}\! \left(x , y , y z \right)
F_{66}\! \left(x , y , z\right) = F_{60}\! \left(x , y\right)+F_{65}\! \left(x , y , z\right)
F_{67}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{66}\! \left(x , y , z\right)
F_{67}\! \left(x , y , z\right) = F_{68}\! \left(x , y , z\right)
F_{68}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{69}\! \left(x , y , z\right)
F_{69}\! \left(x , y , z\right) = F_{50}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)
F_{70}\! \left(x , y , z\right) = F_{71}\! \left(x , y , y z \right)
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y\right)+F_{80}\! \left(x , y , z\right)
F_{28}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{80}\! \left(x , y , z\right) = F_{81}\! \left(x , y , z\right)
F_{81}\! \left(x , y , z\right) = -\frac{z \left(F_{82}\! \left(x , y , 1\right)-F_{82}\! \left(x , y , z\right)\right)}{-1+z}
F_{82}\! \left(x , y , z\right) = F_{83}\! \left(x , y , z\right)
F_{83}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{64}\! \left(x , y , z\right)
F_{84}\! \left(x , y , z\right) = F_{124}\! \left(x , y , z\right)+F_{85}\! \left(x , y , z\right)
F_{85}\! \left(x , y , z\right) = F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y , z\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{88}\! \left(x , y , z\right) = F_{89}\! \left(x , y , z\right)
F_{89}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{90}\! \left(x , y , z\right)
F_{90}\! \left(x , y , z\right) = F_{110}\! \left(x , y , z\right)+F_{91}\! \left(x , y , z\right)
F_{91}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{92}\! \left(x , y , z\right)
F_{92}\! \left(x , y , z\right) = F_{6}\! \left(x \right)+F_{93}\! \left(x , y , z\right)+F_{94}\! \left(x , y , z\right)+F_{95}\! \left(x , y , z\right)
F_{93}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right) F_{92}\! \left(x , y , z\right)
F_{94}\! \left(x , y , z\right) = F_{55}\! \left(x , y , y z \right)
F_{95}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{96}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{97}\! \left(x , y , z\right)
F_{97}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{98}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{103}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{106}\! \left(x , y\right)
F_{104}\! \left(x , y , z\right) = F_{103}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{104}\! \left(x , y , z\right) = F_{105}\! \left(x , y , z\right)
F_{105}\! \left(x , y , z\right) = F_{88}\! \left(x , y , z\right)+F_{92}\! \left(x , y , z\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{110}\! \left(x , y , z\right) = F_{111}\! \left(x , y , z\right) F_{112}\! \left(x , y , z\right)
F_{111}\! \left(x , y , z\right) = \frac{y z \left(F_{96}\! \left(x , y , z\right)-F_{96}\! \left(x , y , \frac{1}{y}\right)\right)}{y z -1}
F_{112}\! \left(x , y , z\right) = F_{113}\! \left(x , y z \right)+F_{116}\! \left(x , y , z\right)
F_{113}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{116}\! \left(x , y , z\right) = F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y , z\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)
F_{120}\! \left(x , y , z\right) = F_{121}\! \left(x , y , z\right)+F_{123}\! \left(x , y , z\right)+F_{6}\! \left(x \right)
F_{121}\! \left(x , y , z\right) = F_{122}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)
F_{122}\! \left(x , y , z\right) = F_{114}\! \left(x , y z \right)+F_{120}\! \left(x , y , z\right)
F_{123}\! \left(x , y , z\right) = F_{116}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{124}\! \left(x , y , z\right) = F_{125}\! \left(x , y , y z \right)
F_{125}\! \left(x , y , z\right) = F_{126}\! \left(x , y , z\right)
F_{126}\! \left(x , y , z\right) = F_{127}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{127}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right)
F_{128}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{59}\! \left(x , y , z\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y , 1\right)
F_{130}\! \left(x , y , z\right) = \frac{y z \left(F_{131}\! \left(x , y , z\right)-F_{131}\! \left(x , y , \frac{1}{y}\right)\right)}{y z -1}
F_{131}\! \left(x , y , z\right) = F_{82}\! \left(x , y , y z \right)
F_{132}\! \left(x , y , z\right) = F_{133}\! \left(x , y , z\right)
F_{133}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{24}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{134}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{135}\! \left(x , y , z\right) = \frac{y z F_{24}\! \left(x , y , z\right)-F_{24}\! \left(x , y , \frac{1}{y}\right)}{y z -1}
F_{22}\! \left(x , y , z\right) = F_{136}\! \left(x , y , y z \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{43}\! \left(x \right)
F_{138}\! \left(x \right) = F_{32}\! \left(x , 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_43(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_137(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_43(x)*F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_4(x)*F_43(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0, 1))
Eq(F_13(x, k_0, k_1), (-k_1*F_12(x, k_0, k_1) + F_12(x, k_0, 1))/(1 - k_1))
Eq(F_14(x, k_0, k_1), F_13(x, k_0, k_1)*F_43(x))
Eq(F_15(x, k_0, k_1), F_1(x) + F_136(x, k_0, k_1) + F_14(x, k_0, k_1) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_15(x, k_0, k_0*k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_134(x, k_0, k_1) + F_17(x, k_0, k_1) + F_20(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_0*k_1))
Eq(F_18(x, k_0, k_1), F_15(x, k_0, k_1)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_0*k_1))
Eq(F_21(x, k_0, k_1), F_15(x, k_0, k_1)*F_19(x, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_43(x))
Eq(F_23(x, k_0, k_1), F_132(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0) + F_96(x, k_0, k_1))
Eq(F_25(x, k_0), F_26(x, k_0) + F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_19(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_46(x, k_0))
Eq(F_30(x, k_0), F_19(x, k_0)*F_29(x, k_0))
Eq(F_30(x, k_0), 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_1(x) + F_33(x, k_0) + F_35(x, k_0) + F_44(x, k_0))
Eq(F_33(x, k_0), F_19(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0, 1))
Eq(F_35(x, k_0), F_36(x, k_0)*F_43(x))
Eq(F_36(x, k_0), F_32(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_43(x))
Eq(F_39(x, k_0), F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_4(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_42(x, k_0), F_11(x, k_0)*F_31(x, k_0))
Eq(F_43(x), x)
Eq(F_44(x, k_0), F_43(x)*F_45(x, k_0))
Eq(F_45(x, k_0), (-k_0*F_32(x, k_0) + F_32(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_129(x, k_0) + F_48(x, k_0))
Eq(F_49(x, k_0), F_48(x, k_0) + F_73(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0, 1))
Eq(F_50(x, k_0, k_1), F_51(x, k_0, k_1) + F_84(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_0*k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_1(x) + F_54(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_19(x, k_0)*F_53(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_19(x, k_1)*F_53(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_12(x, k_0, k_1)*F_43(x))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_43(x)*F_59(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_60(x, k_0) + F_64(x, k_0, k_1))
Eq(F_61(x, k_0), F_43(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_28(x, k_0)*F_43(x))
Eq(F_65(x, k_0, k_1), F_64(x, k_0, k_0*k_1))
Eq(F_66(x, k_0, k_1), F_60(x, k_0) + F_65(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_43(x)*F_66(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_68(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), F_43(x)*F_69(x, k_0, k_1))
Eq(F_69(x, k_0, k_1), F_50(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_71(x, k_0, k_0*k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0) + F_80(x, k_0, k_1))
Eq(F_28(x, k_0), F_72(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_78(x, k_0))
Eq(F_74(x, k_0), F_62(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_1(x) + F_76(x, k_0) + F_77(x, k_0))
Eq(F_76(x, k_0), F_19(x, k_0)*F_75(x, k_0))
Eq(F_77(x, k_0), F_25(x, k_0)*F_43(x))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_11(x, k_0)*F_43(x)*F_74(x, k_0))
Eq(F_80(x, k_0, k_1), F_81(x, k_0, k_1))
Eq(F_81(x, k_0, k_1), -F_82(x, k_0, 1) + (-k_1*F_82(x, k_0, k_1) + F_82(x, k_0, 1))/(1 - k_1))
Eq(F_82(x, k_0, k_1), F_83(x, k_0, k_1))
Eq(F_83(x, k_0, k_1), F_43(x)*F_64(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), F_124(x, k_0, k_1) + F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_86(x, k_0) + F_88(x, k_0, k_1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_11(x, k_0)*F_43(x)*F_75(x, k_0))
Eq(F_88(x, k_0, k_1), F_89(x, k_0, k_1))
Eq(F_89(x, k_0, k_1), F_43(x)*F_90(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_110(x, k_0, k_1) + F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_11(x, k_0)*F_92(x, k_0, k_1))
Eq(F_92(x, k_0, k_1), F_6(x) + F_93(x, k_0, k_1) + F_94(x, k_0, k_1) + F_95(x, k_0, k_1))
Eq(F_93(x, k_0, k_1), F_19(x, k_0)*F_92(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_55(x, k_0, k_0*k_1))
Eq(F_95(x, k_0, k_1), F_43(x)*F_96(x, k_0, k_1))
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_1)*F_98(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_102(x, k_0, k_1) + F_99(x, k_0))
Eq(F_100(x, k_0), F_43(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_25(x, k_0), F_101(x, k_0) + F_75(x, k_0))
Eq(F_103(x, k_0, k_1), F_102(x, k_0, k_1) + F_106(x, k_0))
Eq(F_104(x, k_0, k_1), F_103(x, k_0, k_1)*F_19(x, k_1))
Eq(F_104(x, k_0, k_1), F_105(x, k_0, k_1))
Eq(F_105(x, k_0, k_1), F_88(x, k_0, k_1) + F_92(x, k_0, k_1))
