01324_01342_01432_03124_03142_03412_04132_04312_30124_30142_30412
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2557, 12664, 63106, 315638, 1582498, 7946510, 39945020, 200934762, 1011249110, 5091077640, 25637145762, 129125635225, 650462390513, 3277096387052, 16512317023140, 83210029666812, 419363736058283, 2113748069671008, 10655230383645355, 53718027174435999, 270847730158110572, 1365773055839938519, 6887794566774146710, 34740020128953060016, 175237853321456783648, 884042861571164880247, 4460316207197347904118, 22506302106033954942683, 113576352546602001138740, 573212914302789668390268, 2893258244758606644608031, 14604962761991207408350056, 73731745329251264699380455, 372261503440944081511504310, 1879663095078796794308601431, 9491806770529322280597426822, 47935080195701532418291023673, 242098691058037658286853642806, 1222825734395947194601157131356, 6176871929867872571746412309280, 31203499339194161131724852241065, 157640386426657521554125154948708, 796452733481317191183888322605662, 4024201567169893287291820080733081, 20334128284980514219509862522484511, 102753460426692375508608296766710502, 519267815393099147853473494244818333, 2624275535147623483638827209666939239, 13263239093474388389478596605332929623, 67036449931491393964133818131633348534, 338838534866750730843523968367494532117, 1712750632274459296665037410765550889396, 8657933386834221893854139521784794260881, 43767561317885120523091088731955953248023, 221262461126211914572378241084751222341915, 1118612627513014174805446468023060473559063, 5655455943464175070564753164428218641064859, 28593730818489661170628441711252133430899851, 144573507012602704078902201521024013903367620, 731005629665430512819043471798143868563343092, 3696292147161181882937297891332399158468363642, 18690671033269520880088732263586753918078640947, 94513975462733988981742836763545347503315029938, 477946428644666724294963194158453255557160919342, 2416985273531382489264727533580753117707361733683, 12223059980055450909174677636658488818094979312648, 61815390551488111526022429568627926117935855704666, 312624944346664805867970251489061405796790022431319, 1581104554893138729908792613106038239639192350364085, 7996632513834367132196109170697313597321144543505206, 40444821504716976081661852952861380518324335510360081, 204563247093876942269933603855085372175278257350947750, 1034667660170359465642493786816971494914591291522667471, 5233381738468736098237878471559199717957001400482534676, 26471096683019579127868012083756400540244437009258603330, 133896477673776171638504426356133990382630178078250858314, 677288653171312287424140965496331758380925840430921101868, 3425986269311972946409717893017923682224890244552638886136, 17330231327775154557308851163886180944660572603495278353129, 87665716722881914716071657072931203565372745153767161767283, 443467374290226291590437406010198827880078833968136833031265, 2243364285619380556808547763884069180541871713077240866789558, 11348643663078765758407133724139436115509282517380707131716988, 57410846172499431475053389648095197980476803519714537805315115, 290435415660749491879611359404608734124557182199724175989132733, 1469300579322094634494165652236476190256795280303278859769846539, 7433220228965867156867580149438495858696846154175063226476872692, 37605247628386015976759330104153549758800407673026161153323041636, 190250077976642787311234272166236925739005256755627393735257630108, 962511692131766356092897563902394084350690603050262890332077991056, 4869583439776885293541984865656005220782047071262106595935402972110, 24636674810896980416898379141409610306375558737693848747588643622214, 124645530665119486256472393730488161741110397931054137853758122985185, 630631319449905011253494488171422668006879958438386025457859070971147
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob
Tree: http://permpal.com/tree/24452/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[101,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[18,x]*F[8,x]
F[8,x] = F[1,x]+F[100,x]+F[52,x]+F[9,x]
F[9,x] = F[10,x]*F[18,x]
F[10,x] = F[11,x]+F[8,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]+F[25,x]+F[50,x]+F[6,x]
F[13,x] = F[14,x]*F[18,x]
F[14,x] = F[15,x]+F[24,x]
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[1,x]+F[17,x]+F[19,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = F[22,x]+F[5,x]
F[22,x] = F[0,x]*F[23,x]
F[23,x] = -1+(x^2-2*x)*F[23,x]^2+(2+x)*F[23,x]
F[24,x] = F[12,x]
F[25,x] = F[26,x,1]
F[26,x,k[0]] = F[18,x]*F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[31,x,k[0]]+F[32,x,k[0]]+F[34,x,k[0]]+F[6,x]
F[28,x,k[0]] = F[29,x,k[0]]*F[30,x,k[0]]
F[29,x,k[0]] = F[15,x]+F[27,x,k[0]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0]] = F[26,x,k[0]]
F[32,x,k[0]] = F[18,x]*F[33,x,k[0]]
F[33,x,k[0]] = -k[0]*(F[27,x,1]-F[27,x,k[0]])/(-1+k[0])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[0,x]*F[18,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[46,x,k[0]]+F[48,x,k[0]]+F[6,x]
F[37,x,k[0]] = F[30,x,k[0]]*F[38,x,k[0]]
F[38,x,k[0]] = F[36,x,k[0]]+F[39,x]
F[39,x] = F[23,x]+F[40,x]
F[40,x] = F[41,x]+F[44,x]+F[6,x]
F[41,x] = F[18,x]*F[42,x]
F[42,x] = F[39,x]+F[43,x]
F[43,x] = F[40,x]
F[44,x] = F[18,x]*F[45,x]
F[45,x] = F[36,x,1]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[18,x]*F[36,x,k[0]]
F[48,x,k[0]] = F[18,x]*F[49,x,k[0]]
F[49,x,k[0]] = -k[0]*(F[36,x,1]-F[36,x,k[0]])/(-1+k[0])
F[50,x] = F[51,x]
F[51,x] = F[0,x]*F[18,x]*F[40,x]
F[52,x] = F[18,x]*F[53,x]
F[53,x] = F[54,x]+F[8,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[56,x,k[0]]+F[58,x,k[0]]+F[59,x,k[0]]+F[6,x]+F[61,x,k[0]]
F[56,x,k[0]] = F[30,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = F[55,x,k[0]]+F[8,x]
F[58,x,k[0]] = F[26,x,k[0]]
F[59,x,k[0]] = F[18,x]*F[60,x,k[0]]
F[60,x,k[0]] = -k[0]*(F[55,x,1]-F[55,x,k[0]])/(-1+k[0])
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[18,x]*F[63,x,k[0]]
F[63,x,k[0]] = 2*F[6,x]+F[64,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[64,x,k[0]] = F[30,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[63,x,k[0]]+F[66,x]
F[66,x] = F[67,x]+F[79,x]
F[67,x] = F[1,x]+F[68,x]+F[69,x]
F[68,x] = F[18,x]*F[66,x]
F[69,x] = F[18,x]*F[70,x]
F[70,x] = F[1,x]+F[52,x]+F[71,x]+F[72,x]
F[71,x] = F[18,x]*F[70,x]
F[72,x] = F[18,x]*F[73,x]
F[73,x] = F[74,x]+F[88,x]
F[74,x] = F[4,x]+F[75,x]
F[75,x] = F[6,x]+F[76,x]+F[86,x]+F[87,x]
F[76,x] = F[18,x]*F[77,x]
F[77,x] = F[74,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = 2*F[6,x]+F[80,x]+F[84,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[66,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[0,x]*F[40,x]
F[84,x] = F[18,x]*F[85,x]
F[85,x] = F[63,x,1]
F[86,x] = F[18,x]*F[54,x]
F[87,x] = F[18,x]*F[88,x]
F[88,x] = F[89,x,1]
F[89,x,k[0]] = F[59,x,k[0]]+F[6,x]+F[90,x,k[0]]+F[92,x,k[0]]+F[94,x,k[0]]
F[90,x,k[0]] = F[30,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[74,x]+F[89,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[18,x]*F[63,x,k[0]]
F[94,x,k[0]] = F[18,x]*F[95,x,k[0]]
F[95,x,k[0]] = -k[0]*(F[89,x,1]-F[89,x,k[0]])/(-1+k[0])
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[0,x]*F[18,x]*F[36,x,k[0]]
F[98,x,k[0]] = F[18,x]*F[99,x,k[0]]
F[99,x,k[0]] = -k[0]*(F[63,x,1]-F[63,x,k[0]])/(-1+k[0])
F[100,x] = F[18,x]*F[77,x]
F[101,x] = F[18,x]*F[75,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_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{101}\! \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_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{52}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{18}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{25}\! \left(x \right)+F_{50}\! \left(x \right)+F_{6}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x^{2} F_{23} \left(x \right)^{2}-2 x F_{23} \left(x \right)^{2}+x F_{23}\! \left(x \right)+2 F_{23}\! \left(x \right)-1
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{26}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{y \left(F_{27}\! \left(x , 1\right)-F_{27}\! \left(x , y\right)\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{23}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x , 1\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = -\frac{y \left(F_{36}\! \left(x , 1\right)-F_{36}\! \left(x , y\right)\right)}{-1+y}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right) F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = -\frac{y \left(F_{55}\! \left(x , 1\right)-F_{55}\! \left(x , y\right)\right)}{-1+y}
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{79}\! \left(x \right)
F_{67}\! \left(x \right) = F_{1}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right) F_{70}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{88}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{6}\! \left(x \right)+F_{76}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{6}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{66}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right) F_{40}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{63}\! \left(x , 1\right)
F_{86}\! \left(x \right) = F_{18}\! \left(x \right) F_{54}\! \left(x \right)
F_{87}\! \left(x \right) = F_{18}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x , 1\right)
F_{89}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{74}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = -\frac{y \left(F_{89}\! \left(x , 1\right)-F_{89}\! \left(x , y\right)\right)}{-1+y}
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{y \left(F_{63}\! \left(x , 1\right)-F_{63}\! \left(x , y\right)\right)}{-1+y}
F_{100}\! \left(x \right) = F_{18}\! \left(x \right) F_{77}\! \left(x \right)
F_{101}\! \left(x \right) = F_{18}\! \left(x \right) F_{75}\! \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_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_101(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_18(x)*F_8(x))
Eq(F_8(x), F_1(x) + F_100(x) + F_52(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_18(x))
Eq(F_10(x), F_11(x) + F_8(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x) + F_25(x) + F_50(x) + F_6(x))