Eq(F_107(x, k_0), F_106(x, k_0)*F_43(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0) + F_75(x, k_0))
Eq(F_109(x, k_0), F_75(x, k_0) + F_86(x, k_0))
Eq(F_110(x, k_0, k_1), F_111(x, k_0, k_1)*F_112(x, k_0, k_1))
Eq(F_111(x, k_0, k_1), -F_96(x, k_0, 1/k_0) + (-k_0*k_1*F_96(x, k_0, k_1) + F_96(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0*k_1) + F_116(x, k_0, k_1))
Eq(F_113(x, k_0), F_1(x) + F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_113(x, k_0)*F_19(x, k_0))
Eq(F_116(x, k_0, k_1), F_117(x, k_0) + F_120(x, k_0, k_1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_19(x, k_0))
Eq(F_119(x, k_0), F_1(x) + F_117(x, k_0))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1) + F_123(x, k_0, k_1) + F_6(x))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1)*F_19(x, k_0))
Eq(F_122(x, k_0, k_1), F_114(x, k_0*k_1) + F_120(x, k_0, k_1))
Eq(F_123(x, k_0, k_1), F_116(x, k_0, k_1)*F_19(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))
Eq(F_126(x, k_0, k_1), F_127(x, k_0, k_1)*F_43(x))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1))
Eq(F_128(x, k_0, k_1), F_11(x, k_0)*F_43(x)*F_59(x, k_0, k_1))
Eq(F_129(x, k_0), F_130(x, k_0, 1))
Eq(F_130(x, k_0, k_1), -F_131(x, k_0, 1/k_0) + (-k_0*k_1*F_131(x, k_0, k_1) + F_131(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_131(x, k_0, k_1), F_82(x, k_0, k_0*k_1))
Eq(F_132(x, k_0, k_1), F_133(x, k_0, k_1))
Eq(F_133(x, k_0, k_1), F_11(x, k_0)*F_24(x, k_0, k_1)*F_43(x))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1)*F_43(x))
Eq(F_135(x, k_0, k_1), (-k_0*k_1*F_24(x, k_0, k_1) + F_24(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_22(x, k_0, k_1), F_136(x, k_0, k_0*k_1))
Eq(F_137(x), F_138(x)*F_43(x))
Eq(F_138(x), F_32(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "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}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": 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"comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 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], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25918/
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[65,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[65,x]*F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = F[4,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[295,x]*F[65,x]
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[16,x,k[0],1]
F[16,x,k[0],k[1]] = F[17,x,k[0]]+F[294,x,k[0],k[1]]
F[18,x,k[0]] = F[17,x,k[0]]*F[65,x]
F[18,x,k[0]] = F[19,x,k[0]]
F[20,x,k[0]] = F[19,x,k[0]]+F[292,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]+F[288,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[65,x]
F[25,x,k[0]] = F[26,x,k[0]]+F[283,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[34,x,k[0]]
F[27,x,k[0]] = F[23,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[32,x,k[0]] = F[28,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[65,x]
F[36,x,k[0]] = F[270,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[26,x,1]-F[26,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[63,x]*F[65,x]
F[41,x,k[0]] = -k[0]*(F[42,x,1]-F[42,x,k[0]])/(-1+k[0])
F[43,x,k[0]] = F[184,x]+F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[4,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[17,x,k[0]]*F[33,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0],1]
F[49,x,k[0],k[1]] = F[48,x,k[0],k[1]]*F[59,x,k[0]]
F[50,x,k[0],k[1]] = F[179,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[50,x,k[0],k[1]]*F[65,x]
F[51,x,k[0],k[1]] = F[52,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[52,x,k[0],k[1]]+F[68,x,k[0]]
F[54,x,k[0],k[1]] = F[53,x,k[0],k[1]]*F[87,x]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[175,x,k[0],k[1]]+F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[57,x,k[0]]+F[90,x,k[0],k[1]]
F[57,x,k[0]] = F[58,x,k[0]]+F[66,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]*F[62,x]
F[59,x,k[0]] = F[1,x]+F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]*F[59,x,k[0]]
F[62,x] = F[63,x]
F[63,x] = 1/F[65,x]*F[64,x]
F[64,x] = F[2,x]
F[65,x] = x
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[87,x]
F[68,x,k[0]] = F[69,x,k[0]]+F[71,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[44,x,k[0]]*F[59,x,k[0]]*F[65,x]
F[71,x,k[0]] = F[72,x,k[0]]*F[81,x]
F[72,x,k[0]] = F[73,x]+F[76,x,k[0]]
F[73,x] = F[74,x]
F[74,x] = F[65,x]*F[75,x]
F[75,x] = F[1,x]+F[73,x]
F[76,x,k[0]] = F[77,x]+F[78,x,k[0]]+F[79,x,k[0]]
F[77,x] = 0
F[78,x,k[0]] = F[33,x,k[0]]*F[72,x,k[0]]
F[79,x,k[0]] = F[65,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[60,x,k[0]]+F[76,x,k[0]]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[65,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[1,x]+F[82,x]
F[86,x] = F[82,x]
F[87,x] = F[1,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[65,x]*F[87,x]
F[90,x,k[0],k[1]] = F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[87,x]*F[92,x,k[0],k[1]]
F[92,x,k[0],k[1]] = F[157,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[154,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[95,x,k[0],k[1]]
F[95,x,k[0],k[1]] = F[33,x,k[1]]*F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[97,x,k[1],k[0]]
F[97,x,k[0],k[1]] = F[104,x,k[0],k[1]]+F[98,x,k[1]]
F[98,x,k[0]] = F[101,x,k[0]]+F[99,x,k[0]]
F[100,x,k[0]] = F[65,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[69,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[65,x]
F[103,x,k[0]] = F[96,x,k[0],1]
F[104,x,k[0],k[1]] = F[105,x,k[1],k[0]]
F[105,x,k[0],k[1]] = F[106,x,k[0],k[1]]+F[141,x,k[0],k[1]]
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]+F[94,x,k[0],k[1]]
F[107,x,k[0],k[1]] = F[108,x,k[1],k[0]]
F[108,x,k[0],k[1]] = F[109,x,k[0],k[1]]*F[65,x]
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1],1]
F[110,x,k[0],k[1],k[2]] = (F[111,x,k[0],k[1],k[2]]*k[2]-F[111,x,k[0],k[1],1])/(-1+k[2])
F[111,x,k[0],k[1],k[2]] = F[112,x,k[1],k[0],k[2]]
F[112,x,k[0],k[1],k[2]] = F[113,x,k[0],k[1]]+F[138,x,k[0],k[1],k[2]]
F[113,x,k[0],k[1]] = F[114,x,k[1],k[0]]
F[114,x,k[0],k[1]] = F[115,x,k[0],k[1]]+F[121,x,k[0],k[1]]
F[115,x,k[0],k[1]] = F[116,x,k[1],k[0]]
F[116,x,k[0],k[1]] = F[117,x,k[0],k[1]]+F[93,x,k[0],k[1]]
F[117,x,k[0],k[1]] = F[118,x,k[0],k[1]]
F[118,x,k[0],k[1]] = F[119,x,k[0],k[1]]*F[65,x]
F[119,x,k[0],k[1]] = F[113,x,k[0],k[1]]+F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = -k[1]*(F[117,x,k[0],1]-F[117,x,k[0],k[1]])/(-1+k[1])
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]
F[122,x,k[0],k[1]] = F[123,x,k[0],k[1]]*F[65,x]
F[123,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[125,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[115,x,k[0],k[1]]*F[43,x,k[1]]
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[128,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[127,x,k[1],k[0]]
F[127,x,k[0],k[1]] = -k[1]*(F[48,x,k[0],1]-F[48,x,k[0],k[1]])/(-1+k[1])
F[128,x,k[0],k[1]] = F[129,x,k[0]]+F[133,x,k[0],k[1]]
F[129,x,k[0]] = F[1,x]+F[130,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[129,x,k[0]]*F[132,x,k[0]]
F[132,x,k[0]] = k[0]*x
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]+F[60,x,k[1]]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]+F[137,x,k[0],k[1]]+F[77,x]
F[135,x,k[0],k[1]] = F[136,x,k[0],k[1]]*F[33,x,k[1]]
F[136,x,k[0],k[1]] = F[130,x,k[0]]+F[134,x,k[0],k[1]]
F[137,x,k[0],k[1]] = F[132,x,k[0]]*F[133,x,k[0],k[1]]
F[138,x,k[0],k[1],k[2]] = F[139,x,k[0],k[1],k[2]]
F[139,x,k[0],k[1],k[2]] = F[140,x,k[0],k[1],k[2]]*F[33,x,k[2]]
F[140,x,k[0],k[1],k[2]] = -k[1]*(F[112,x,k[0],1,k[2]]-F[112,x,k[0],k[1],k[2]])/(-1+k[1])
F[142,x,k[0],k[1]] = F[141,x,k[0],k[1]]+F[146,x,k[0]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]
F[143,x,k[0],k[1]] = F[144,x,k[0],k[1]]*F[33,x,k[0]]
F[145,x,k[0],k[1]] = F[144,x,k[0],k[1]]*F[33,x,k[1]]
F[145,x,k[0],k[1]] = F[106,x,k[0],k[1]]
F[146,x,k[0]] = F[147,x,k[0]]+F[150,x,k[0]]
F[99,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]+F[19,x,k[0]]
F[149,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[65,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[142,x,k[0],1]
F[154,x,k[0],k[1]] = F[155,x,k[0],k[1]]
F[155,x,k[0],k[1]] = F[156,x,k[0],k[1]]*F[65,x]
F[156,x,k[0],k[1]] = -k[1]*(F[94,x,k[0],1]-F[94,x,k[0],k[1]])/(-1+k[1])
F[157,x,k[0],k[1]] = F[158,x,k[0],k[1]]*F[81,x]
F[158,x,k[0],k[1]] = F[159,x,k[1]]+F[165,x,k[0],k[1]]
F[159,x,k[0]] = F[160,x,k[0]]+F[163,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]*F[33,x,k[0]]
F[162,x,k[0]] = F[1,x]+F[160,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[159,x,k[0]]*F[65,x]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[171,x,k[0],k[1]]
F[166,x,k[0],k[1]] = F[167,x,k[0],k[1]]+F[169,x,k[0],k[1]]+F[77,x]
F[167,x,k[0],k[1]] = F[168,x,k[0],k[1]]*F[33,x,k[0]]
F[168,x,k[0],k[1]] = F[160,x,k[1]]+F[166,x,k[0],k[1]]
F[169,x,k[0],k[1]] = F[170,x,k[0],k[1]]*F[33,x,k[1]]
F[170,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[60,x,k[0]]
F[171,x,k[0],k[1]] = 2*F[77,x]+F[172,x,k[0],k[1]]+F[174,x,k[0],k[1]]
F[172,x,k[0],k[1]] = F[173,x,k[0],k[1]]*F[33,x,k[0]]
F[173,x,k[0],k[1]] = F[163,x,k[1]]+F[171,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[165,x,k[0],k[1]]*F[65,x]
F[175,x,k[0],k[1]] = F[176,x,k[0],k[1]]+F[58,x,k[0]]
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[168,x,k[0],k[1]]*F[178,x]*F[87,x]
F[178,x] = F[1,x]+F[81,x]
F[179,x,k[0],k[1]] = F[168,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[182,x,k[0]]
F[181,x,k[0],k[1]] = F[44,x,k[0]]+F[48,x,k[0],k[1]]
F[182,x,k[0]] = F[183,x,k[0]]*F[81,x]
F[183,x,k[0]] = F[75,x]+F[80,x,k[0]]
F[184,x] = F[185,x]+F[4,x]
F[185,x] = F[186,x]
F[186,x] = F[187,x]*F[65,x]