Eq(F_13(x), F_14(x)*F_18(x))
Eq(F_14(x), F_15(x) + F_24(x))
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_1(x) + F_17(x) + F_19(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_5(x))
Eq(F_22(x), F_0(x)*F_23(x))
Eq(F_23(x), x*(x - 2)*F_23(x)**2 + (x + 2)*F_23(x) - 1)
Eq(F_24(x), F_12(x))
Eq(F_25(x), F_26(x, 1))
Eq(F_26(x, k_0), F_18(x)*F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_31(x, k_0) + F_32(x, k_0) + F_34(x, k_0) + F_6(x))
Eq(F_28(x, k_0), F_29(x, k_0)*F_30(x, k_0))
Eq(F_29(x, k_0), F_15(x) + F_27(x, k_0))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0), F_26(x, k_0))
Eq(F_32(x, k_0), F_18(x)*F_33(x, k_0))
Eq(F_33(x, k_0), -F_27(x, 1) + (-k_0*F_27(x, k_0) + F_27(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_0(x)*F_18(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_46(x, k_0) + F_48(x, k_0) + F_6(x))
Eq(F_37(x, k_0), F_30(x, k_0)*F_38(x, k_0))
Eq(F_38(x, k_0), F_36(x, k_0) + F_39(x))
Eq(F_39(x), F_23(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_44(x) + F_6(x))
Eq(F_41(x), F_18(x)*F_42(x))
Eq(F_42(x), F_39(x) + F_43(x))
Eq(F_43(x), F_40(x))
Eq(F_44(x), F_18(x)*F_45(x))
Eq(F_45(x), F_36(x, 1))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_18(x)*F_36(x, k_0))
Eq(F_48(x, k_0), F_18(x)*F_49(x, k_0))
Eq(F_49(x, k_0), -F_36(x, 1) + (-k_0*F_36(x, k_0) + F_36(x, 1))/(1 - k_0))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_0(x)*F_18(x)*F_40(x))
Eq(F_52(x), F_18(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_8(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_56(x, k_0) + F_58(x, k_0) + F_59(x, k_0) + F_6(x) + F_61(x, k_0))
Eq(F_56(x, k_0), F_30(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), F_55(x, k_0) + F_8(x))
Eq(F_58(x, k_0), F_26(x, k_0))
Eq(F_59(x, k_0), F_18(x)*F_60(x, k_0))
Eq(F_60(x, k_0), -F_55(x, 1) + (-k_0*F_55(x, k_0) + F_55(x, 1))/(1 - k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_18(x)*F_63(x, k_0))
Eq(F_63(x, k_0), 2*F_6(x) + F_64(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_64(x, k_0), F_30(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_63(x, k_0) + F_66(x))
Eq(F_66(x), F_67(x) + F_79(x))
Eq(F_67(x), F_1(x) + F_68(x) + F_69(x))
Eq(F_68(x), F_18(x)*F_66(x))
Eq(F_69(x), F_18(x)*F_70(x))
Eq(F_70(x), F_1(x) + F_52(x) + F_71(x) + F_72(x))
Eq(F_71(x), F_18(x)*F_70(x))
Eq(F_72(x), F_18(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_88(x))
Eq(F_74(x), F_4(x) + F_75(x))
Eq(F_75(x), F_6(x) + F_76(x) + F_86(x) + F_87(x))
Eq(F_76(x), F_18(x)*F_77(x))
Eq(F_77(x), F_74(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), 2*F_6(x) + F_80(x) + F_84(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_66(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_0(x)*F_40(x))
Eq(F_84(x), F_18(x)*F_85(x))
Eq(F_85(x), F_63(x, 1))
Eq(F_86(x), F_18(x)*F_54(x))
Eq(F_87(x), F_18(x)*F_88(x))
Eq(F_88(x), F_89(x, 1))
Eq(F_89(x, k_0), F_59(x, k_0) + F_6(x) + F_90(x, k_0) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_90(x, k_0), F_30(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_74(x) + F_89(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_18(x)*F_63(x, k_0))
Eq(F_94(x, k_0), F_18(x)*F_95(x, k_0))
Eq(F_95(x, k_0), -F_89(x, 1) + (-k_0*F_89(x, k_0) + F_89(x, 1))/(1 - k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_0(x)*F_18(x)*F_36(x, k_0))
Eq(F_98(x, k_0), F_18(x)*F_99(x, k_0))
Eq(F_99(x, k_0), -F_63(x, 1) + (-k_0*F_63(x, k_0) + F_63(x, 1))/(1 - k_0))
Eq(F_100(x), F_18(x)*F_77(x))
Eq(F_101(x), F_18(x)*F_75(x))
Pack JSON:
{"name": "point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], 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5]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 4]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "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": [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.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "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"}}]}
Specification 2
Strategy pack name: col_placements_untracked_component_fusion_req_corrob
Tree: http://permpal.com/tree/24605/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[16,x]*F[3,x]
F[3,x] = F[1,x]+F[226,x]+F[4,x]
F[4,x] = F[16,x]*F[5,x]
F[5,x] = F[1,x]+F[180,x]+F[222,x]+F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[1,x]+F[175,x]+F[180,x]+F[217,x]+F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[1,x]+F[10,x]+F[156,x]+F[165,x]+F[8,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]+F[154,x,k[0]]+F[156,x]+F[158,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[25,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]+F[19,x,k[0]]
F[15,x,k[0]] = F[12,x,k[0]]*F[16,x]
F[16,x] = x
F[17,x,k[0]] = F[16,x]*F[18,x,k[0]]
F[18,x,k[0]] = (F[14,x,k[0]]*k[0]-F[14,x,1])/(-1+k[0])
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[16,x]*F[21,x,k[0]]
F[21,x,k[0]] = F[152,x,k[0]]+F[153,x,k[0]]+F[22,x,k[0]]+F[3,x]
F[22,x,k[0]] = F[0,x]*F[23,x,k[0]]*F[25,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[150,x,k[0]]+F[24,x,k[0]]+F[26,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[16,x]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[148,x,k[0]]+F[149,x]+F[28,x,k[0]]+F[76,x,k[0]]
F[28,x,k[0]] = F[25,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[48,x,k[0]]
F[30,x] = F[31,x]+F[47,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[16,x]*F[35,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[1,x]+F[39,x]
F[42,x] = F[43,x]+F[44,x]+F[46,x]
F[43,x] = 0
F[44,x] = F[16,x]*F[45,x]
F[45,x] = F[36,x]+F[42,x]
F[46,x] = F[16,x]*F[38,x]
F[47,x] = F[32,x]
F[48,x,k[0]] = F[49,x,k[0]]+F[75,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[53,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[25,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[53,x,k[0]] = F[43,x]+F[54,x,k[0]]+F[56,x,k[0]]
F[54,x,k[0]] = F[25,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[32,x]+F[53,x,k[0]]
F[56,x,k[0]] = F[16,x]*F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[63,x,k[0]]
F[58,x,k[0]] = F[50,x,k[0]]+F[59,x,k[0]]
F[59,x,k[0]] = F[43,x]+F[60,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[25,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[36,x]+F[59,x,k[0]]
F[62,x,k[0]] = F[16,x]*F[58,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[69,x,k[0]]
F[64,x,k[0]] = F[43,x]+F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[25,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[39,x]+F[64,x,k[0]]
F[67,x,k[0]] = F[16,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[50,x,k[0]]+F[64,x,k[0]]
F[69,x,k[0]] = F[43,x]+F[70,x,k[0]]+F[72,x,k[0]]+F[74,x,k[0]]
F[70,x,k[0]] = F[25,x,k[0]]*F[71,x,k[0]]
F[71,x,k[0]] = F[42,x]+F[69,x,k[0]]
F[72,x,k[0]] = F[16,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[74,x,k[0]] = F[16,x]*F[63,x,k[0]]
F[75,x,k[0]] = F[53,x,k[0]]
F[76,x,k[0]] = F[16,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[1,x]+F[116,x,k[0]]+F[117,x,k[0]]+F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[25,x,k[0]]*F[77,x,k[0]]
F[79,x,k[0]] = F[16,x]*F[80,x,k[0]]
F[80,x,k[0]] = (F[81,x,k[0]]*k[0]-F[81,x,1])/(-1+k[0])
F[81,x,k[0]] = F[1,x]+F[116,x,k[0]]+F[79,x,k[0]]+F[82,x,k[0]]+F[94,x]
F[82,x,k[0]] = F[25,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[1,x]+F[116,x,k[0]]+F[82,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[16,x]*F[85,x,k[0]]
F[86,x,k[0]] = F[25,x,k[0]]*F[85,x,k[0]]
F[80,x,k[0]] = F[1,x]+F[86,x,k[0]]+F[87,x]+F[89,x,k[0]]+F[91,x,k[0]]+F[94,x]
F[87,x] = F[16,x]*F[88,x]
F[88,x] = F[83,x,1]
F[89,x,k[0]] = F[16,x]*F[90,x,k[0]]
F[90,x,k[0]] = (F[80,x,k[0]]*k[0]-F[80,x,1])/(-1+k[0])
F[91,x,k[0]] = F[16,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0],1]
F[93,x,k[0],k[1]] = (F[77,x,k[0]]*k[0]-F[77,x,k[1]]*k[1])/(-k[1]+k[0])
F[94,x] = F[16,x]*F[95,x]
F[95,x] = F[30,x]+F[96,x]
F[96,x] = F[115,x]+F[97,x]
F[97,x] = F[39,x]+F[98,x]
F[98,x] = F[101,x]+F[43,x]+F[99,x]
F[99,x] = F[100,x]*F[16,x]
F[100,x] = F[32,x]+F[98,x]
F[101,x] = F[102,x]*F[16,x]
F[102,x] = F[103,x]+F[38,x]
F[103,x] = F[104,x]+F[109,x]
F[104,x] = F[105,x]+F[107,x]+F[43,x]
F[105,x] = F[106,x]*F[16,x]
F[106,x] = F[104,x]+F[39,x]
F[107,x] = F[108,x]*F[16,x]
F[108,x] = F[104,x]+F[39,x]
F[109,x] = F[110,x]+F[112,x]+F[114,x]+F[43,x]
F[110,x] = F[111,x]*F[16,x]
F[111,x] = F[109,x]+F[42,x]
F[112,x] = F[113,x]*F[16,x]
F[113,x] = F[109,x]+F[42,x]
F[114,x] = F[103,x]*F[16,x]
F[115,x] = F[98,x]
F[116,x,k[0]] = F[16,x]*F[77,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[16,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[95,x]
F[119,x,k[0]] = F[120,x,k[0]]+F[48,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[147,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[125,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[16,x]
F[124,x,k[0]] = F[122,x,k[0]]+F[50,x,k[0]]
F[125,x,k[0]] = 2*F[43,x]+F[126,x,k[0]]+F[128,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]*F[16,x]
F[127,x,k[0]] = F[125,x,k[0]]+F[53,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[16,x]
F[129,x,k[0]] = F[130,x,k[0]]+F[135,x,k[0]]
F[130,x,k[0]] = F[122,x,k[0]]+F[131,x,k[0]]
F[131,x,k[0]] = 2*F[43,x]+F[132,x,k[0]]+F[134,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]*F[16,x]
F[133,x,k[0]] = F[131,x,k[0]]+F[59,x,k[0]]
F[134,x,k[0]] = F[130,x,k[0]]*F[16,x]
F[135,x,k[0]] = F[136,x,k[0]]+F[141,x,k[0]]
F[136,x,k[0]] = 2*F[43,x]+F[137,x,k[0]]+F[139,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]*F[16,x]
F[138,x,k[0]] = F[136,x,k[0]]+F[64,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[16,x]
F[140,x,k[0]] = F[122,x,k[0]]+F[136,x,k[0]]
F[141,x,k[0]] = 2*F[43,x]+F[142,x,k[0]]+F[144,x,k[0]]+F[146,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[16,x]
F[143,x,k[0]] = F[141,x,k[0]]+F[69,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]*F[16,x]
F[145,x,k[0]] = F[131,x,k[0]]+F[141,x,k[0]]
F[146,x,k[0]] = F[135,x,k[0]]*F[16,x]
F[147,x,k[0]] = F[125,x,k[0]]
F[148,x,k[0]] = F[16,x]*F[80,x,k[0]]
F[149,x] = F[16,x]*F[88,x]
F[150,x,k[0]] = F[151,x,k[0]]*F[16,x]
F[151,x,k[0]] = (F[23,x,k[0]]*k[0]-F[23,x,1])/(-1+k[0])
F[152,x,k[0]] = F[0,x]*F[16,x]*F[27,x,k[0]]
F[153,x,k[0]] = F[0,x]*F[151,x,k[0]]*F[16,x]
F[154,x,k[0]] = F[155,x,k[0]]*F[16,x]
F[155,x,k[0]] = (F[12,x,k[0]]*k[0]-F[12,x,1])/(-1+k[0])
F[156,x] = F[157,x]*F[16,x]
F[157,x] = F[14,x,1]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[16,x]*F[160,x,k[0]]
F[160,x,k[0]] = F[152,x,k[0]]+F[161,x,k[0]]+F[163,x]+F[22,x,k[0]]+F[3,x]
F[161,x,k[0]] = F[0,x]*F[16,x]*F[162,x,k[0]]
F[162,x,k[0]] = (F[27,x,k[0]]*k[0]-F[27,x,1])/(-1+k[0])
F[163,x] = F[0,x]*F[16,x]*F[164,x]
F[164,x] = F[23,x,1]
F[165,x] = F[166,x]
F[166,x] = F[16,x]*F[167,x]
F[167,x] = F[163,x]+F[168,x]+F[174,x]+F[3,x]
F[168,x] = F[0,x]*F[16,x]*F[169,x]
F[169,x] = F[1,x]+F[170,x]+F[171,x]+F[173,x]
F[170,x] = F[16,x]*F[169,x]
F[171,x] = F[16,x]*F[172,x]
F[172,x] = F[27,x,1]
F[173,x] = F[16,x]*F[164,x]
F[174,x] = F[0,x]*F[16,x]*F[172,x]
F[175,x] = F[16,x]*F[176,x]
F[176,x] = F[177,x,1]
F[177,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]+F[178,x,k[0]]+F[180,x]+F[213,x,k[0]]
F[178,x,k[0]] = F[16,x]*F[179,x,k[0]]
F[179,x,k[0]] = (F[177,x,k[0]]*k[0]-F[177,x,1])/(-1+k[0])
F[180,x] = F[16,x]*F[181,x]
F[181,x] = F[182,x,1]
F[182,x,k[0]] = F[1,x]+F[183,x,k[0]]+F[184,x,k[0]]+F[185,x,k[0]]+F[187,x,k[0]]
F[183,x,k[0]] = F[182,x,k[0]]*F[25,x,k[0]]
F[184,x,k[0]] = F[16,x]*F[177,x,k[0]]
F[185,x,k[0]] = F[16,x]*F[186,x,k[0]]
F[186,x,k[0]] = (F[182,x,k[0]]*k[0]-F[182,x,1])/(-1+k[0])
F[187,x,k[0]] = F[16,x]*F[188,x,k[0]]
F[188,x,k[0]] = F[1,x]+F[180,x]+F[189,x,k[0]]+F[191,x,k[0]]+F[202,x]+F[211,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[25,x,k[0]]
F[190,x,k[0]] = F[1,x]+F[189,x,k[0]]+F[191,x,k[0]]+F[199,x]+F[209,x,k[0]]
F[191,x,k[0]] = F[16,x]*F[192,x,k[0]]
F[192,x,k[0]] = F[1,x]+F[193,x,k[0]]+F[194,x,k[0]]+F[195,x,k[0]]+F[197,x]+F[199,x]
F[193,x,k[0]] = F[22,x,k[0]]
F[194,x,k[0]] = F[152,x,k[0]]
F[195,x,k[0]] = F[16,x]*F[196,x,k[0]]
F[196,x,k[0]] = (F[192,x,k[0]]*k[0]-F[192,x,1])/(-1+k[0])
F[197,x] = F[16,x]*F[198,x]
F[198,x] = F[190,x,1]
F[199,x] = F[16,x]*F[200,x]
F[200,x] = F[1,x]+F[180,x]+F[201,x]+F[202,x]
F[201,x] = F[16,x]*F[200,x]
F[202,x] = F[16,x]*F[203,x]
F[203,x] = F[204,x,1]
F[204,x,k[0]] = F[1,x]+F[185,x,k[0]]+F[205,x,k[0]]+F[206,x,k[0]]+F[207,x,k[0]]
F[205,x,k[0]] = F[204,x,k[0]]*F[25,x,k[0]]
F[206,x,k[0]] = F[16,x]*F[188,x,k[0]]
F[207,x,k[0]] = F[16,x]*F[208,x,k[0]]
F[208,x,k[0]] = (F[204,x,k[0]]*k[0]-F[204,x,1])/(-1+k[0])
F[209,x,k[0]] = F[16,x]*F[210,x,k[0]]
F[210,x,k[0]] = (F[190,x,k[0]]*k[0]-F[190,x,1])/(-1+k[0])
F[211,x,k[0]] = F[16,x]*F[212,x,k[0]]
F[212,x,k[0]] = (F[188,x,k[0]]*k[0]-F[188,x,1])/(-1+k[0])
F[213,x,k[0]] = F[16,x]*F[214,x,k[0]]
F[214,x,k[0]] = F[1,x]+F[180,x]+F[193,x,k[0]]+F[194,x,k[0]]+F[195,x,k[0]]+F[202,x]+F[215,x]
F[215,x] = F[16,x]*F[216,x]
F[216,x] = F[188,x,1]
F[217,x] = F[16,x]*F[218,x]
F[218,x] = F[1,x]+F[180,x]+F[202,x]+F[215,x]+F[219,x]+F[220,x]
F[219,x] = F[168,x]
F[220,x] = F[16,x]*F[221,x]
F[221,x] = F[192,x,1]
F[222,x] = F[16,x]*F[223,x]
F[223,x] = F[1,x]+F[180,x]+F[202,x]+F[215,x]+F[224,x]
F[224,x] = F[16,x]*F[225,x]
F[225,x] = F[1,x]+F[197,x]+F[199,x]+F[219,x]+F[220,x]
F[226,x] = F[16,x]*F[227,x]
F[227,x] = F[1,x]+F[180,x]+F[202,x]+F[228,x]
F[228,x] = F[16,x]*F[223,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_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{226}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{222}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{175}\! \left(x \right)+F_{180}\! \left(x \right)+F_{217}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{156}\! \left(x \right)+F_{165}\! \left(x \right)+F_{8}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{156}\! \left(x \right)+F_{158}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{23}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{150}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{149}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{47}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = 0
F_{44}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{38}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = -\frac{-F_{81}\! \left(x , y\right) y +F_{81}\! \left(x , 1\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{82}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{87}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{87}\! \left(x \right) = F_{16}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{89}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-F_{80}\! \left(x , y\right) y +F_{80}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y , 1\right)
F_{93}\! \left(x , y , z\right) = \frac{F_{77}\! \left(x , y\right) y -F_{77}\! \left(x , z\right) z}{-z +y}
F_{94}\! \left(x \right) = F_{16}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{30}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{115}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{39}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right)+F_{43}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{16}\! \left(x \right)
F_{100}\! \left(x \right) = F_{32}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{16}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{38}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{109}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{43}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{16}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)+F_{39}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{16}\! \left(x \right)
F_{108}\! \left(x \right) = F_{104}\! \left(x \right)+F_{39}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{112}\! \left(x \right)+F_{114}\! \left(x \right)+F_{43}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{16}\! \left(x \right)
F_{111}\! \left(x \right) = F_{109}\! \left(x \right)+F_{42}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{16}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)+F_{42}\! \left(x \right)
F_{114}\! \left(x \right) = F_{103}\! \left(x \right) F_{16}\! \left(x \right)
F_{115}\! \left(x \right) = F_{98}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{95}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = 2 F_{43}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = 2 F_{43}\! \left(x \right)+F_{132}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = 2 F_{43}\! \left(x \right)+F_{137}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = 2 F_{43}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{149}\! \left(x \right) = F_{16}\! \left(x \right) F_{88}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{151}\! \left(x , y\right) = -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{151}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{155}\! \left(x , y\right) = -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{16}\! \left(x \right)
F_{157}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{163}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{163}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{16}\! \left(x \right) F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{163}\! \left(x \right)+F_{168}\! \left(x \right)+F_{174}\! \left(x \right)+F_{3}\! \left(x \right)
F_{168}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{1}\! \left(x \right)+F_{170}\! \left(x \right)+F_{171}\! \left(x \right)+F_{173}\! \left(x \right)
F_{170}\! \left(x \right) = F_{16}\! \left(x \right) F_{169}\! \left(x \right)
F_{171}\! \left(x \right) = F_{16}\! \left(x \right) F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{173}\! \left(x \right) = F_{16}\! \left(x \right) F_{164}\! \left(x \right)
F_{174}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{172}\! \left(x \right)
F_{175}\! \left(x \right) = F_{16}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x , 1\right)
F_{177}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{180}\! \left(x \right)+F_{213}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = -\frac{-F_{177}\! \left(x , y\right) y +F_{177}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x \right) = F_{16}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x , 1\right)
F_{182}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{183}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{177}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = -\frac{-F_{182}\! \left(x , y\right) y +F_{182}\! \left(x , 1\right)}{-1+y}
F_{187}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{202}\! \left(x \right)+F_{211}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{199}\! \left(x \right)+F_{209}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{197}\! \left(x \right)+F_{199}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = -\frac{-F_{192}\! \left(x , y\right) y +F_{192}\! \left(x , 1\right)}{-1+y}
F_{197}\! \left(x \right) = F_{16}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{190}\! \left(x , 1\right)
F_{199}\! \left(x \right) = F_{16}\! \left(x \right) F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{201}\! \left(x \right)+F_{202}\! \left(x \right)
F_{201}\! \left(x \right) = F_{16}\! \left(x \right) F_{200}\! \left(x \right)
F_{202}\! \left(x \right) = F_{16}\! \left(x \right) F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x , 1\right)
F_{204}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{185}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{206}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{204}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = -\frac{-F_{204}\! \left(x , y\right) y +F_{204}\! \left(x , 1\right)}{-1+y}
F_{209}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = -\frac{-F_{190}\! \left(x , y\right) y +F_{190}\! \left(x , 1\right)}{-1+y}
F_{211}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{-y F_{188}\! \left(x , y\right)+F_{188}\! \left(x , 1\right)}{-1+y}
F_{213}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{202}\! \left(x \right)+F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = F_{16}\! \left(x \right) F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{188}\! \left(x , 1\right)