F[187,x] = F[188,x]+F[192,x]
F[188,x] = F[189,x]
F[189,x] = 1/F[65,x]*F[190,x]
F[190,x] = F[191,x]
F[191,x] = -F[0,x]+F[63,x]
F[192,x] = F[193,x]
F[193,x] = F[194,x,1]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[65,x]
F[196,x,k[0]] = F[197,x,k[0]]+F[259,x]
F[197,x,k[0]] = F[198,x,k[0]]+F[255,x,k[0]]
F[198,x,k[0]] = F[194,x,k[0]]+F[199,x,k[0]]
F[199,x,k[0]] = F[200,x]+F[254,x,k[0]]
F[200,x] = F[201,x]+F[210,x]
F[201,x] = F[0,x]+F[202,x]
F[202,x] = F[2,x]+F[203,x]
F[203,x] = F[204,x]
F[204,x] = F[205,x]*F[65,x]
F[205,x] = F[206,x]+F[208,x]
F[206,x] = F[207,x]
F[207,x] = F[184,x]*F[62,x]*F[65,x]
F[208,x] = F[209,x]
F[209,x] = F[187,x]*F[65,x]
F[210,x] = F[211,x]+F[252,x]
F[211,x] = F[212,x,1]
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[214,x,k[0]]*F[33,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0],1]
F[215,x,k[0],k[1]] = F[216,x,k[0],k[0]*k[1]]
F[216,x,k[0],k[1]] = F[217,x,k[0],k[1]]+F[230,x,k[0],k[1]]
F[217,x,k[0],k[1]] = F[218,x,k[0]]+F[226,x,k[0],k[1]]
F[218,x,k[0]] = F[219,x,k[0]]+F[59,x,k[0]]
F[219,x,k[0]] = F[2,x]+F[220,x,k[0]]
F[220,x,k[0]] = F[221,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]*F[33,x,k[0]]
F[222,x,k[0]] = F[219,x,k[0]]+F[223,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]
F[224,x,k[0]] = F[218,x,k[0]]*F[225,x]*F[65,x]
F[225,x] = F[184,x]
F[226,x,k[0],k[1]] = F[227,x,k[0],k[1]]
F[227,x,k[0],k[1]] = F[228,x,k[0],k[1]]*F[33,x,k[1]]
F[228,x,k[0],k[1]] = (-F[229,x,1,k[1]]*k[1]+F[229,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[229,x,k[0],k[1]] = F[216,x,k[0]*k[1],k[1]]
F[230,x,k[0],k[1]] = F[231,x,k[1]]+F[247,x,k[0],k[1]]
F[231,x,k[0]] = F[202,x]+F[232,x,k[0]]
F[232,x,k[0]] = F[233,x,k[0],1]
F[233,x,k[0],k[1]] = F[234,x,k[0],k[1]]
F[234,x,k[0],k[1]] = F[235,x,k[0],k[1]]*F[33,x,k[1]]
F[235,x,k[0],k[1]] = F[236,x,k[0]]+F[246,x,k[0],k[1]]
F[236,x,k[0]] = F[212,x,k[0]]+F[237,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]*F[33,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[244,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]+F[242,x,k[0]]
F[241,x,k[0]] = F[191,x]+F[237,x,k[0]]
F[242,x,k[0]] = F[243,x,k[0]]
F[243,x,k[0]] = F[225,x]*F[241,x,k[0]]*F[65,x]
F[244,x,k[0]] = F[241,x,k[0]]+F[245,x,k[0]]
F[245,x,k[0]] = (F[232,x,k[0]]-F[232,x,1])/(-1+k[0])
F[246,x,k[0],k[1]] = -k[0]*(F[233,x,1,k[1]]-F[233,x,k[0],k[1]])/(-1+k[0])
F[247,x,k[0],k[1]] = F[248,x,k[0],k[1]]
F[248,x,k[0],k[1]] = F[249,x,k[0],k[1]]*F[33,x,k[0]]
F[249,x,k[0],k[1]] = F[230,x,k[0],k[1]]+F[250,x,k[0],k[1]]
F[250,x,k[0],k[1]] = F[251,x,k[0],k[1]]
F[251,x,k[0],k[1]] = F[225,x]*F[230,x,k[0],k[1]]*F[65,x]
F[252,x] = F[253,x]
F[253,x] = F[211,x]*F[225,x]*F[65,x]
F[254,x,k[0]] = F[212,x,k[0]]+F[232,x,k[0]]
F[255,x,k[0]] = F[256,x,k[0],1]
F[256,x,k[0],k[1]] = (F[257,x,k[0],k[1]]*k[1]-F[257,x,k[0],1])/(-1+k[1])
F[257,x,k[0],k[1]] = F[241,x,k[0]]+F[258,x,k[0],k[1]]
F[258,x,k[0],k[1]] = (F[233,x,k[0],k[1]]-F[233,x,1,k[1]])/(-1+k[0])
F[259,x] = F[260,x]+F[261,x]
F[260,x] = F[240,x,1]
F[261,x] = F[262,x,1]
F[262,x,k[0]] = (F[263,x,k[0]]-F[263,x,1])/(-1+k[0])
F[263,x,k[0]] = F[264,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]*F[65,x]
F[265,x,k[0]] = F[266,x,k[0]]+F[269,x,k[0]]
F[266,x,k[0]] = F[236,x,k[0]]+F[267,x,k[0]]
F[267,x,k[0]] = F[268,x,k[0]]
F[268,x,k[0]] = F[225,x]*F[236,x,k[0]]*F[65,x]
F[269,x,k[0]] = -k[0]*(-F[263,x,k[0]]+F[263,x,1])/(-1+k[0])
F[270,x,k[0]] = F[271,x,k[0]]
F[271,x,k[0]] = F[272,x,k[0]]*F[33,x,k[0]]
F[272,x,k[0]] = F[273,x,k[0],1]
F[273,x,k[0],k[1]] = F[274,x,k[0],k[0]*k[1]]
F[274,x,k[0],k[1]] = F[275,x,k[0],k[1]]
F[275,x,k[0],k[1]] = F[276,x,k[0],k[1]]+F[280,x,k[0],k[1]]
F[276,x,k[0],k[1]] = F[277,x,k[1],k[0]]
F[277,x,k[0],k[1]] = F[278,x,k[0],k[1]]*F[43,x,k[1]]
F[278,x,k[0],k[1]] = F[279,x,k[1],k[0]]
F[279,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[148,x,k[0]]
F[280,x,k[0],k[1]] = F[281,x,k[0],k[1]]
F[281,x,k[0],k[1]] = F[127,x,k[0],k[1]]*F[282,x,k[0],k[1]]
F[282,x,k[0],k[1]] = F[162,x,k[1]]+F[170,x,k[0],k[1]]
F[283,x,k[0]] = F[284,x,k[0]]
F[284,x,k[0]] = F[285,x,k[0]]*F[31,x,k[0]]*F[33,x,k[0]]*F[59,x,k[0]]
F[285,x,k[0]] = F[286,x,k[0]]+F[44,x,k[0]]
F[286,x,k[0]] = F[287,x,k[0],1]
F[287,x,k[0],k[1]] = F[48,x,k[0],k[0]*k[1]]
F[288,x,k[0]] = F[289,x,k[0],1]
F[289,x,k[0],k[1]] = F[290,x,k[0],k[0]*k[1]]
F[290,x,k[0],k[1]] = F[291,x,k[0],k[1]]
F[291,x,k[0],k[1]] = F[181,x,k[0],k[1]]*F[282,x,k[0],k[1]]*F[65,x]
F[292,x,k[0]] = F[293,x,k[0],1]
F[293,x,k[0],k[1]] = F[117,x,k[0],k[0]*k[1]]
F[294,x,k[0],k[1]] = F[119,x,k[0],k[1]]
F[295,x] = F[0,x]+F[2,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_{65}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{65}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{295}\! \left(x \right) F_{65}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}, 1\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}\right)+F_{294}\! \left(x , y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)+F_{292}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{288}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\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_{25}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)+F_{283}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{34}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{23}\! \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_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{28}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = y_{0} x
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{36}\! \left(x , y_{0}\right) = F_{270}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{26}\! \left(x , 1\right)-F_{26}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}\right) = F_{40}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right) F_{63}\! \left(x \right) F_{65}\! \left(x \right)
F_{41}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{42}\! \left(x , 1\right)-F_{42}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{43}\! \left(x , y_{0}\right) = F_{184}\! \left(x \right)+F_{42}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{44}\! \left(x , y_{0}\right)+F_{47}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right)+F_{45}\! \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_{17}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}, 1\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{1}\right) F_{59}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{179}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{50}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{51}\! \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_{52}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right) F_{87}\! \left(x \right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{0}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right) F_{62}\! \left(x \right)
F_{59}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)
F_{65}\! \left(x \right) = x
F_{66}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right) F_{87}\! \left(x \right)
F_{68}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{44}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}\right) F_{81}\! \left(x \right)
F_{72}\! \left(x , y_{0}\right) = F_{73}\! \left(x \right)+F_{76}\! \left(x , y_{0}\right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x , y_{0}\right) = F_{77}\! \left(x \right)+F_{78}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)
F_{77}\! \left(x \right) = 0
F_{78}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right) F_{72}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{65}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{65}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{82}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{65}\! \left(x \right) F_{87}\! \left(x \right)
F_{90}\! \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_{87}\! \left(x \right) F_{92}\! \left(x , y_{0}, y_{1}\right)
F_{92}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{154}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{95}\! \left(x , y_{0}, y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{1}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = F_{97}\! \left(x , y_{1}, y_{0}\right)
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{104}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{1}\right)
F_{98}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{99}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{65}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\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_{65}\! \left(x \right)
F_{103}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}, 1\right)
F_{104}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , y_{1}, y_{0}\right)
F_{105}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)+F_{141}\! \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_{94}\! \left(x , y_{0}, y_{1}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{1}, y_{0}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = F_{109}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0}, y_{1}, 1\right)
F_{110}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{111}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{112}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right)+F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{1}, y_{0}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{0}, y_{1}\right)+F_{121}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{1}, y_{0}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{117}\! \left(x , y_{0}, y_{1}\right) = F_{118}\! \left(x , y_{0}, y_{1}\right)
F_{118}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \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) = -\frac{y_{1} \left(F_{117}\! \left(x , y_{0}, 1\right)-F_{117}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \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_{65}\! \left(x \right)
F_{123}\! \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_{124}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{0}, y_{1}\right) F_{43}\! \left(x , y_{1}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{128}\! \left(x , y_{0}, y_{1}\right)
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{1}, y_{0}\right)
F_{127}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{48}\! \left(x , y_{0}, 1\right)-F_{48}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{128}\! \left(x , y_{0}, y_{1}\right) = F_{129}\! \left(x , y_{0}\right)+F_{133}\! \left(x , y_{0}, y_{1}\right)
F_{129}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{130}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , y_{0}\right)
F_{131}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right) F_{132}\! \left(x , y_{0}\right)
F_{132}\! \left(x , y_{0}\right) = y_{0} x
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{1}\right)
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{135}\! \left(x , y_{0}, y_{1}\right)+F_{137}\! \left(x , y_{0}, y_{1}\right)+F_{77}\! \left(x \right)
F_{135}\! \left(x , y_{0}, y_{1}\right) = F_{136}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}\right)+F_{134}\! \left(x , y_{0}, y_{1}\right)
F_{137}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{0}\right) F_{133}\! \left(x , y_{0}, y_{1}\right)
F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{33}\! \left(x , y_{2}\right)
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} \left(F_{112}\! \left(x , y_{0}, 1, y_{2}\right)-F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{1}}
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{146}\! \left(x , y_{0}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = F_{143}\! \left(x , y_{0}, y_{1}\right)
F_{143}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{144}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)
F_{146}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{148}\! \left(x , y_{0}\right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{149}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{151}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)
F_{153}\! \left(x , y_{0}\right) = F_{142}\! \left(x , y_{0}, 1\right)
F_{154}\! \left(x , y_{0}, y_{1}\right) = F_{155}\! \left(x , y_{0}, y_{1}\right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{156}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{94}\! \left(x , y_{0}, 1\right)-F_{94}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{157}\! \left(x , y_{0}, y_{1}\right) = F_{158}\! \left(x , y_{0}, y_{1}\right) F_{81}\! \left(x \right)
F_{158}\! \left(x , y_{0}, y_{1}\right) = F_{159}\! \left(x , y_{1}\right)+F_{165}\! \left(x , y_{0}, y_{1}\right)
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{163}\! \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 , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x , y_{0}\right)
F_{163}\! \left(x , y_{0}\right) = F_{164}\! \left(x , y_{0}\right)
F_{164}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{165}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{166}\! \left(x , y_{0}, y_{1}\right) = F_{167}\! \left(x , y_{0}, y_{1}\right)+F_{169}\! \left(x , y_{0}, y_{1}\right)+F_{77}\! \left(x \right)
F_{167}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{168}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , y_{1}\right)+F_{166}\! \left(x , y_{0}, y_{1}\right)
F_{169}\! \left(x , y_{0}, y_{1}\right) = F_{170}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = F_{166}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}\right)
F_{171}\! \left(x , y_{0}, y_{1}\right) = 2 F_{77}\! \left(x \right)+F_{172}\! \left(x , y_{0}, y_{1}\right)+F_{174}\! \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_{33}\! \left(x , y_{0}\right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{163}\! \left(x , y_{1}\right)+F_{171}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{165}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = F_{176}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}\right)
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \left(x , y_{0}, y_{1}\right) F_{178}\! \left(x \right) F_{87}\! \left(x \right)
F_{178}\! \left(x \right) = F_{1}\! \left(x \right)+F_{81}\! \left(x \right)
F_{179}\! \left(x , y_{0}, y_{1}\right) = F_{168}\! \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_{182}\! \left(x , y_{0}\right)
F_{181}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)
F_{182}\! \left(x , y_{0}\right) = F_{183}\! \left(x , y_{0}\right) F_{81}\! \left(x \right)
F_{183}\! \left(x , y_{0}\right) = F_{75}\! \left(x \right)+F_{80}\! \left(x , y_{0}\right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{4}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{65}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{192}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = \frac{F_{190}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{63}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{194}\! \left(x , y_{0}\right) = F_{195}\! \left(x , y_{0}\right)
F_{195}\! \left(x , y_{0}\right) = F_{196}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{196}\! \left(x , y_{0}\right) = F_{197}\! \left(x , y_{0}\right)+F_{259}\! \left(x \right)
F_{197}\! \left(x , y_{0}\right) = F_{198}\! \left(x , y_{0}\right)+F_{255}\! \left(x , y_{0}\right)
F_{198}\! \left(x , y_{0}\right) = F_{194}\! \left(x , y_{0}\right)+F_{199}\! \left(x , y_{0}\right)
F_{199}\! \left(x , y_{0}\right) = F_{200}\! \left(x \right)+F_{254}\! \left(x , y_{0}\right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{210}\! \left(x \right)
F_{201}\! \left(x \right) = F_{0}\! \left(x \right)+F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{2}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{65}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{208}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{184}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{187}\! \left(x \right) F_{65}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{252}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x , 1\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_{33}\! \left(x , y_{0}\right)
F_{214}\! \left(x , y_{0}\right) = F_{215}\! \left(x , y_{0}, 1\right)
F_{215}\! \left(x , y_{0}, y_{1}\right) = F_{216}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{216}\! \left(x , y_{0}, y_{1}\right) = F_{217}\! \left(x , y_{0}, y_{1}\right)+F_{230}\! \left(x , y_{0}, y_{1}\right)
F_{217}\! \left(x , y_{0}, y_{1}\right) = F_{218}\! \left(x , y_{0}\right)+F_{226}\! \left(x , y_{0}, y_{1}\right)
F_{218}\! \left(x , y_{0}\right) = F_{219}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{219}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{220}\! \left(x , y_{0}\right)
F_{220}\! \left(x , y_{0}\right) = F_{221}\! \left(x , y_{0}\right)
F_{221}\! \left(x , y_{0}\right) = F_{222}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{222}\! \left(x , y_{0}\right) = F_{219}\! \left(x , y_{0}\right)+F_{223}\! \left(x , y_{0}\right)
F_{223}\! \left(x , y_{0}\right) = F_{224}\! \left(x , y_{0}\right)
F_{224}\! \left(x , y_{0}\right) = F_{218}\! \left(x , y_{0}\right) F_{225}\! \left(x \right) F_{65}\! \left(x \right)
F_{225}\! \left(x \right) = F_{184}\! \left(x \right)
F_{226}\! \left(x , y_{0}, y_{1}\right) = F_{227}\! \left(x , y_{0}, y_{1}\right)
F_{227}\! \left(x , y_{0}, y_{1}\right) = F_{228}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{228}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{229}\! \left(x , 1, y_{1}\right) y_{1}-F_{229}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{229}\! \left(x , y_{0}, y_{1}\right) = F_{216}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{230}\! \left(x , y_{0}, y_{1}\right) = F_{231}\! \left(x , y_{1}\right)+F_{247}\! \left(x , y_{0}, y_{1}\right)
F_{231}\! \left(x , y_{0}\right) = F_{202}\! \left(x \right)+F_{232}\! \left(x , y_{0}\right)
F_{232}\! \left(x , y_{0}\right) = F_{233}\! \left(x , y_{0}, 1\right)
F_{233}\! \left(x , y_{0}, y_{1}\right) = F_{234}\! \left(x , y_{0}, y_{1}\right)
F_{234}\! \left(x , y_{0}, y_{1}\right) = F_{235}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{1}\right)
F_{235}\! \left(x , y_{0}, y_{1}\right) = F_{236}\! \left(x , y_{0}\right)+F_{246}\! \left(x , y_{0}, y_{1}\right)
F_{236}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)+F_{237}\! \left(x , y_{0}\right)
F_{237}\! \left(x , y_{0}\right) = F_{238}\! \left(x , y_{0}\right)
F_{238}\! \left(x , y_{0}\right) = F_{239}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{239}\! \left(x , y_{0}\right) = F_{240}\! \left(x , y_{0}\right)+F_{244}\! \left(x , y_{0}\right)
F_{240}\! \left(x , y_{0}\right) = F_{241}\! \left(x , y_{0}\right)+F_{242}\! \left(x , y_{0}\right)
F_{241}\! \left(x , y_{0}\right) = F_{191}\! \left(x \right)+F_{237}\! \left(x , y_{0}\right)
F_{242}\! \left(x , y_{0}\right) = F_{243}\! \left(x , y_{0}\right)
F_{243}\! \left(x , y_{0}\right) = F_{225}\! \left(x \right) F_{241}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{244}\! \left(x , y_{0}\right) = F_{241}\! \left(x , y_{0}\right)+F_{245}\! \left(x , y_{0}\right)
F_{245}\! \left(x , y_{0}\right) = -\frac{-F_{232}\! \left(x , y_{0}\right)+F_{232}\! \left(x , 1\right)}{-1+y_{0}}
F_{246}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{233}\! \left(x , 1, y_{1}\right)-F_{233}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{247}\! \left(x , y_{0}, y_{1}\right) = F_{248}\! \left(x , y_{0}, y_{1}\right)