F_{217}\! \left(x \right) = F_{16}\! \left(x \right) F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{202}\! \left(x \right)+F_{215}\! \left(x \right)+F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{168}\! \left(x \right)
F_{220}\! \left(x \right) = F_{16}\! \left(x \right) F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{192}\! \left(x , 1\right)
F_{222}\! \left(x \right) = F_{16}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{202}\! \left(x \right)+F_{215}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{16}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{1}\! \left(x \right)+F_{197}\! \left(x \right)+F_{199}\! \left(x \right)+F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{226}\! \left(x \right) = F_{16}\! \left(x \right) F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{202}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{16}\! \left(x \right) F_{223}\! \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_16(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_226(x) + F_4(x))
Eq(F_4(x), F_16(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_180(x) + F_222(x) + F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_175(x) + F_180(x) + F_217(x) + F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_1(x) + F_10(x) + F_156(x) + F_165(x) + F_8(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0) + F_154(x, k_0) + F_156(x) + F_158(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_25(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0) + F_17(x, k_0) + F_19(x, k_0))
Eq(F_15(x, k_0), F_12(x, k_0)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x, k_0), F_16(x)*F_18(x, k_0))
Eq(F_18(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_16(x)*F_21(x, k_0))
Eq(F_21(x, k_0), F_152(x, k_0) + F_153(x, k_0) + F_22(x, k_0) + F_3(x))
Eq(F_22(x, k_0), F_0(x)*F_23(x, k_0)*F_25(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_150(x, k_0) + F_24(x, k_0) + F_26(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_16(x)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_148(x, k_0) + F_149(x) + F_28(x, k_0) + F_76(x, k_0))
Eq(F_28(x, k_0), F_25(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_48(x, k_0))
Eq(F_30(x), F_31(x) + F_47(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_16(x)*F_35(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_39(x))
Eq(F_42(x), F_43(x) + F_44(x) + F_46(x))
Eq(F_43(x), 0)
Eq(F_44(x), F_16(x)*F_45(x))
Eq(F_45(x), F_36(x) + F_42(x))
Eq(F_46(x), F_16(x)*F_38(x))
Eq(F_47(x), F_32(x))
Eq(F_48(x, k_0), F_49(x, k_0) + F_75(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_53(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_25(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_53(x, k_0), F_43(x) + F_54(x, k_0) + F_56(x, k_0))
Eq(F_54(x, k_0), F_25(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_32(x) + F_53(x, k_0))
Eq(F_56(x, k_0), F_16(x)*F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_63(x, k_0))
Eq(F_58(x, k_0), F_50(x, k_0) + F_59(x, k_0))
Eq(F_59(x, k_0), F_43(x) + F_60(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_25(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_36(x) + F_59(x, k_0))
Eq(F_62(x, k_0), F_16(x)*F_58(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_69(x, k_0))
Eq(F_64(x, k_0), F_43(x) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_25(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_39(x) + F_64(x, k_0))
Eq(F_67(x, k_0), F_16(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_50(x, k_0) + F_64(x, k_0))
Eq(F_69(x, k_0), F_43(x) + F_70(x, k_0) + F_72(x, k_0) + F_74(x, k_0))
Eq(F_70(x, k_0), F_25(x, k_0)*F_71(x, k_0))
Eq(F_71(x, k_0), F_42(x) + F_69(x, k_0))
Eq(F_72(x, k_0), F_16(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_74(x, k_0), F_16(x)*F_63(x, k_0))
Eq(F_75(x, k_0), F_53(x, k_0))
Eq(F_76(x, k_0), F_16(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_1(x) + F_116(x, k_0) + F_117(x, k_0) + F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_25(x, k_0)*F_77(x, k_0))
Eq(F_79(x, k_0), F_16(x)*F_80(x, k_0))
Eq(F_80(x, k_0), (-k_0*F_81(x, k_0) + F_81(x, 1))/(1 - k_0))
Eq(F_81(x, k_0), F_1(x) + F_116(x, k_0) + F_79(x, k_0) + F_82(x, k_0) + F_94(x))
Eq(F_82(x, k_0), F_25(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_1(x) + F_116(x, k_0) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_16(x)*F_85(x, k_0))
Eq(F_86(x, k_0), F_25(x, k_0)*F_85(x, k_0))
Eq(F_80(x, k_0), F_1(x) + F_86(x, k_0) + F_87(x) + F_89(x, k_0) + F_91(x, k_0) + F_94(x))
Eq(F_87(x), F_16(x)*F_88(x))
Eq(F_88(x), F_83(x, 1))
Eq(F_89(x, k_0), F_16(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (-k_0*F_80(x, k_0) + F_80(x, 1))/(1 - k_0))
Eq(F_91(x, k_0), F_16(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0, 1))
Eq(F_93(x, k_0, k_1), (-k_0*F_77(x, k_0) + k_1*F_77(x, k_1))/(-k_0 + k_1))
Eq(F_94(x), F_16(x)*F_95(x))
Eq(F_95(x), F_30(x) + F_96(x))
Eq(F_96(x), F_115(x) + F_97(x))
Eq(F_97(x), F_39(x) + F_98(x))
Eq(F_98(x), F_101(x) + F_43(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_16(x))
Eq(F_100(x), F_32(x) + F_98(x))
Eq(F_101(x), F_102(x)*F_16(x))
Eq(F_102(x), F_103(x) + F_38(x))
Eq(F_103(x), F_104(x) + F_109(x))
Eq(F_104(x), F_105(x) + F_107(x) + F_43(x))
Eq(F_105(x), F_106(x)*F_16(x))
Eq(F_106(x), F_104(x) + F_39(x))
Eq(F_107(x), F_108(x)*F_16(x))
Eq(F_108(x), F_104(x) + F_39(x))
Eq(F_109(x), F_110(x) + F_112(x) + F_114(x) + F_43(x))
Eq(F_110(x), F_111(x)*F_16(x))
Eq(F_111(x), F_109(x) + F_42(x))
Eq(F_112(x), F_113(x)*F_16(x))
Eq(F_113(x), F_109(x) + F_42(x))
Eq(F_114(x), F_103(x)*F_16(x))
Eq(F_115(x), F_98(x))
Eq(F_116(x, k_0), F_16(x)*F_77(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_16(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_95(x))
Eq(F_119(x, k_0), F_120(x, k_0) + F_48(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_147(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_125(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0)*F_16(x))
Eq(F_124(x, k_0), F_122(x, k_0) + F_50(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_128(x, k_0) + 2*F_43(x))
Eq(F_126(x, k_0), F_127(x, k_0)*F_16(x))
Eq(F_127(x, k_0), F_125(x, k_0) + F_53(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_16(x))
Eq(F_129(x, k_0), F_130(x, k_0) + F_135(x, k_0))
Eq(F_130(x, k_0), F_122(x, k_0) + F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_134(x, k_0) + 2*F_43(x))
Eq(F_132(x, k_0), F_133(x, k_0)*F_16(x))
Eq(F_133(x, k_0), F_131(x, k_0) + F_59(x, k_0))
Eq(F_134(x, k_0), F_130(x, k_0)*F_16(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_141(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_139(x, k_0) + 2*F_43(x))
Eq(F_137(x, k_0), F_138(x, k_0)*F_16(x))
Eq(F_138(x, k_0), F_136(x, k_0) + F_64(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_16(x))
Eq(F_140(x, k_0), F_122(x, k_0) + F_136(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_144(x, k_0) + F_146(x, k_0) + 2*F_43(x))
Eq(F_142(x, k_0), F_143(x, k_0)*F_16(x))
Eq(F_143(x, k_0), F_141(x, k_0) + F_69(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0)*F_16(x))
Eq(F_145(x, k_0), F_131(x, k_0) + F_141(x, k_0))
Eq(F_146(x, k_0), F_135(x, k_0)*F_16(x))
Eq(F_147(x, k_0), F_125(x, k_0))
Eq(F_148(x, k_0), F_16(x)*F_80(x, k_0))
Eq(F_149(x), F_16(x)*F_88(x))
Eq(F_150(x, k_0), F_151(x, k_0)*F_16(x))
Eq(F_151(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_152(x, k_0), F_0(x)*F_16(x)*F_27(x, k_0))
Eq(F_153(x, k_0), F_0(x)*F_151(x, k_0)*F_16(x))
Eq(F_154(x, k_0), F_155(x, k_0)*F_16(x))
Eq(F_155(x, k_0), (-k_0*F_12(x, k_0) + F_12(x, 1))/(1 - k_0))
Eq(F_156(x), F_157(x)*F_16(x))
Eq(F_157(x), F_14(x, 1))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_16(x)*F_160(x, k_0))
Eq(F_160(x, k_0), F_152(x, k_0) + F_161(x, k_0) + F_163(x) + F_22(x, k_0) + F_3(x))
Eq(F_161(x, k_0), F_0(x)*F_16(x)*F_162(x, k_0))
Eq(F_162(x, k_0), (-k_0*F_27(x, k_0) + F_27(x, 1))/(1 - k_0))
Eq(F_163(x), F_0(x)*F_16(x)*F_164(x))
Eq(F_164(x), F_23(x, 1))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_16(x)*F_167(x))
Eq(F_167(x), F_163(x) + F_168(x) + F_174(x) + F_3(x))
Eq(F_168(x), F_0(x)*F_16(x)*F_169(x))
Eq(F_169(x), F_1(x) + F_170(x) + F_171(x) + F_173(x))
Eq(F_170(x), F_16(x)*F_169(x))
Eq(F_171(x), F_16(x)*F_172(x))
Eq(F_172(x), F_27(x, 1))
Eq(F_173(x), F_16(x)*F_164(x))
Eq(F_174(x), F_0(x)*F_16(x)*F_172(x))
Eq(F_175(x), F_16(x)*F_176(x))
Eq(F_176(x), F_177(x, 1))
Eq(F_177(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0) + F_178(x, k_0) + F_180(x) + F_213(x, k_0))
Eq(F_178(x, k_0), F_16(x)*F_179(x, k_0))
Eq(F_179(x, k_0), (-k_0*F_177(x, k_0) + F_177(x, 1))/(1 - k_0))
Eq(F_180(x), F_16(x)*F_181(x))
Eq(F_181(x), F_182(x, 1))
Eq(F_182(x, k_0), F_1(x) + F_183(x, k_0) + F_184(x, k_0) + F_185(x, k_0) + F_187(x, k_0))
Eq(F_183(x, k_0), F_182(x, k_0)*F_25(x, k_0))
Eq(F_184(x, k_0), F_16(x)*F_177(x, k_0))
Eq(F_185(x, k_0), F_16(x)*F_186(x, k_0))
Eq(F_186(x, k_0), (-k_0*F_182(x, k_0) + F_182(x, 1))/(1 - k_0))
Eq(F_187(x, k_0), F_16(x)*F_188(x, k_0))
Eq(F_188(x, k_0), F_1(x) + F_180(x) + F_189(x, k_0) + F_191(x, k_0) + F_202(x) + F_211(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0)*F_25(x, k_0))
Eq(F_190(x, k_0), F_1(x) + F_189(x, k_0) + F_191(x, k_0) + F_199(x) + F_209(x, k_0))
Eq(F_191(x, k_0), F_16(x)*F_192(x, k_0))
Eq(F_192(x, k_0), F_1(x) + F_193(x, k_0) + F_194(x, k_0) + F_195(x, k_0) + F_197(x) + F_199(x))
Eq(F_193(x, k_0), F_22(x, k_0))
Eq(F_194(x, k_0), F_152(x, k_0))
Eq(F_195(x, k_0), F_16(x)*F_196(x, k_0))
Eq(F_196(x, k_0), (-k_0*F_192(x, k_0) + F_192(x, 1))/(1 - k_0))
Eq(F_197(x), F_16(x)*F_198(x))
Eq(F_198(x), F_190(x, 1))
Eq(F_199(x), F_16(x)*F_200(x))
Eq(F_200(x), F_1(x) + F_180(x) + F_201(x) + F_202(x))
Eq(F_201(x), F_16(x)*F_200(x))
Eq(F_202(x), F_16(x)*F_203(x))
Eq(F_203(x), F_204(x, 1))
Eq(F_204(x, k_0), F_1(x) + F_185(x, k_0) + F_205(x, k_0) + F_206(x, k_0) + F_207(x, k_0))
Eq(F_205(x, k_0), F_204(x, k_0)*F_25(x, k_0))