F_{248}\! \left(x , y_{0}, y_{1}\right) = F_{249}\! \left(x , y_{0}, y_{1}\right) F_{33}\! \left(x , y_{0}\right)
F_{249}\! \left(x , y_{0}, y_{1}\right) = F_{230}\! \left(x , y_{0}, y_{1}\right)+F_{250}\! \left(x , y_{0}, y_{1}\right)
F_{250}\! \left(x , y_{0}, y_{1}\right) = F_{251}\! \left(x , y_{0}, y_{1}\right)
F_{251}\! \left(x , y_{0}, y_{1}\right) = F_{225}\! \left(x \right) F_{230}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{211}\! \left(x \right) F_{225}\! \left(x \right) F_{65}\! \left(x \right)
F_{254}\! \left(x , y_{0}\right) = F_{212}\! \left(x , y_{0}\right)+F_{232}\! \left(x , y_{0}\right)
F_{255}\! \left(x , y_{0}\right) = F_{256}\! \left(x , y_{0}, 1\right)
F_{256}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{257}\! \left(x , y_{0}, y_{1}\right)+F_{257}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{257}\! \left(x , y_{0}, y_{1}\right) = F_{241}\! \left(x , y_{0}\right)+F_{258}\! \left(x , y_{0}, y_{1}\right)
F_{258}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{233}\! \left(x , 1, y_{1}\right)-F_{233}\! \left(x , y_{0}, y_{1}\right)}{-1+y_{0}}
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)+F_{261}\! \left(x \right)
F_{260}\! \left(x \right) = F_{240}\! \left(x , 1\right)
F_{261}\! \left(x \right) = F_{262}\! \left(x , 1\right)
F_{262}\! \left(x , y_{0}\right) = -\frac{-F_{263}\! \left(x , y_{0}\right)+F_{263}\! \left(x , 1\right)}{-1+y_{0}}
F_{263}\! \left(x , y_{0}\right) = F_{264}\! \left(x , y_{0}\right)
F_{264}\! \left(x , y_{0}\right) = F_{265}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{265}\! \left(x , y_{0}\right) = F_{266}\! \left(x , y_{0}\right)+F_{269}\! \left(x , y_{0}\right)
F_{266}\! \left(x , y_{0}\right) = F_{236}\! \left(x , y_{0}\right)+F_{267}\! \left(x , y_{0}\right)
F_{267}\! \left(x , y_{0}\right) = F_{268}\! \left(x , y_{0}\right)
F_{268}\! \left(x , y_{0}\right) = F_{225}\! \left(x \right) F_{236}\! \left(x , y_{0}\right) F_{65}\! \left(x \right)
F_{269}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(-F_{263}\! \left(x , y_{0}\right)+F_{263}\! \left(x , 1\right)\right)}{-1+y_{0}}
F_{270}\! \left(x , y_{0}\right) = F_{271}\! \left(x , y_{0}\right)
F_{271}\! \left(x , y_{0}\right) = F_{272}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right)
F_{272}\! \left(x , y_{0}\right) = F_{273}\! \left(x , y_{0}, 1\right)
F_{273}\! \left(x , y_{0}, y_{1}\right) = F_{274}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{274}\! \left(x , y_{0}, y_{1}\right) = F_{275}\! \left(x , y_{0}, y_{1}\right)
F_{275}\! \left(x , y_{0}, y_{1}\right) = F_{276}\! \left(x , y_{0}, y_{1}\right)+F_{280}\! \left(x , y_{0}, y_{1}\right)
F_{276}\! \left(x , y_{0}, y_{1}\right) = F_{277}\! \left(x , y_{1}, y_{0}\right)
F_{277}\! \left(x , y_{0}, y_{1}\right) = F_{278}\! \left(x , y_{0}, y_{1}\right) F_{43}\! \left(x , y_{1}\right)
F_{278}\! \left(x , y_{0}, y_{1}\right) = F_{279}\! \left(x , y_{1}, y_{0}\right)
F_{279}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)+F_{148}\! \left(x , y_{0}\right)
F_{280}\! \left(x , y_{0}, y_{1}\right) = F_{281}\! \left(x , y_{0}, y_{1}\right)
F_{281}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{0}, y_{1}\right) F_{282}\! \left(x , y_{0}, y_{1}\right)
F_{282}\! \left(x , y_{0}, y_{1}\right) = F_{162}\! \left(x , y_{1}\right)+F_{170}\! \left(x , y_{0}, y_{1}\right)
F_{283}\! \left(x , y_{0}\right) = F_{284}\! \left(x , y_{0}\right)
F_{284}\! \left(x , y_{0}\right) = F_{285}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{0}\right)
F_{285}\! \left(x , y_{0}\right) = F_{286}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{286}\! \left(x , y_{0}\right) = F_{287}\! \left(x , y_{0}, 1\right)
F_{287}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{288}\! \left(x , y_{0}\right) = F_{289}\! \left(x , y_{0}, 1\right)
F_{289}\! \left(x , y_{0}, y_{1}\right) = F_{290}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{290}\! \left(x , y_{0}, y_{1}\right) = F_{291}\! \left(x , y_{0}, y_{1}\right)
F_{291}\! \left(x , y_{0}, y_{1}\right) = F_{181}\! \left(x , y_{0}, y_{1}\right) F_{282}\! \left(x , y_{0}, y_{1}\right) F_{65}\! \left(x \right)
F_{292}\! \left(x , y_{0}\right) = F_{293}\! \left(x , y_{0}, 1\right)
F_{293}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{294}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right)
F_{295}\! \left(x \right) = F_{0}\! \left(x \right)+F_{2}\! \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_65(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_65(x)*F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_4(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_295(x)*F_65(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_16(x, k_0, 1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0) + F_294(x, k_0, k_1))
Eq(F_18(x, k_0), F_17(x, k_0)*F_65(x))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_20(x, k_0), F_19(x, k_0) + F_292(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0) + F_288(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_65(x))
Eq(F_25(x, k_0), F_26(x, k_0) + F_283(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_34(x, k_0))
Eq(F_27(x, k_0), F_23(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_33(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_32(x, k_0), F_28(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_65(x))
Eq(F_36(x, k_0), F_270(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), -F_26(x, 1) + (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_63(x)*F_65(x))
Eq(F_41(x, k_0), -F_42(x, 1) + (-k_0*F_42(x, k_0) + F_42(x, 1))/(1 - k_0))
Eq(F_43(x, k_0), F_184(x) + F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_4(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_17(x, k_0)*F_33(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0, 1))
Eq(F_49(x, k_0, k_1), F_48(x, k_0, k_1)*F_59(x, k_0))
Eq(F_50(x, k_0, k_1), F_179(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_50(x, k_0, k_1)*F_65(x))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_52(x, k_0, k_1) + F_68(x, k_0))
Eq(F_54(x, k_0, k_1), F_53(x, k_0, k_1)*F_87(x))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_175(x, k_0, k_1) + F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0) + F_90(x, k_0, k_1))
Eq(F_57(x, k_0), F_58(x, k_0) + F_66(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0)*F_62(x))
Eq(F_59(x, k_0), F_1(x) + F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0)*F_59(x, k_0))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)/F_65(x))
Eq(F_64(x), F_2(x))
Eq(F_65(x), x)
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_87(x))
Eq(F_68(x, k_0), F_69(x, k_0) + F_71(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_44(x, k_0)*F_59(x, k_0)*F_65(x))
Eq(F_71(x, k_0), F_72(x, k_0)*F_81(x))
Eq(F_72(x, k_0), F_73(x) + F_76(x, k_0))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_65(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_73(x))
Eq(F_76(x, k_0), F_77(x) + F_78(x, k_0) + F_79(x, k_0))
Eq(F_77(x), 0)
Eq(F_78(x, k_0), F_33(x, k_0)*F_72(x, k_0))
Eq(F_79(x, k_0), F_65(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_60(x, k_0) + F_76(x, k_0))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_65(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_1(x) + F_82(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_1(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_65(x)*F_87(x))
Eq(F_90(x, k_0, k_1), F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_87(x)*F_92(x, k_0, k_1))
Eq(F_92(x, k_0, k_1), F_157(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_154(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_95(x, k_0, k_1))
Eq(F_95(x, k_0, k_1), F_33(x, k_1)*F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_97(x, k_1, k_0))
Eq(F_97(x, k_0, k_1), F_104(x, k_0, k_1) + F_98(x, k_1))
Eq(F_98(x, k_0), F_101(x, k_0) + F_99(x, k_0))
Eq(F_100(x, k_0), F_65(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_69(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_65(x))
Eq(F_103(x, k_0), F_96(x, k_0, 1))
Eq(F_104(x, k_0, k_1), F_105(x, k_1, k_0))
Eq(F_105(x, k_0, k_1), F_106(x, k_0, k_1) + F_141(x, k_0, k_1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1) + F_94(x, k_0, k_1))
Eq(F_107(x, k_0, k_1), F_108(x, k_1, k_0))
Eq(F_108(x, k_0, k_1), F_109(x, k_0, k_1)*F_65(x))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1, 1))
Eq(F_110(x, k_0, k_1, k_2), (-k_2*F_111(x, k_0, k_1, k_2) + F_111(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_111(x, k_0, k_1, k_2), F_112(x, k_1, k_0, k_2))
Eq(F_112(x, k_0, k_1, k_2), F_113(x, k_0, k_1) + F_138(x, k_0, k_1, k_2))
Eq(F_113(x, k_0, k_1), F_114(x, k_1, k_0))
Eq(F_114(x, k_0, k_1), F_115(x, k_0, k_1) + F_121(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), F_116(x, k_1, k_0))
Eq(F_116(x, k_0, k_1), F_117(x, k_0, k_1) + F_93(x, k_0, k_1))
Eq(F_117(x, k_0, k_1), F_118(x, k_0, k_1))
Eq(F_118(x, k_0, k_1), F_119(x, k_0, k_1)*F_65(x))
Eq(F_119(x, k_0, k_1), F_113(x, k_0, k_1) + F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), -F_117(x, k_0, 1) + (-k_1*F_117(x, k_0, k_1) + F_117(x, k_0, 1))/(1 - k_1))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1))
Eq(F_122(x, k_0, k_1), F_123(x, k_0, k_1)*F_65(x))
Eq(F_123(x, k_0, k_1), F_124(x, k_0, k_1) + F_125(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_115(x, k_0, k_1)*F_43(x, k_1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1)*F_128(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_127(x, k_1, k_0))
Eq(F_127(x, k_0, k_1), -F_48(x, k_0, 1) + (-k_1*F_48(x, k_0, k_1) + F_48(x, k_0, 1))/(1 - k_1))
Eq(F_128(x, k_0, k_1), F_129(x, k_0) + F_133(x, k_0, k_1))
Eq(F_129(x, k_0), F_1(x) + F_130(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_129(x, k_0)*F_132(x, k_0))
Eq(F_132(x, k_0), k_0*x)
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1) + F_60(x, k_1))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1) + F_137(x, k_0, k_1) + F_77(x))
Eq(F_135(x, k_0, k_1), F_136(x, k_0, k_1)*F_33(x, k_1))
Eq(F_136(x, k_0, k_1), F_130(x, k_0) + F_134(x, k_0, k_1))
Eq(F_137(x, k_0, k_1), F_132(x, k_0)*F_133(x, k_0, k_1))
Eq(F_138(x, k_0, k_1, k_2), F_139(x, k_0, k_1, k_2))
Eq(F_139(x, k_0, k_1, k_2), F_140(x, k_0, k_1, k_2)*F_33(x, k_2))
Eq(F_140(x, k_0, k_1, k_2), -F_112(x, k_0, 1, k_2) + (-k_1*F_112(x, k_0, k_1, k_2) + F_112(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_142(x, k_0, k_1), F_141(x, k_0, k_1) + F_146(x, k_0))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1))
Eq(F_143(x, k_0, k_1), F_144(x, k_0, k_1)*F_33(x, k_0))
Eq(F_145(x, k_0, k_1), F_144(x, k_0, k_1)*F_33(x, k_1))
Eq(F_145(x, k_0, k_1), F_106(x, k_0, k_1))
Eq(F_146(x, k_0), F_147(x, k_0) + F_150(x, k_0))
Eq(F_99(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0) + F_19(x, k_0))
Eq(F_149(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0)*F_65(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_142(x, k_0, 1))
Eq(F_154(x, k_0, k_1), F_155(x, k_0, k_1))
Eq(F_155(x, k_0, k_1), F_156(x, k_0, k_1)*F_65(x))
Eq(F_156(x, k_0, k_1), -F_94(x, k_0, 1) + (-k_1*F_94(x, k_0, k_1) + F_94(x, k_0, 1))/(1 - k_1))
Eq(F_157(x, k_0, k_1), F_158(x, k_0, k_1)*F_81(x))
Eq(F_158(x, k_0, k_1), F_159(x, k_1) + F_165(x, k_0, k_1))
Eq(F_159(x, k_0), F_160(x, k_0) + F_163(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0)*F_33(x, k_0))
Eq(F_162(x, k_0), F_1(x) + F_160(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_159(x, k_0)*F_65(x))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1) + F_171(x, k_0, k_1))
Eq(F_166(x, k_0, k_1), F_167(x, k_0, k_1) + F_169(x, k_0, k_1) + F_77(x))
Eq(F_167(x, k_0, k_1), F_168(x, k_0, k_1)*F_33(x, k_0))
Eq(F_168(x, k_0, k_1), F_160(x, k_1) + F_166(x, k_0, k_1))
Eq(F_169(x, k_0, k_1), F_170(x, k_0, k_1)*F_33(x, k_1))
Eq(F_170(x, k_0, k_1), F_166(x, k_0, k_1) + F_60(x, k_0))
Eq(F_171(x, k_0, k_1), F_172(x, k_0, k_1) + F_174(x, k_0, k_1) + 2*F_77(x))
Eq(F_172(x, k_0, k_1), F_173(x, k_0, k_1)*F_33(x, k_0))
Eq(F_173(x, k_0, k_1), F_163(x, k_1) + F_171(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_165(x, k_0, k_1)*F_65(x))
Eq(F_175(x, k_0, k_1), F_176(x, k_0, k_1) + F_58(x, k_0))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1))
Eq(F_177(x, k_0, k_1), F_168(x, k_0, k_1)*F_178(x)*F_87(x))
Eq(F_178(x), F_1(x) + F_81(x))
Eq(F_179(x, k_0, k_1), F_168(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_182(x, k_0))
Eq(F_181(x, k_0, k_1), F_44(x, k_0) + F_48(x, k_0, k_1))
Eq(F_182(x, k_0), F_183(x, k_0)*F_81(x))
Eq(F_183(x, k_0), F_75(x) + F_80(x, k_0))
Eq(F_184(x), F_185(x) + F_4(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_187(x)*F_65(x))
Eq(F_187(x), F_188(x) + F_192(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)/F_65(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), -F_0(x) + F_63(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_194(x, 1))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_65(x))
Eq(F_196(x, k_0), F_197(x, k_0) + F_259(x))
Eq(F_197(x, k_0), F_198(x, k_0) + F_255(x, k_0))
Eq(F_198(x, k_0), F_194(x, k_0) + F_199(x, k_0))
Eq(F_199(x, k_0), F_200(x) + F_254(x, k_0))
Eq(F_200(x), F_201(x) + F_210(x))
Eq(F_201(x), F_0(x) + F_202(x))
Eq(F_202(x), F_2(x) + F_203(x))
Eq(F_203(x), F_204(x))
Eq(F_204(x), F_205(x)*F_65(x))
Eq(F_205(x), F_206(x) + F_208(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_184(x)*F_62(x)*F_65(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_187(x)*F_65(x))
Eq(F_210(x), F_211(x) + F_252(x))
Eq(F_211(x), F_212(x, 1))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_214(x, k_0)*F_33(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0, 1))
Eq(F_215(x, k_0, k_1), F_216(x, k_0, k_0*k_1))
Eq(F_216(x, k_0, k_1), F_217(x, k_0, k_1) + F_230(x, k_0, k_1))
Eq(F_217(x, k_0, k_1), F_218(x, k_0) + F_226(x, k_0, k_1))
Eq(F_218(x, k_0), F_219(x, k_0) + F_59(x, k_0))
Eq(F_219(x, k_0), F_2(x) + F_220(x, k_0))
Eq(F_220(x, k_0), F_221(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0)*F_33(x, k_0))
Eq(F_222(x, k_0), F_219(x, k_0) + F_223(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_224(x, k_0), F_218(x, k_0)*F_225(x)*F_65(x))
Eq(F_225(x), F_184(x))
Eq(F_226(x, k_0, k_1), F_227(x, k_0, k_1))
Eq(F_227(x, k_0, k_1), F_228(x, k_0, k_1)*F_33(x, k_1))
Eq(F_228(x, k_0, k_1), (-k_0*F_229(x, k_0/k_1, k_1) + k_1*F_229(x, 1, k_1))/(-k_0 + k_1))
Eq(F_229(x, k_0, k_1), F_216(x, k_0*k_1, k_1))
Eq(F_230(x, k_0, k_1), F_231(x, k_1) + F_247(x, k_0, k_1))
Eq(F_231(x, k_0), F_202(x) + F_232(x, k_0))
Eq(F_232(x, k_0), F_233(x, k_0, 1))
Eq(F_233(x, k_0, k_1), F_234(x, k_0, k_1))
Eq(F_234(x, k_0, k_1), F_235(x, k_0, k_1)*F_33(x, k_1))
Eq(F_235(x, k_0, k_1), F_236(x, k_0) + F_246(x, k_0, k_1))
Eq(F_236(x, k_0), F_212(x, k_0) + F_237(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0)*F_33(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_244(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0) + F_242(x, k_0))
Eq(F_241(x, k_0), F_191(x) + F_237(x, k_0))
Eq(F_242(x, k_0), F_243(x, k_0))
Eq(F_243(x, k_0), F_225(x)*F_241(x, k_0)*F_65(x))
Eq(F_244(x, k_0), F_241(x, k_0) + F_245(x, k_0))
Eq(F_245(x, k_0), -F_232(x, k_0) + (-k_0*F_232(x, k_0) + F_232(x, 1))/(1 - k_0))
Eq(F_246(x, k_0, k_1), -F_233(x, 1, k_1) + (-k_0*F_233(x, k_0, k_1) + F_233(x, 1, k_1))/(1 - k_0))
Eq(F_247(x, k_0, k_1), F_248(x, k_0, k_1))
Eq(F_248(x, k_0, k_1), F_249(x, k_0, k_1)*F_33(x, k_0))
Eq(F_249(x, k_0, k_1), F_230(x, k_0, k_1) + F_250(x, k_0, k_1))
Eq(F_250(x, k_0, k_1), F_251(x, k_0, k_1))
Eq(F_251(x, k_0, k_1), F_225(x)*F_230(x, k_0, k_1)*F_65(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_211(x)*F_225(x)*F_65(x))
Eq(F_254(x, k_0), F_212(x, k_0) + F_232(x, k_0))
Eq(F_255(x, k_0), F_256(x, k_0, 1))
Eq(F_256(x, k_0, k_1), (-k_1*F_257(x, k_0, k_1) + F_257(x, k_0, 1))/(1 - k_1))
Eq(F_257(x, k_0, k_1), F_241(x, k_0) + F_258(x, k_0, k_1))
Eq(F_258(x, k_0, k_1), -F_233(x, k_0, k_1) + (-k_0*F_233(x, k_0, k_1) + F_233(x, 1, k_1))/(1 - k_0))
Eq(F_259(x), F_260(x) + F_261(x))
Eq(F_260(x), F_240(x, 1))
Eq(F_261(x), F_262(x, 1))
Eq(F_262(x, k_0), -F_263(x, k_0) + (-k_0*F_263(x, k_0) + F_263(x, 1))/(1 - k_0))
Eq(F_263(x, k_0), F_264(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0)*F_65(x))
Eq(F_265(x, k_0), F_266(x, k_0) + F_269(x, k_0))
Eq(F_266(x, k_0), F_236(x, k_0) + F_267(x, k_0))
Eq(F_267(x, k_0), F_268(x, k_0))
Eq(F_268(x, k_0), F_225(x)*F_236(x, k_0)*F_65(x))
Eq(F_269(x, k_0), -F_263(x, 1) + (-k_0*F_263(x, k_0) + F_263(x, 1))/(1 - k_0))
Eq(F_270(x, k_0), F_271(x, k_0))
Eq(F_271(x, k_0), F_272(x, k_0)*F_33(x, k_0))
Eq(F_272(x, k_0), F_273(x, k_0, 1))
Eq(F_273(x, k_0, k_1), F_274(x, k_0, k_0*k_1))
Eq(F_274(x, k_0, k_1), F_275(x, k_0, k_1))
Eq(F_275(x, k_0, k_1), F_276(x, k_0, k_1) + F_280(x, k_0, k_1))
Eq(F_276(x, k_0, k_1), F_277(x, k_1, k_0))
Eq(F_277(x, k_0, k_1), F_278(x, k_0, k_1)*F_43(x, k_1))
Eq(F_278(x, k_0, k_1), F_279(x, k_1, k_0))
Eq(F_279(x, k_0, k_1), F_116(x, k_0, k_1) + F_148(x, k_0))
Eq(F_280(x, k_0, k_1), F_281(x, k_0, k_1))
Eq(F_281(x, k_0, k_1), F_127(x, k_0, k_1)*F_282(x, k_0, k_1))
Eq(F_282(x, k_0, k_1), F_162(x, k_1) + F_170(x, k_0, k_1))
Eq(F_283(x, k_0), F_284(x, k_0))
Eq(F_284(x, k_0), F_285(x, k_0)*F_31(x, k_0)*F_33(x, k_0)*F_59(x, k_0))
Eq(F_285(x, k_0), F_286(x, k_0) + F_44(x, k_0))
Eq(F_286(x, k_0), F_287(x, k_0, 1))
Eq(F_287(x, k_0, k_1), F_48(x, k_0, k_0*k_1))
Eq(F_288(x, k_0), F_289(x, k_0, 1))
Eq(F_289(x, k_0, k_1), F_290(x, k_0, k_0*k_1))
Eq(F_290(x, k_0, k_1), F_291(x, k_0, k_1))
Eq(F_291(x, k_0, k_1), F_181(x, k_0, k_1)*F_282(x, k_0, k_1)*F_65(x))
Eq(F_292(x, k_0), F_293(x, k_0, 1))
Eq(F_293(x, k_0, k_1), F_117(x, k_0, k_0*k_1))
Eq(F_294(x, k_0, k_1), F_119(x, k_0, k_1))
Eq(F_295(x), F_0(x) + F_2(x))
Pack JSON:
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Specification JSON:
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[3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [1, 1], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 1], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 0], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 1], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 1], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 0], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 1], [1, 0], [1, 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], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 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], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 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], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25961/
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[43,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[137,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[43,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[4,x]*F[43,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0],1]
F[13,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])/(-1+k[1])
F[14,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[43,x]
F[15,x,k[0],k[1]] = F[1,x]+F[136,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[15,x,k[0],k[0]*k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[134,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[20,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[0]*k[1]]