Eq(F_206(x, k_0), F_16(x)*F_188(x, k_0))
Eq(F_207(x, k_0), F_16(x)*F_208(x, k_0))
Eq(F_208(x, k_0), (-k_0*F_204(x, k_0) + F_204(x, 1))/(1 - k_0))
Eq(F_209(x, k_0), F_16(x)*F_210(x, k_0))
Eq(F_210(x, k_0), (-k_0*F_190(x, k_0) + F_190(x, 1))/(1 - k_0))
Eq(F_211(x, k_0), F_16(x)*F_212(x, k_0))
Eq(F_212(x, k_0), (-k_0*F_188(x, k_0) + F_188(x, 1))/(1 - k_0))
Eq(F_213(x, k_0), F_16(x)*F_214(x, k_0))
Eq(F_214(x, k_0), F_1(x) + F_180(x) + F_193(x, k_0) + F_194(x, k_0) + F_195(x, k_0) + F_202(x) + F_215(x))
Eq(F_215(x), F_16(x)*F_216(x))
Eq(F_216(x), F_188(x, 1))
Eq(F_217(x), F_16(x)*F_218(x))
Eq(F_218(x), F_1(x) + F_180(x) + F_202(x) + F_215(x) + F_219(x) + F_220(x))
Eq(F_219(x), F_168(x))
Eq(F_220(x), F_16(x)*F_221(x))
Eq(F_221(x), F_192(x, 1))
Eq(F_222(x), F_16(x)*F_223(x))
Eq(F_223(x), F_1(x) + F_180(x) + F_202(x) + F_215(x) + F_224(x))
Eq(F_224(x), F_16(x)*F_225(x))
Eq(F_225(x), F_1(x) + F_197(x) + F_199(x) + F_219(x) + F_220(x))
Eq(F_226(x), F_16(x)*F_227(x))
Eq(F_227(x), F_1(x) + F_180(x) + F_202(x) + F_228(x))
Eq(F_228(x), F_16(x)*F_223(x))
Pack JSON:
{"name": "col_placements_untracked_component_fusion_req_corrob", "initial_strats": [{"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.component", "strategy_class": "ComponentFusionFactory", "tracked": false, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 4]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 2], [0, 3]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 1], [0, 2], [0, 3]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 2], [0, 2], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 4], [0, 1], [0, 3], [0, 4]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 4], [0, 2], [0, 3], [0, 4]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 4], [0, 3], [0, 3], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], 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[[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "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": []}, "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": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "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": [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": "SkewComponentAssumption", "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"}}]}
Specification 3
Strategy pack name: col_placements_tracked_fusion_tracked_component_fusion_req_corrob
Tree: http://permpal.com/tree/24693/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[17,x]*F[3,x]
F[3,x] = F[1,x]+F[225,x]+F[4,x]
F[4,x] = F[17,x]*F[5,x]
F[5,x] = F[1,x]+F[174,x]+F[221,x]+F[6,x]
F[6,x] = F[17,x]*F[7,x]
F[7,x] = F[1,x]+F[169,x]+F[174,x]+F[217,x]+F[8,x]
F[8,x] = F[17,x]*F[9,x]
F[9,x] = F[1,x]+F[10,x]+F[148,x]+F[157,x]+F[8,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]*F[17,x]
F[12,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[146,x,k[0]]+F[148,x]+F[150,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[24,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[15,x,k[0]]+F[18,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[17,x]
F[16,x,k[0]] = (F[14,x,k[0]]*k[0]-F[14,x,1])/(-1+k[0])
F[17,x] = x
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[17,x]*F[20,x,k[0]]
F[20,x,k[0]] = F[144,x,k[0]]+F[145,x,k[0]]+F[21,x,k[0]]+F[3,x]
F[21,x,k[0]] = F[0,x]*F[22,x,k[0]]*F[24,x,k[0]]
F[22,x,k[0]] = F[1,x]+F[142,x,k[0]]+F[23,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[17,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[1,x]+F[139,x,k[0]]+F[140,x]+F[27,x,k[0]]+F[75,x,k[0]]
F[27,x,k[0]] = F[24,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[47,x,k[0]]
F[29,x] = F[30,x]+F[46,x]
F[30,x] = F[1,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[17,x]*F[33,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[1,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[17,x]*F[34,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[17,x]*F[40,x]
F[40,x] = F[1,x]+F[38,x]
F[41,x] = F[42,x]+F[43,x]+F[45,x]
F[42,x] = 0
F[43,x] = F[17,x]*F[44,x]
F[44,x] = F[35,x]+F[41,x]
F[45,x] = F[17,x]*F[37,x]
F[46,x] = F[31,x]
F[47,x,k[0]] = F[48,x,k[0]]+F[74,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[52,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[24,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[1,x]+F[49,x,k[0]]
F[52,x,k[0]] = F[42,x]+F[53,x,k[0]]+F[55,x,k[0]]
F[53,x,k[0]] = F[24,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[31,x]+F[52,x,k[0]]
F[55,x,k[0]] = F[17,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[62,x,k[0]]
F[57,x,k[0]] = F[49,x,k[0]]+F[58,x,k[0]]
F[58,x,k[0]] = F[42,x]+F[59,x,k[0]]+F[61,x,k[0]]
F[59,x,k[0]] = F[24,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[35,x]+F[58,x,k[0]]
F[61,x,k[0]] = F[17,x]*F[57,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[68,x,k[0]]
F[63,x,k[0]] = F[42,x]+F[64,x,k[0]]+F[66,x,k[0]]
F[64,x,k[0]] = F[24,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[38,x]+F[63,x,k[0]]
F[66,x,k[0]] = F[17,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[49,x,k[0]]+F[63,x,k[0]]
F[68,x,k[0]] = F[42,x]+F[69,x,k[0]]+F[71,x,k[0]]+F[73,x,k[0]]
F[69,x,k[0]] = F[24,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[41,x]+F[68,x,k[0]]
F[71,x,k[0]] = F[17,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[58,x,k[0]]+F[68,x,k[0]]
F[73,x,k[0]] = F[17,x]*F[62,x,k[0]]
F[74,x,k[0]] = F[52,x,k[0]]
F[75,x,k[0]] = F[17,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[77,x,k[0]]+F[78,x,k[0]]+F[85,x,k[0]]
F[77,x,k[0]] = F[24,x,k[0]]*F[76,x,k[0]]
F[78,x,k[0]] = F[17,x]*F[79,x,k[0]]
F[79,x,k[0]] = (F[80,x,k[0]]*k[0]-F[80,x,1])/(-1+k[0])
F[80,x,k[0]] = F[1,x]+F[78,x,k[0]]+F[81,x,k[0]]+F[85,x,k[0]]+F[86,x]
F[81,x,k[0]] = F[24,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[1,x]+F[81,x,k[0]]+F[83,x,k[0]]+F[85,x,k[0]]
F[83,x,k[0]] = F[17,x]*F[84,x,k[0]]
F[84,x,k[0]] = (F[82,x,k[0]]*k[0]-F[82,x,1])/(-1+k[0])
F[85,x,k[0]] = F[17,x]*F[76,x,k[0]]
F[86,x] = F[17,x]*F[87,x]
F[87,x] = F[29,x]+F[88,x]
F[88,x] = F[107,x]+F[89,x]
F[89,x] = F[38,x]+F[90,x]
F[90,x] = F[42,x]+F[91,x]+F[93,x]
F[91,x] = F[17,x]*F[92,x]
F[92,x] = F[31,x]+F[90,x]
F[93,x] = F[17,x]*F[94,x]
F[94,x] = F[37,x]+F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[42,x]+F[97,x]+F[99,x]
F[97,x] = F[17,x]*F[98,x]
F[98,x] = F[38,x]+F[96,x]
F[99,x] = F[100,x]*F[17,x]
F[100,x] = F[38,x]+F[96,x]
F[101,x] = F[102,x]+F[104,x]+F[106,x]+F[42,x]
F[102,x] = F[103,x]*F[17,x]
F[103,x] = F[101,x]+F[41,x]
F[104,x] = F[105,x]*F[17,x]
F[105,x] = F[101,x]+F[41,x]
F[106,x] = F[17,x]*F[95,x]
F[107,x] = F[90,x]
F[108,x,k[0]] = F[109,x,k[0]]*F[17,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[87,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[47,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[138,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[116,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[17,x]
F[115,x,k[0]] = F[113,x,k[0]]+F[49,x,k[0]]
F[116,x,k[0]] = 2*F[42,x]+F[117,x,k[0]]+F[119,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[17,x]
F[118,x,k[0]] = F[116,x,k[0]]+F[52,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[17,x]
F[120,x,k[0]] = F[121,x,k[0]]+F[126,x,k[0]]
F[121,x,k[0]] = F[113,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = 2*F[42,x]+F[123,x,k[0]]+F[125,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[17,x]
F[124,x,k[0]] = F[122,x,k[0]]+F[58,x,k[0]]
F[125,x,k[0]] = F[121,x,k[0]]*F[17,x]
F[126,x,k[0]] = F[127,x,k[0]]+F[132,x,k[0]]
F[127,x,k[0]] = 2*F[42,x]+F[128,x,k[0]]+F[130,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[17,x]
F[129,x,k[0]] = F[127,x,k[0]]+F[63,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]*F[17,x]
F[131,x,k[0]] = F[113,x,k[0]]+F[127,x,k[0]]
F[132,x,k[0]] = 2*F[42,x]+F[133,x,k[0]]+F[135,x,k[0]]+F[137,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[17,x]
F[134,x,k[0]] = F[132,x,k[0]]+F[68,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[17,x]
F[136,x,k[0]] = F[122,x,k[0]]+F[132,x,k[0]]
F[137,x,k[0]] = F[126,x,k[0]]*F[17,x]
F[138,x,k[0]] = F[116,x,k[0]]
F[139,x,k[0]] = F[17,x]*F[79,x,k[0]]
F[140,x] = F[141,x]*F[17,x]
F[141,x] = F[82,x,1]
F[142,x,k[0]] = F[143,x,k[0]]*F[17,x]
F[143,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[144,x,k[0]] = F[0,x]*F[17,x]*F[26,x,k[0]]
F[145,x,k[0]] = F[0,x]*F[143,x,k[0]]*F[17,x]
F[146,x,k[0]] = F[147,x,k[0]]*F[17,x]
F[147,x,k[0]] = (F[12,x,k[0]]*k[0]-F[12,x,1])/(-1+k[0])
F[148,x] = F[149,x]*F[17,x]
F[149,x] = F[14,x,1]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[17,x]
F[152,x,k[0]] = F[144,x,k[0]]+F[153,x,k[0]]+F[155,x]+F[21,x,k[0]]+F[3,x]
F[153,x,k[0]] = F[0,x]*F[154,x,k[0]]*F[17,x]
F[154,x,k[0]] = (F[26,x,k[0]]*k[0]-F[26,x,1])/(-1+k[0])
F[155,x] = F[0,x]*F[156,x]*F[17,x]
F[156,x] = F[22,x,1]
F[157,x] = F[158,x]
F[158,x] = F[159,x]*F[17,x]
F[159,x] = F[155,x]+F[160,x]+F[168,x]+F[3,x]
F[160,x] = F[0,x]*F[161,x]*F[17,x]
F[161,x] = F[1,x]+F[140,x]+F[162,x]+F[167,x]
F[162,x] = F[163,x]*F[17,x]
F[163,x] = F[1,x]+F[164,x]+F[166,x]+F[86,x]
F[164,x] = F[165,x]*F[17,x]
F[165,x] = F[80,x,1]
F[166,x] = F[163,x]*F[17,x]
F[167,x] = F[165,x]*F[17,x]
F[168,x] = F[144,x,1]
F[169,x] = F[170,x,1]
F[170,x,k[0]] = F[17,x]*F[171,x,k[0]]
F[171,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[172,x,k[0]]+F[174,x]+F[215,x,k[0]]
F[172,x,k[0]] = F[17,x]*F[173,x,k[0]]
F[173,x,k[0]] = (F[171,x,k[0]]*k[0]-F[171,x,1])/(-1+k[0])
F[174,x] = F[17,x]*F[175,x]
F[175,x] = F[1,x]+F[169,x]+F[176,x]+F[177,x]+F[214,x]
F[176,x] = F[17,x]*F[175,x]
F[177,x] = F[17,x]*F[178,x]
F[178,x] = F[179,x,1]
F[179,x,k[0]] = (F[180,x,k[0]]*k[0]-F[180,x,1])/(-1+k[0])
F[180,x,k[0]] = F[1,x]+F[170,x,k[0]]+F[181,x,k[0]]+F[182,x,k[0]]+F[183,x,k[0]]
F[181,x,k[0]] = F[180,x,k[0]]*F[24,x,k[0]]
F[182,x,k[0]] = F[17,x]*F[179,x,k[0]]
F[183,x,k[0]] = F[17,x]*F[184,x,k[0]]
F[184,x,k[0]] = F[1,x]+F[174,x]+F[185,x,k[0]]+F[187,x,k[0]]+F[198,x]+F[212,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[24,x,k[0]]
F[186,x,k[0]] = F[1,x]+F[185,x,k[0]]+F[187,x,k[0]]+F[195,x]+F[210,x,k[0]]
F[187,x,k[0]] = F[17,x]*F[188,x,k[0]]
F[188,x,k[0]] = F[1,x]+F[189,x,k[0]]+F[190,x,k[0]]+F[191,x,k[0]]+F[193,x]+F[195,x]
F[189,x,k[0]] = F[21,x,k[0]]
F[190,x,k[0]] = F[144,x,k[0]]
F[191,x,k[0]] = F[17,x]*F[192,x,k[0]]
F[192,x,k[0]] = (F[188,x,k[0]]*k[0]-F[188,x,1])/(-1+k[0])
F[193,x] = F[17,x]*F[194,x]
F[194,x] = F[186,x,1]
F[195,x] = F[17,x]*F[196,x]
F[196,x] = F[1,x]+F[174,x]+F[197,x]+F[198,x]
F[197,x] = F[17,x]*F[196,x]
F[198,x] = F[17,x]*F[199,x]
F[199,x] = F[1,x]+F[177,x]+F[200,x]+F[201,x]+F[203,x]
F[200,x] = F[17,x]*F[199,x]
F[201,x] = F[17,x]*F[202,x]
F[202,x] = F[184,x,1]
F[203,x] = F[17,x]*F[204,x]
F[204,x] = F[205,x,1]
F[205,x,k[0]] = (F[206,x,k[0]]*k[0]-F[206,x,1])/(-1+k[0])
F[206,x,k[0]] = F[1,x]+F[182,x,k[0]]+F[207,x,k[0]]+F[208,x,k[0]]+F[209,x,k[0]]
F[207,x,k[0]] = F[206,x,k[0]]*F[24,x,k[0]]
F[208,x,k[0]] = F[17,x]*F[184,x,k[0]]
F[209,x,k[0]] = F[17,x]*F[205,x,k[0]]
F[210,x,k[0]] = F[17,x]*F[211,x,k[0]]
F[211,x,k[0]] = (F[186,x,k[0]]*k[0]-F[186,x,1])/(-1+k[0])
F[212,x,k[0]] = F[17,x]*F[213,x,k[0]]
F[213,x,k[0]] = (F[184,x,k[0]]*k[0]-F[184,x,1])/(-1+k[0])
F[214,x] = F[17,x]*F[202,x]
F[215,x,k[0]] = F[17,x]*F[216,x,k[0]]
F[216,x,k[0]] = F[1,x]+F[174,x]+F[189,x,k[0]]+F[190,x,k[0]]+F[191,x,k[0]]+F[198,x]+F[201,x]
F[217,x] = F[17,x]*F[218,x]
F[218,x] = F[1,x]+F[174,x]+F[198,x]+F[201,x]+F[219,x]+F[220,x]
F[219,x] = F[160,x]
F[220,x] = F[187,x,1]
F[221,x] = F[17,x]*F[222,x]
F[222,x] = F[1,x]+F[174,x]+F[198,x]+F[201,x]+F[223,x]
F[223,x] = F[17,x]*F[224,x]
F[224,x] = F[1,x]+F[193,x]+F[195,x]+F[219,x]+F[220,x]
F[225,x] = F[17,x]*F[226,x]
F[226,x] = F[1,x]+F[174,x]+F[198,x]+F[227,x]
F[227,x] = F[17,x]*F[222,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_{17}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{225}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{221}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{17}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{169}\! \left(x \right)+F_{174}\! \left(x \right)+F_{217}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{17}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{148}\! \left(x \right)+F_{157}\! \left(x \right)+F_{8}\! \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\right) F_{17}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{146}\! \left(x , y\right)+F_{148}\! \left(x \right)+F_{150}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{16}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x \right) = x
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{145}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{142}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{139}\! \left(x , y\right)+F_{140}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{46}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = 0
F_{43}\! \left(x \right) = F_{17}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{35}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{46}\! \left(x \right) = F_{31}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{78}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = -\frac{-F_{80}\! \left(x , y\right) y +F_{80}\! \left(x , 1\right)}{-1+y}
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{85}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = -\frac{-F_{82}\! \left(x , y\right) y +F_{82}\! \left(x , 1\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{86}\! \left(x \right) = F_{17}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{29}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{107}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{38}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{42}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{91}\! \left(x \right) = F_{17}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{31}\! \left(x \right)+F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{17}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{37}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{42}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{17}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{38}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{17}\! \left(x \right)
F_{100}\! \left(x \right) = F_{38}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)+F_{106}\! \left(x \right)+F_{42}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{17}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right)+F_{41}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{17}\! \left(x \right)
F_{105}\! \left(x \right) = F_{101}\! \left(x \right)+F_{41}\! \left(x \right)
F_{106}\! \left(x \right) = F_{17}\! \left(x \right) F_{95}\! \left(x \right)
F_{107}\! \left(x \right) = F_{90}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{128}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{133}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{17}\! \left(x \right)
F_{141}\! \left(x \right) = F_{82}\! \left(x , 1\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{143}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{143}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{147}\! \left(x , y\right) = -\frac{-y F_{12}\! \left(x , y\right)+F_{12}\! \left(x , 1\right)}{-1+y}
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{17}\! \left(x \right)
F_{149}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{153}\! \left(x , y\right)+F_{155}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{154}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{154}\! \left(x , y\right) = -\frac{-F_{26}\! \left(x , y\right) y +F_{26}\! \left(x , 1\right)}{-1+y}
F_{155}\! \left(x \right) = F_{0}\! \left(x \right) F_{156}\! \left(x \right) F_{17}\! \left(x \right)
F_{156}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{17}\! \left(x \right)
F_{159}\! \left(x \right) = F_{155}\! \left(x \right)+F_{160}\! \left(x \right)+F_{168}\! \left(x \right)+F_{3}\! \left(x \right)
F_{160}\! \left(x \right) = F_{0}\! \left(x \right) F_{161}\! \left(x \right) F_{17}\! \left(x \right)
F_{161}\! \left(x \right) = F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{162}\! \left(x \right)+F_{167}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{17}\! \left(x \right)
F_{163}\! \left(x \right) = F_{1}\! \left(x \right)+F_{164}\! \left(x \right)+F_{166}\! \left(x \right)+F_{86}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{17}\! \left(x \right)
F_{165}\! \left(x \right) = F_{80}\! \left(x , 1\right)
F_{166}\! \left(x \right) = F_{163}\! \left(x \right) F_{17}\! \left(x \right)
F_{167}\! \left(x \right) = F_{165}\! \left(x \right) F_{17}\! \left(x \right)
F_{168}\! \left(x \right) = F_{144}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{170}\! \left(x , 1\right)
F_{170}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{171}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{174}\! \left(x \right)+F_{215}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = -\frac{-F_{171}\! \left(x , y\right) y +F_{171}\! \left(x , 1\right)}{-1+y}
F_{174}\! \left(x \right) = F_{17}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{1}\! \left(x \right)+F_{169}\! \left(x \right)+F_{176}\! \left(x \right)+F_{177}\! \left(x \right)+F_{214}\! \left(x \right)
F_{176}\! \left(x \right) = F_{17}\! \left(x \right) F_{175}\! \left(x \right)
F_{177}\! \left(x \right) = F_{17}\! \left(x \right) F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x , 1\right)
F_{179}\! \left(x , y\right) = -\frac{-F_{180}\! \left(x , y\right) y +F_{180}\! \left(x , 1\right)}{-1+y}
F_{180}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{170}\! \left(x , y\right)+F_{181}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{180}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{179}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{185}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{198}\! \left(x \right)+F_{212}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{185}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{195}\! \left(x \right)+F_{210}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{190}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{193}\! \left(x \right)+F_{195}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = -\frac{-F_{188}\! \left(x , y\right) y +F_{188}\! \left(x , 1\right)}{-1+y}
F_{193}\! \left(x \right) = F_{17}\! \left(x \right) F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{186}\! \left(x , 1\right)
F_{195}\! \left(x \right) = F_{17}\! \left(x \right) F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{197}\! \left(x \right)+F_{198}\! \left(x \right)
F_{197}\! \left(x \right) = F_{17}\! \left(x \right) F_{196}\! \left(x \right)
F_{198}\! \left(x \right) = F_{17}\! \left(x \right) F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{1}\! \left(x \right)+F_{177}\! \left(x \right)+F_{200}\! \left(x \right)+F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{200}\! \left(x \right) = F_{17}\! \left(x \right) F_{199}\! \left(x \right)
F_{201}\! \left(x \right) = F_{17}\! \left(x \right) F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{184}\! \left(x , 1\right)
F_{203}\! \left(x \right) = F_{17}\! \left(x \right) F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x , 1\right)
F_{205}\! \left(x , y\right) = -\frac{-F_{206}\! \left(x , y\right) y +F_{206}\! \left(x , 1\right)}{-1+y}
F_{206}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{182}\! \left(x , y\right)+F_{207}\! \left(x , y\right)+F_{208}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{206}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{184}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{205}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = -\frac{-F_{186}\! \left(x , y\right) y +F_{186}\! \left(x , 1\right)}{-1+y}
F_{212}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = -\frac{-y F_{184}\! \left(x , y\right)+F_{184}\! \left(x , 1\right)}{-1+y}
F_{214}\! \left(x \right) = F_{17}\! \left(x \right) F_{202}\! \left(x \right)