F[18,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0],k[1]] = F[21,x,k[0],k[0]*k[1]]
F[21,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[19,x,k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[43,x]
F[23,x,k[0],k[1]] = F[132,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0]]+F[96,x,k[0],k[1]]
F[25,x,k[0]] = F[26,x,k[0]]+F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[19,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[46,x,k[0]]
F[30,x,k[0]] = F[19,x,k[0]]*F[29,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]+F[4,x]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[35,x,k[0]]+F[44,x,k[0]]
F[33,x,k[0]] = F[19,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0],1]
F[35,x,k[0]] = F[36,x,k[0]]*F[43,x]
F[36,x,k[0]] = F[32,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[43,x]
F[39,x,k[0]] = F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[4,x]*F[41,x,k[0]]
F[41,x,k[0]] = (F[11,x,k[0]]*k[0]-F[11,x,1])/(-1+k[0])
F[42,x,k[0]] = F[11,x,k[0]]*F[31,x,k[0]]
F[43,x] = x
F[44,x,k[0]] = F[43,x]*F[45,x,k[0]]
F[45,x,k[0]] = (F[32,x,k[0]]*k[0]-F[32,x,1])/(-1+k[0])
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[129,x,k[0]]+F[48,x,k[0]]
F[49,x,k[0]] = F[48,x,k[0]]+F[73,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0],1]
F[50,x,k[0],k[1]] = F[51,x,k[0],k[1]]+F[84,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[52,x,k[0],k[0]*k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[1,x]+F[54,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[19,x,k[0]]*F[53,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[19,x,k[1]]*F[53,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[43,x]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[43,x]*F[59,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[60,x,k[0]]+F[64,x,k[0],k[1]]
F[61,x,k[0]] = F[43,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[28,x,k[0]]*F[43,x]
F[65,x,k[0],k[1]] = F[64,x,k[0],k[0]*k[1]]
F[66,x,k[0],k[1]] = F[60,x,k[0]]+F[65,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[43,x]*F[66,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[68,x,k[0],k[1]]
F[68,x,k[0],k[1]] = F[43,x]*F[69,x,k[0],k[1]]
F[69,x,k[0],k[1]] = F[50,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[71,x,k[0],k[0]*k[1]]
F[71,x,k[0],k[1]] = F[72,x,k[0]]+F[80,x,k[0],k[1]]
F[28,x,k[0]] = F[72,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[78,x,k[0]]
F[74,x,k[0]] = F[62,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[1,x]+F[76,x,k[0]]+F[77,x,k[0]]
F[76,x,k[0]] = F[19,x,k[0]]*F[75,x,k[0]]
F[77,x,k[0]] = F[25,x,k[0]]*F[43,x]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[11,x,k[0]]*F[43,x]*F[74,x,k[0]]
F[80,x,k[0],k[1]] = F[81,x,k[0],k[1]]
F[81,x,k[0],k[1]] = -k[1]*(F[82,x,k[0],1]-F[82,x,k[0],k[1]])/(-1+k[1])
F[82,x,k[0],k[1]] = F[83,x,k[0],k[1]]
F[83,x,k[0],k[1]] = F[43,x]*F[64,x,k[0],k[1]]
F[84,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[86,x,k[0]]+F[88,x,k[0],k[1]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[11,x,k[0]]*F[43,x]*F[75,x,k[0]]
F[88,x,k[0],k[1]] = F[89,x,k[0],k[1]]
F[89,x,k[0],k[1]] = F[43,x]*F[90,x,k[0],k[1]]
F[90,x,k[0],k[1]] = F[110,x,k[0],k[1]]+F[91,x,k[0],k[1]]
F[91,x,k[0],k[1]] = F[11,x,k[0]]*F[92,x,k[0],k[1]]
F[92,x,k[0],k[1]] = F[6,x]+F[93,x,k[0],k[1]]+F[94,x,k[0],k[1]]+F[95,x,k[0],k[1]]
F[93,x,k[0],k[1]] = F[19,x,k[0]]*F[92,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[55,x,k[0],k[0]*k[1]]
F[95,x,k[0],k[1]] = F[43,x]*F[96,x,k[0],k[1]]
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[1]]*F[98,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[99,x,k[0]]
F[100,x,k[0]] = F[43,x]*F[99,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[25,x,k[0]] = F[101,x,k[0]]+F[75,x,k[0]]
F[103,x,k[0],k[1]] = F[102,x,k[0],k[1]]+F[106,x,k[0]]
F[104,x,k[0],k[1]] = F[103,x,k[0],k[1]]*F[19,x,k[1]]
F[104,x,k[0],k[1]] = F[105,x,k[0],k[1]]
F[105,x,k[0],k[1]] = F[88,x,k[0],k[1]]+F[92,x,k[0],k[1]]
F[107,x,k[0]] = F[106,x,k[0]]*F[43,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]+F[75,x,k[0]]
F[109,x,k[0]] = F[75,x,k[0]]+F[86,x,k[0]]
F[110,x,k[0],k[1]] = F[111,x,k[0],k[1]]*F[112,x,k[0],k[1]]
F[111,x,k[0],k[1]] = k[0]*k[1]*(F[96,x,k[0],k[1]]-F[96,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[112,x,k[0],k[1]] = F[113,x,k[0]*k[1]]+F[116,x,k[0],k[1]]
F[113,x,k[0]] = F[1,x]+F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[113,x,k[0]]*F[19,x,k[0]]
F[116,x,k[0],k[1]] = F[117,x,k[0]]+F[120,x,k[0],k[1]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[19,x,k[0]]
F[119,x,k[0]] = F[1,x]+F[117,x,k[0]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]+F[123,x,k[0],k[1]]+F[6,x]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]*F[19,x,k[0]]
F[122,x,k[0],k[1]] = F[114,x,k[0]*k[1]]+F[120,x,k[0],k[1]]
F[123,x,k[0],k[1]] = F[116,x,k[0],k[1]]*F[19,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[126,x,k[0],k[1]] = F[127,x,k[0],k[1]]*F[43,x]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]
F[128,x,k[0],k[1]] = F[11,x,k[0]]*F[43,x]*F[59,x,k[0],k[1]]
F[129,x,k[0]] = F[130,x,k[0],1]
F[130,x,k[0],k[1]] = k[0]*k[1]*(F[131,x,k[0],k[1]]-F[131,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[131,x,k[0],k[1]] = F[82,x,k[0],k[0]*k[1]]
F[132,x,k[0],k[1]] = F[133,x,k[0],k[1]]
F[133,x,k[0],k[1]] = F[11,x,k[0]]*F[24,x,k[0],k[1]]*F[43,x]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]*F[43,x]
F[135,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]*k[1]-F[24,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[22,x,k[0],k[1]] = F[136,x,k[0],k[0]*k[1]]
F[137,x] = F[138,x]*F[43,x]
F[138,x] = F[32,x,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_{43}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{137}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y , 1\right)
F_{13}\! \left(x , y , z\right) = -\frac{-F_{12}\! \left(x , y , z\right) z +F_{12}\! \left(x , y , 1\right)}{-1+z}
F_{14}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{136}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = F_{15}\! \left(x , y , y z \right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{134}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , y z \right)
F_{18}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , y z \right)
F_{21}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{23}\! \left(x , y , z\right) = F_{132}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y\right)+F_{96}\! \left(x , y , z\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y , 1\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}
F_{42}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{43}\! \left(x \right) = x
F_{44}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y , 1\right)
F_{50}\! \left(x , y , z\right) = F_{51}\! \left(x , y , z\right)+F_{84}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{52}\! \left(x , y , y z \right)
F_{52}\! \left(x , y , z\right) = F_{53}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)
F_{53}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)+F_{56}\! \left(x , y , z\right)
F_{54}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right) F_{53}\! \left(x , y , z\right)
F_{55}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{53}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{57}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{59}\! \left(x , y , z\right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y\right)+F_{64}\! \left(x , y , z\right)
F_{61}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{65}\! \left(x , y , z\right) = F_{64}\! \left(x , y , y z \right)
F_{66}\! \left(x , y , z\right) = F_{60}\! \left(x , y\right)+F_{65}\! \left(x , y , z\right)
F_{67}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{66}\! \left(x , y , z\right)
F_{67}\! \left(x , y , z\right) = F_{68}\! \left(x , y , z\right)
F_{68}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{69}\! \left(x , y , z\right)
F_{69}\! \left(x , y , z\right) = F_{50}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)
F_{70}\! \left(x , y , z\right) = F_{71}\! \left(x , y , y z \right)
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y\right)+F_{80}\! \left(x , y , z\right)
F_{28}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{80}\! \left(x , y , z\right) = F_{81}\! \left(x , y , z\right)
F_{81}\! \left(x , y , z\right) = -\frac{z \left(F_{82}\! \left(x , y , 1\right)-F_{82}\! \left(x , y , z\right)\right)}{-1+z}
F_{82}\! \left(x , y , z\right) = F_{83}\! \left(x , y , z\right)
F_{83}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{64}\! \left(x , y , z\right)
F_{84}\! \left(x , y , z\right) = F_{124}\! \left(x , y , z\right)+F_{85}\! \left(x , y , z\right)
F_{85}\! \left(x , y , z\right) = F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y , z\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{88}\! \left(x , y , z\right) = F_{89}\! \left(x , y , z\right)
F_{89}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{90}\! \left(x , y , z\right)
F_{90}\! \left(x , y , z\right) = F_{110}\! \left(x , y , z\right)+F_{91}\! \left(x , y , z\right)
F_{91}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{92}\! \left(x , y , z\right)
F_{92}\! \left(x , y , z\right) = F_{6}\! \left(x \right)+F_{93}\! \left(x , y , z\right)+F_{94}\! \left(x , y , z\right)+F_{95}\! \left(x , y , z\right)
F_{93}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right) F_{92}\! \left(x , y , z\right)
F_{94}\! \left(x , y , z\right) = F_{55}\! \left(x , y , y z \right)
F_{95}\! \left(x , y , z\right) = F_{43}\! \left(x \right) F_{96}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{97}\! \left(x , y , z\right)