F_{215}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{190}\! \left(x , y\right)+F_{191}\! \left(x , y\right)+F_{198}\! \left(x \right)+F_{201}\! \left(x \right)
F_{217}\! \left(x \right) = F_{17}\! \left(x \right) F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{198}\! \left(x \right)+F_{201}\! \left(x \right)+F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{160}\! \left(x \right)
F_{220}\! \left(x \right) = F_{187}\! \left(x , 1\right)
F_{221}\! \left(x \right) = F_{17}\! \left(x \right) F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{198}\! \left(x \right)+F_{201}\! \left(x \right)+F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{17}\! \left(x \right) F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{1}\! \left(x \right)+F_{193}\! \left(x \right)+F_{195}\! \left(x \right)+F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{225}\! \left(x \right) = F_{17}\! \left(x \right) F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{198}\! \left(x \right)+F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{17}\! \left(x \right) F_{222}\! \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_17(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_225(x) + F_4(x))
Eq(F_4(x), F_17(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_174(x) + F_221(x) + F_6(x))
Eq(F_6(x), F_17(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_169(x) + F_174(x) + F_217(x) + F_8(x))
Eq(F_8(x), F_17(x)*F_9(x))
Eq(F_9(x), F_1(x) + F_10(x) + F_148(x) + F_157(x) + F_8(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0)*F_17(x))
Eq(F_12(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_146(x, k_0) + F_148(x) + F_150(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_24(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_15(x, k_0) + F_18(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_17(x))
Eq(F_16(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_17(x), x)
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_17(x)*F_20(x, k_0))
Eq(F_20(x, k_0), F_144(x, k_0) + F_145(x, k_0) + F_21(x, k_0) + F_3(x))
Eq(F_21(x, k_0), F_0(x)*F_22(x, k_0)*F_24(x, k_0))
Eq(F_22(x, k_0), F_1(x) + F_142(x, k_0) + F_23(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_17(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_1(x) + F_139(x, k_0) + F_140(x) + F_27(x, k_0) + F_75(x, k_0))
Eq(F_27(x, k_0), F_24(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_47(x, k_0))
Eq(F_29(x), F_30(x) + F_46(x))
Eq(F_30(x), F_1(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_17(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_1(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_17(x)*F_34(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_17(x)*F_40(x))
Eq(F_40(x), F_1(x) + F_38(x))
Eq(F_41(x), F_42(x) + F_43(x) + F_45(x))
Eq(F_42(x), 0)
Eq(F_43(x), F_17(x)*F_44(x))
Eq(F_44(x), F_35(x) + F_41(x))
Eq(F_45(x), F_17(x)*F_37(x))
Eq(F_46(x), F_31(x))
Eq(F_47(x, k_0), F_48(x, k_0) + F_74(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_52(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_24(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_1(x) + F_49(x, k_0))
Eq(F_52(x, k_0), F_42(x) + F_53(x, k_0) + F_55(x, k_0))
Eq(F_53(x, k_0), F_24(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_31(x) + F_52(x, k_0))
Eq(F_55(x, k_0), F_17(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_62(x, k_0))
Eq(F_57(x, k_0), F_49(x, k_0) + F_58(x, k_0))
Eq(F_58(x, k_0), F_42(x) + F_59(x, k_0) + F_61(x, k_0))
Eq(F_59(x, k_0), F_24(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_35(x) + F_58(x, k_0))
Eq(F_61(x, k_0), F_17(x)*F_57(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_68(x, k_0))
Eq(F_63(x, k_0), F_42(x) + F_64(x, k_0) + F_66(x, k_0))
Eq(F_64(x, k_0), F_24(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_38(x) + F_63(x, k_0))
Eq(F_66(x, k_0), F_17(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_49(x, k_0) + F_63(x, k_0))
Eq(F_68(x, k_0), F_42(x) + F_69(x, k_0) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_69(x, k_0), F_24(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_41(x) + F_68(x, k_0))
Eq(F_71(x, k_0), F_17(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_58(x, k_0) + F_68(x, k_0))
Eq(F_73(x, k_0), F_17(x)*F_62(x, k_0))
Eq(F_74(x, k_0), F_52(x, k_0))
Eq(F_75(x, k_0), F_17(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_108(x, k_0) + F_77(x, k_0) + F_78(x, k_0) + F_85(x, k_0))
Eq(F_77(x, k_0), F_24(x, k_0)*F_76(x, k_0))
Eq(F_78(x, k_0), F_17(x)*F_79(x, k_0))
Eq(F_79(x, k_0), (-k_0*F_80(x, k_0) + F_80(x, 1))/(1 - k_0))
Eq(F_80(x, k_0), F_1(x) + F_78(x, k_0) + F_81(x, k_0) + F_85(x, k_0) + F_86(x))
Eq(F_81(x, k_0), F_24(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_1(x) + F_81(x, k_0) + F_83(x, k_0) + F_85(x, k_0))
Eq(F_83(x, k_0), F_17(x)*F_84(x, k_0))
Eq(F_84(x, k_0), (-k_0*F_82(x, k_0) + F_82(x, 1))/(1 - k_0))
Eq(F_85(x, k_0), F_17(x)*F_76(x, k_0))
Eq(F_86(x), F_17(x)*F_87(x))
Eq(F_87(x), F_29(x) + F_88(x))
Eq(F_88(x), F_107(x) + F_89(x))
Eq(F_89(x), F_38(x) + F_90(x))
Eq(F_90(x), F_42(x) + F_91(x) + F_93(x))
Eq(F_91(x), F_17(x)*F_92(x))
Eq(F_92(x), F_31(x) + F_90(x))
Eq(F_93(x), F_17(x)*F_94(x))
Eq(F_94(x), F_37(x) + F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_42(x) + F_97(x) + F_99(x))
Eq(F_97(x), F_17(x)*F_98(x))
Eq(F_98(x), F_38(x) + F_96(x))
Eq(F_99(x), F_100(x)*F_17(x))
Eq(F_100(x), F_38(x) + F_96(x))
Eq(F_101(x), F_102(x) + F_104(x) + F_106(x) + F_42(x))
Eq(F_102(x), F_103(x)*F_17(x))
Eq(F_103(x), F_101(x) + F_41(x))
Eq(F_104(x), F_105(x)*F_17(x))
Eq(F_105(x), F_101(x) + F_41(x))
Eq(F_106(x), F_17(x)*F_95(x))
Eq(F_107(x), F_90(x))
Eq(F_108(x, k_0), F_109(x, k_0)*F_17(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_87(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_47(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_138(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_116(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_17(x))
Eq(F_115(x, k_0), F_113(x, k_0) + F_49(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_119(x, k_0) + 2*F_42(x))
Eq(F_117(x, k_0), F_118(x, k_0)*F_17(x))
Eq(F_118(x, k_0), F_116(x, k_0) + F_52(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0)*F_17(x))
Eq(F_120(x, k_0), F_121(x, k_0) + F_126(x, k_0))
Eq(F_121(x, k_0), F_113(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_125(x, k_0) + 2*F_42(x))
Eq(F_123(x, k_0), F_124(x, k_0)*F_17(x))
Eq(F_124(x, k_0), F_122(x, k_0) + F_58(x, k_0))
Eq(F_125(x, k_0), F_121(x, k_0)*F_17(x))
Eq(F_126(x, k_0), F_127(x, k_0) + F_132(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_130(x, k_0) + 2*F_42(x))
Eq(F_128(x, k_0), F_129(x, k_0)*F_17(x))
Eq(F_129(x, k_0), F_127(x, k_0) + F_63(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_17(x))
Eq(F_131(x, k_0), F_113(x, k_0) + F_127(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_135(x, k_0) + F_137(x, k_0) + 2*F_42(x))
Eq(F_133(x, k_0), F_134(x, k_0)*F_17(x))
Eq(F_134(x, k_0), F_132(x, k_0) + F_68(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_17(x))
Eq(F_136(x, k_0), F_122(x, k_0) + F_132(x, k_0))
Eq(F_137(x, k_0), F_126(x, k_0)*F_17(x))
Eq(F_138(x, k_0), F_116(x, k_0))
Eq(F_139(x, k_0), F_17(x)*F_79(x, k_0))
Eq(F_140(x), F_141(x)*F_17(x))
Eq(F_141(x), F_82(x, 1))
Eq(F_142(x, k_0), F_143(x, k_0)*F_17(x))
Eq(F_143(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_144(x, k_0), F_0(x)*F_17(x)*F_26(x, k_0))
Eq(F_145(x, k_0), F_0(x)*F_143(x, k_0)*F_17(x))
Eq(F_146(x, k_0), F_147(x, k_0)*F_17(x))
Eq(F_147(x, k_0), (-k_0*F_12(x, k_0) + F_12(x, 1))/(1 - k_0))
Eq(F_148(x), F_149(x)*F_17(x))
Eq(F_149(x), F_14(x, 1))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0)*F_17(x))
Eq(F_152(x, k_0), F_144(x, k_0) + F_153(x, k_0) + F_155(x) + F_21(x, k_0) + F_3(x))
Eq(F_153(x, k_0), F_0(x)*F_154(x, k_0)*F_17(x))
Eq(F_154(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_155(x), F_0(x)*F_156(x)*F_17(x))
Eq(F_156(x), F_22(x, 1))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_159(x)*F_17(x))
Eq(F_159(x), F_155(x) + F_160(x) + F_168(x) + F_3(x))
Eq(F_160(x), F_0(x)*F_161(x)*F_17(x))
Eq(F_161(x), F_1(x) + F_140(x) + F_162(x) + F_167(x))
Eq(F_162(x), F_163(x)*F_17(x))
Eq(F_163(x), F_1(x) + F_164(x) + F_166(x) + F_86(x))
Eq(F_164(x), F_165(x)*F_17(x))
Eq(F_165(x), F_80(x, 1))
Eq(F_166(x), F_163(x)*F_17(x))
Eq(F_167(x), F_165(x)*F_17(x))
Eq(F_168(x), F_144(x, 1))
Eq(F_169(x), F_170(x, 1))
Eq(F_170(x, k_0), F_17(x)*F_171(x, k_0))
Eq(F_171(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_172(x, k_0) + F_174(x) + F_215(x, k_0))
Eq(F_172(x, k_0), F_17(x)*F_173(x, k_0))
Eq(F_173(x, k_0), (-k_0*F_171(x, k_0) + F_171(x, 1))/(1 - k_0))
Eq(F_174(x), F_17(x)*F_175(x))
Eq(F_175(x), F_1(x) + F_169(x) + F_176(x) + F_177(x) + F_214(x))
Eq(F_176(x), F_17(x)*F_175(x))
Eq(F_177(x), F_17(x)*F_178(x))
Eq(F_178(x), F_179(x, 1))
Eq(F_179(x, k_0), (-k_0*F_180(x, k_0) + F_180(x, 1))/(1 - k_0))
Eq(F_180(x, k_0), F_1(x) + F_170(x, k_0) + F_181(x, k_0) + F_182(x, k_0) + F_183(x, k_0))
Eq(F_181(x, k_0), F_180(x, k_0)*F_24(x, k_0))
Eq(F_182(x, k_0), F_17(x)*F_179(x, k_0))
Eq(F_183(x, k_0), F_17(x)*F_184(x, k_0))
Eq(F_184(x, k_0), F_1(x) + F_174(x) + F_185(x, k_0) + F_187(x, k_0) + F_198(x) + F_212(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_24(x, k_0))
Eq(F_186(x, k_0), F_1(x) + F_185(x, k_0) + F_187(x, k_0) + F_195(x) + F_210(x, k_0))
Eq(F_187(x, k_0), F_17(x)*F_188(x, k_0))
Eq(F_188(x, k_0), F_1(x) + F_189(x, k_0) + F_190(x, k_0) + F_191(x, k_0) + F_193(x) + F_195(x))
Eq(F_189(x, k_0), F_21(x, k_0))
Eq(F_190(x, k_0), F_144(x, k_0))
Eq(F_191(x, k_0), F_17(x)*F_192(x, k_0))
Eq(F_192(x, k_0), (-k_0*F_188(x, k_0) + F_188(x, 1))/(1 - k_0))
Eq(F_193(x), F_17(x)*F_194(x))
Eq(F_194(x), F_186(x, 1))
Eq(F_195(x), F_17(x)*F_196(x))
Eq(F_196(x), F_1(x) + F_174(x) + F_197(x) + F_198(x))
Eq(F_197(x), F_17(x)*F_196(x))
Eq(F_198(x), F_17(x)*F_199(x))
Eq(F_199(x), F_1(x) + F_177(x) + F_200(x) + F_201(x) + F_203(x))
Eq(F_200(x), F_17(x)*F_199(x))
Eq(F_201(x), F_17(x)*F_202(x))
Eq(F_202(x), F_184(x, 1))
Eq(F_203(x), F_17(x)*F_204(x))