F_{97}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{98}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{103}\! \left(x , y , z\right) = F_{102}\! \left(x , y , z\right)+F_{106}\! \left(x , y\right)
F_{104}\! \left(x , y , z\right) = F_{103}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{104}\! \left(x , y , z\right) = F_{105}\! \left(x , y , z\right)
F_{105}\! \left(x , y , z\right) = F_{88}\! \left(x , y , z\right)+F_{92}\! \left(x , y , z\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{110}\! \left(x , y , z\right) = F_{111}\! \left(x , y , z\right) F_{112}\! \left(x , y , z\right)
F_{111}\! \left(x , y , z\right) = \frac{y z \left(F_{96}\! \left(x , y , z\right)-F_{96}\! \left(x , y , \frac{1}{y}\right)\right)}{y z -1}
F_{112}\! \left(x , y , z\right) = F_{113}\! \left(x , y z \right)+F_{116}\! \left(x , y , z\right)
F_{113}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{116}\! \left(x , y , z\right) = F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y , z\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{117}\! \left(x , y\right)
F_{120}\! \left(x , y , z\right) = F_{121}\! \left(x , y , z\right)+F_{123}\! \left(x , y , z\right)+F_{6}\! \left(x \right)
F_{121}\! \left(x , y , z\right) = F_{122}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)
F_{122}\! \left(x , y , z\right) = F_{114}\! \left(x , y z \right)+F_{120}\! \left(x , y , z\right)
F_{123}\! \left(x , y , z\right) = F_{116}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)
F_{124}\! \left(x , y , z\right) = F_{125}\! \left(x , y , y z \right)
F_{125}\! \left(x , y , z\right) = F_{126}\! \left(x , y , z\right)
F_{126}\! \left(x , y , z\right) = F_{127}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{127}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right)
F_{128}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{43}\! \left(x \right) F_{59}\! \left(x , y , z\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y , 1\right)
F_{130}\! \left(x , y , z\right) = \frac{y z \left(F_{131}\! \left(x , y , z\right)-F_{131}\! \left(x , y , \frac{1}{y}\right)\right)}{y z -1}
F_{131}\! \left(x , y , z\right) = F_{82}\! \left(x , y , y z \right)
F_{132}\! \left(x , y , z\right) = F_{133}\! \left(x , y , z\right)
F_{133}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{24}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{134}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right) F_{43}\! \left(x \right)
F_{135}\! \left(x , y , z\right) = \frac{y z F_{24}\! \left(x , y , z\right)-F_{24}\! \left(x , y , \frac{1}{y}\right)}{y z -1}
F_{22}\! \left(x , y , z\right) = F_{136}\! \left(x , y , y z \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{43}\! \left(x \right)
F_{138}\! \left(x \right) = F_{32}\! \left(x , 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_43(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_137(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_43(x)*F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_4(x)*F_43(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0, 1))
Eq(F_13(x, k_0, k_1), (-k_1*F_12(x, k_0, k_1) + F_12(x, k_0, 1))/(1 - k_1))
Eq(F_14(x, k_0, k_1), F_13(x, k_0, k_1)*F_43(x))
Eq(F_15(x, k_0, k_1), F_1(x) + F_136(x, k_0, k_1) + F_14(x, k_0, k_1) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_15(x, k_0, k_0*k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_134(x, k_0, k_1) + F_17(x, k_0, k_1) + F_20(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_0*k_1))
Eq(F_18(x, k_0, k_1), F_15(x, k_0, k_1)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_0*k_1))
Eq(F_21(x, k_0, k_1), F_15(x, k_0, k_1)*F_19(x, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_43(x))
Eq(F_23(x, k_0, k_1), F_132(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0) + F_96(x, k_0, k_1))
Eq(F_25(x, k_0), F_26(x, k_0) + F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_19(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_46(x, k_0))
Eq(F_30(x, k_0), F_19(x, k_0)*F_29(x, k_0))
Eq(F_30(x, k_0), 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_1(x) + F_33(x, k_0) + F_35(x, k_0) + F_44(x, k_0))
Eq(F_33(x, k_0), F_19(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0, 1))
Eq(F_35(x, k_0), F_36(x, k_0)*F_43(x))
Eq(F_36(x, k_0), F_32(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_43(x))
Eq(F_39(x, k_0), F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_4(x)*F_41(x, k_0))
Eq(F_41(x, k_0), (-k_0*F_11(x, k_0) + F_11(x, 1))/(1 - k_0))
Eq(F_42(x, k_0), F_11(x, k_0)*F_31(x, k_0))
Eq(F_43(x), x)
Eq(F_44(x, k_0), F_43(x)*F_45(x, k_0))
Eq(F_45(x, k_0), (-k_0*F_32(x, k_0) + F_32(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_129(x, k_0) + F_48(x, k_0))
Eq(F_49(x, k_0), F_48(x, k_0) + F_73(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0, 1))
Eq(F_50(x, k_0, k_1), F_51(x, k_0, k_1) + F_84(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_0*k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_1(x) + F_54(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_19(x, k_0)*F_53(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_19(x, k_1)*F_53(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_12(x, k_0, k_1)*F_43(x))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_43(x)*F_59(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_60(x, k_0) + F_64(x, k_0, k_1))
Eq(F_61(x, k_0), F_43(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_28(x, k_0)*F_43(x))
Eq(F_65(x, k_0, k_1), F_64(x, k_0, k_0*k_1))
Eq(F_66(x, k_0, k_1), F_60(x, k_0) + F_65(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_43(x)*F_66(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_68(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), F_43(x)*F_69(x, k_0, k_1))
Eq(F_69(x, k_0, k_1), F_50(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_71(x, k_0, k_0*k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0) + F_80(x, k_0, k_1))
Eq(F_28(x, k_0), F_72(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_78(x, k_0))
Eq(F_74(x, k_0), F_62(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_1(x) + F_76(x, k_0) + F_77(x, k_0))
Eq(F_76(x, k_0), F_19(x, k_0)*F_75(x, k_0))
Eq(F_77(x, k_0), F_25(x, k_0)*F_43(x))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_11(x, k_0)*F_43(x)*F_74(x, k_0))
Eq(F_80(x, k_0, k_1), F_81(x, k_0, k_1))
Eq(F_81(x, k_0, k_1), -F_82(x, k_0, 1) + (-k_1*F_82(x, k_0, k_1) + F_82(x, k_0, 1))/(1 - k_1))
Eq(F_82(x, k_0, k_1), F_83(x, k_0, k_1))
Eq(F_83(x, k_0, k_1), F_43(x)*F_64(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), F_124(x, k_0, k_1) + F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_86(x, k_0) + F_88(x, k_0, k_1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_11(x, k_0)*F_43(x)*F_75(x, k_0))
Eq(F_88(x, k_0, k_1), F_89(x, k_0, k_1))
Eq(F_89(x, k_0, k_1), F_43(x)*F_90(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), F_110(x, k_0, k_1) + F_91(x, k_0, k_1))
Eq(F_91(x, k_0, k_1), F_11(x, k_0)*F_92(x, k_0, k_1))
Eq(F_92(x, k_0, k_1), F_6(x) + F_93(x, k_0, k_1) + F_94(x, k_0, k_1) + F_95(x, k_0, k_1))
Eq(F_93(x, k_0, k_1), F_19(x, k_0)*F_92(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_55(x, k_0, k_0*k_1))
Eq(F_95(x, k_0, k_1), F_43(x)*F_96(x, k_0, k_1))
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_1)*F_98(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_102(x, k_0, k_1) + F_99(x, k_0))
Eq(F_100(x, k_0), F_43(x)*F_99(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_25(x, k_0), F_101(x, k_0) + F_75(x, k_0))
Eq(F_103(x, k_0, k_1), F_102(x, k_0, k_1) + F_106(x, k_0))
Eq(F_104(x, k_0, k_1), F_103(x, k_0, k_1)*F_19(x, k_1))
Eq(F_104(x, k_0, k_1), F_105(x, k_0, k_1))
Eq(F_105(x, k_0, k_1), F_88(x, k_0, k_1) + F_92(x, k_0, k_1))
Eq(F_107(x, k_0), F_106(x, k_0)*F_43(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0) + F_75(x, k_0))
Eq(F_109(x, k_0), F_75(x, k_0) + F_86(x, k_0))
Eq(F_110(x, k_0, k_1), F_111(x, k_0, k_1)*F_112(x, k_0, k_1))
Eq(F_111(x, k_0, k_1), -F_96(x, k_0, 1/k_0) + (-k_0*k_1*F_96(x, k_0, k_1) + F_96(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_112(x, k_0, k_1), F_113(x, k_0*k_1) + F_116(x, k_0, k_1))
Eq(F_113(x, k_0), F_1(x) + F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_113(x, k_0)*F_19(x, k_0))
Eq(F_116(x, k_0, k_1), F_117(x, k_0) + F_120(x, k_0, k_1))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_19(x, k_0))
Eq(F_119(x, k_0), F_1(x) + F_117(x, k_0))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1) + F_123(x, k_0, k_1) + F_6(x))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1)*F_19(x, k_0))
Eq(F_122(x, k_0, k_1), F_114(x, k_0*k_1) + F_120(x, k_0, k_1))
Eq(F_123(x, k_0, k_1), F_116(x, k_0, k_1)*F_19(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))
Eq(F_126(x, k_0, k_1), F_127(x, k_0, k_1)*F_43(x))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1))
Eq(F_128(x, k_0, k_1), F_11(x, k_0)*F_43(x)*F_59(x, k_0, k_1))
Eq(F_129(x, k_0), F_130(x, k_0, 1))
Eq(F_130(x, k_0, k_1), -F_131(x, k_0, 1/k_0) + (-k_0*k_1*F_131(x, k_0, k_1) + F_131(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_131(x, k_0, k_1), F_82(x, k_0, k_0*k_1))
Eq(F_132(x, k_0, k_1), F_133(x, k_0, k_1))
Eq(F_133(x, k_0, k_1), F_11(x, k_0)*F_24(x, k_0, k_1)*F_43(x))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1)*F_43(x))
Eq(F_135(x, k_0, k_1), (-k_0*k_1*F_24(x, k_0, k_1) + F_24(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_22(x, k_0, k_1), F_136(x, k_0, k_0*k_1))
Eq(F_137(x), F_138(x)*F_43(x))
Eq(F_138(x), F_32(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]], "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}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
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