Eq(F_204(x), F_205(x, 1))
Eq(F_205(x, k_0), (-k_0*F_206(x, k_0) + F_206(x, 1))/(1 - k_0))
Eq(F_206(x, k_0), F_1(x) + F_182(x, k_0) + F_207(x, k_0) + F_208(x, k_0) + F_209(x, k_0))
Eq(F_207(x, k_0), F_206(x, k_0)*F_24(x, k_0))
Eq(F_208(x, k_0), F_17(x)*F_184(x, k_0))
Eq(F_209(x, k_0), F_17(x)*F_205(x, k_0))
Eq(F_210(x, k_0), F_17(x)*F_211(x, k_0))
Eq(F_211(x, k_0), (-k_0*F_186(x, k_0) + F_186(x, 1))/(1 - k_0))
Eq(F_212(x, k_0), F_17(x)*F_213(x, k_0))
Eq(F_213(x, k_0), (-k_0*F_184(x, k_0) + F_184(x, 1))/(1 - k_0))
Eq(F_214(x), F_17(x)*F_202(x))
Eq(F_215(x, k_0), F_17(x)*F_216(x, k_0))
Eq(F_216(x, k_0), F_1(x) + F_174(x) + F_189(x, k_0) + F_190(x, k_0) + F_191(x, k_0) + F_198(x) + F_201(x))
Eq(F_217(x), F_17(x)*F_218(x))
Eq(F_218(x), F_1(x) + F_174(x) + F_198(x) + F_201(x) + F_219(x) + F_220(x))
Eq(F_219(x), F_160(x))
Eq(F_220(x), F_187(x, 1))
Eq(F_221(x), F_17(x)*F_222(x))
Eq(F_222(x), F_1(x) + F_174(x) + F_198(x) + F_201(x) + F_223(x))
Eq(F_223(x), F_17(x)*F_224(x))
Eq(F_224(x), F_1(x) + F_193(x) + F_195(x) + F_219(x) + F_220(x))
Eq(F_225(x), F_17(x)*F_226(x))
Eq(F_226(x), F_1(x) + F_174(x) + F_198(x) + F_227(x))
Eq(F_227(x), F_17(x)*F_222(x))
Pack JSON:
{"name": "col_placements_tracked_fusion_tracked_component_fusion_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": true}}, {"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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 2], [0, 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[]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "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], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 2]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "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": [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.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": [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"}}]}
Specification 4
Strategy pack name: point_and_col_placements_untracked_component_fusion_req_corrob
Tree: http://permpal.com/tree/25441/
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[17,x]*F[4,x]
F[4,x] = F[1,x]+F[107,x]+F[5,x]
F[5,x] = F[17,x]*F[6,x]
F[6,x] = F[1,x]+F[105,x]+F[37,x]+F[7,x]
F[7,x] = F[17,x]*F[8,x]
F[8,x] = F[6,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[103,x]+F[11,x]+F[12,x]+F[24,x]
F[11,x] = 0
F[12,x] = F[13,x]*F[17,x]
F[13,x] = F[14,x]+F[23,x]
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[1,x]+F[16,x]+F[18,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = x
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[20,x]
F[20,x] = F[21,x]+F[4,x]
F[21,x] = F[0,x]*F[22,x]
F[22,x] = (x*F[22,x]+x-1)*(x*F[22,x]+x-2*F[22,x])
F[23,x] = F[10,x]
F[24,x] = F[17,x]*F[25,x]
F[25,x] = F[26,x,1]
F[26,x,k[0]] = F[27,x,k[0]]
F[28,x,k[0]] = F[27,x,k[0]]+F[8,x]
F[28,x,k[0]] = F[1,x]+F[29,x,k[0]]+F[32,x,k[0]]+F[35,x,k[0]]+F[37,x]+F[99,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[31,x,k[0]]
F[30,x,k[0]] = F[14,x]+F[26,x,k[0]]
F[31,x,k[0]] = k[0]*x
F[32,x,k[0]] = F[17,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[13,x]+F[34,x,k[0]]
F[34,x,k[0]] = F[26,x,k[0]]
F[35,x,k[0]] = F[17,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[28,x,k[0]]*k[0]-F[28,x,1])/(-1+k[0])
F[37,x] = F[17,x]*F[38,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[41,x,k[0]]+F[42,x,k[0]]+F[44,x,k[0]]
F[40,x,k[0]] = F[31,x,k[0]]*F[39,x,k[0]]
F[41,x,k[0]] = F[17,x]*F[28,x,k[0]]
F[42,x,k[0]] = F[17,x]*F[43,x,k[0]]
F[43,x,k[0]] = (F[39,x,k[0]]*k[0]-F[39,x,1])/(-1+k[0])
F[44,x,k[0]] = F[17,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[37,x]+F[46,x,k[0]]+F[48,x,k[0]]+F[78,x]+F[97,x,k[0]]
F[46,x,k[0]] = F[31,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[1,x]+F[46,x,k[0]]+F[48,x,k[0]]+F[75,x]+F[95,x,k[0]]
F[48,x,k[0]] = F[17,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]+F[73,x]+F[75,x]+F[91,x,k[0]]+F[93,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[0,x]*F[31,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[54,x,k[0]]+F[89,x,k[0]]
F[53,x,k[0]] = F[31,x,k[0]]*F[52,x,k[0]]
F[54,x,k[0]] = F[17,x]*F[55,x,k[0]]
F[49,x,k[0]] = F[55,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x]+F[87,x,k[0]]
F[57,x] = F[58,x]+F[85,x]
F[58,x] = -F[67,x]+F[59,x]
F[59,x] = F[1,x]+F[60,x]+F[73,x]+F[75,x]
F[60,x] = F[17,x]*F[61,x]
F[61,x] = F[59,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[0,x]*F[64,x]
F[64,x] = F[11,x]+F[65,x]+F[70,x]
F[65,x] = F[17,x]*F[66,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[64,x]+F[68,x]
F[68,x] = -1+(x^2-2*x)*F[68,x]^2+(2+x)*F[68,x]
F[69,x] = F[64,x]
F[70,x] = F[17,x]*F[71,x]
F[71,x] = F[72,x,1]
F[52,x,k[0]] = F[67,x]+F[72,x,k[0]]
F[73,x] = F[17,x]*F[74,x]
F[74,x] = F[47,x,1]
F[75,x] = F[17,x]*F[76,x]
F[76,x] = F[1,x]+F[37,x]+F[77,x]+F[78,x]
F[77,x] = F[17,x]*F[76,x]
F[78,x] = F[17,x]*F[79,x]
F[79,x] = F[80,x,1]
F[80,x,k[0]] = F[1,x]+F[42,x,k[0]]+F[81,x,k[0]]+F[82,x,k[0]]+F[83,x,k[0]]
F[81,x,k[0]] = F[31,x,k[0]]*F[80,x,k[0]]
F[82,x,k[0]] = F[17,x]*F[45,x,k[0]]
F[83,x,k[0]] = F[17,x]*F[84,x,k[0]]
F[84,x,k[0]] = (F[80,x,k[0]]*k[0]-F[80,x,1])/(-1+k[0])
F[85,x] = F[86,x]
F[86,x] = F[2,x]*F[64,x]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[2,x]*F[72,x,k[0]]
F[89,x,k[0]] = F[17,x]*F[90,x,k[0]]
F[90,x,k[0]] = (F[52,x,k[0]]*k[0]-F[52,x,1])/(-1+k[0])
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[0,x]*F[17,x]*F[55,x,k[0]]
F[93,x,k[0]] = F[17,x]*F[94,x,k[0]]
F[94,x,k[0]] = (F[49,x,k[0]]*k[0]-F[49,x,1])/(-1+k[0])
F[95,x,k[0]] = F[17,x]*F[96,x,k[0]]
F[96,x,k[0]] = (F[47,x,k[0]]*k[0]-F[47,x,1])/(-1+k[0])
F[97,x,k[0]] = F[17,x]*F[98,x,k[0]]
F[98,x,k[0]] = (F[45,x,k[0]]*k[0]-F[45,x,1])/(-1+k[0])
F[99,x,k[0]] = F[100,x,k[0]]*F[17,x]
F[100,x,k[0]] = F[1,x]+F[101,x]+F[37,x]+F[50,x,k[0]]+F[78,x]+F[91,x,k[0]]+F[93,x,k[0]]
F[101,x] = F[102,x]*F[17,x]
F[102,x] = F[45,x,1]
F[103,x] = F[104,x]
F[104,x] = F[0,x]*F[17,x]*F[64,x]
F[105,x] = F[106,x]*F[17,x]
F[106,x] = F[1,x]+F[101,x]+F[37,x]+F[60,x]+F[78,x]
F[107,x] = F[108,x]*F[17,x]
F[108,x] = F[1,x]+F[109,x]+F[37,x]+F[78,x]
F[109,x] = F[106,x]*F[17,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{17}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)+F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{103}\! \left(x \right)+F_{11}\! \left(x \right)+F_{12}\! \left(x \right)+F_{24}\! \left(x \right)
F_{11}\! \left(x \right) = 0
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{23}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2} F_{22} \left(x \right)^{2}+2 x^{2} F_{22}\! \left(x \right)-2 x F_{22} \left(x \right)^{2}+x^{2}-3 x F_{22}\! \left(x \right)-x +2 F_{22}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = y x
F_{32}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x \right) = F_{17}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = -\frac{-F_{39}\! \left(x , y\right) y +F_{39}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{78}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{75}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)+F_{91}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{31}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{85}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{60}\! \left(x \right) = F_{17}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{0}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)+F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = x^{2} F_{68} \left(x \right)^{2}-2 x F_{68} \left(x \right)^{2}+F_{68}\! \left(x \right) x +2 F_{68}\! \left(x \right)-1
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x , 1\right)
F_{52}\! \left(x , y\right) = F_{67}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{75}\! \left(x \right) = F_{17}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right) F_{76}\! \left(x \right)
F_{78}\! \left(x \right) = F_{17}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x , 1\right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = -\frac{-F_{80}\! \left(x , y\right) y +F_{80}\! \left(x , 1\right)}{-1+y}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{2}\! \left(x \right) F_{64}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-F_{52}\! \left(x , y\right) y +F_{52}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{-F_{49}\! \left(x , y\right) y +F_{49}\! \left(x , 1\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = -\frac{-F_{47}\! \left(x , y\right) y +F_{47}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = -\frac{-y F_{45}\! \left(x , y\right)+F_{45}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{37}\! \left(x \right)+F_{50}\! \left(x , y\right)+F_{78}\! \left(x \right)+F_{91}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{17}\! \left(x \right)
F_{102}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{64}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{17}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{37}\! \left(x \right)+F_{60}\! \left(x \right)+F_{78}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{17}\! \left(x \right)
F_{108}\! \left(x \right) = F_{1}\! \left(x \right)+F_{109}\! \left(x \right)+F_{37}\! \left(x \right)+F_{78}\! \left(x \right)
F_{109}\! \left(x \right) = F_{106}\! \left(x \right) F_{17}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_107(x) + F_5(x))
Eq(F_5(x), F_17(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_105(x) + F_37(x) + F_7(x))
Eq(F_7(x), F_17(x)*F_8(x))
Eq(F_8(x), F_6(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_103(x) + F_11(x) + F_12(x) + F_24(x))
Eq(F_11(x), 0)
Eq(F_12(x), F_13(x)*F_17(x))
Eq(F_13(x), F_14(x) + F_23(x))
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_1(x) + F_16(x) + F_18(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_4(x))
Eq(F_21(x), F_0(x)*F_22(x))
Eq(F_22(x), x*(x - 2)*(F_22(x) + 1)**2 + (x + 1)*(F_22(x) + 1) + F_22(x) - 1)
Eq(F_23(x), F_10(x))
Eq(F_24(x), F_17(x)*F_25(x))
Eq(F_25(x), F_26(x, 1))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_28(x, k_0), F_27(x, k_0) + F_8(x))
Eq(F_28(x, k_0), F_1(x) + F_29(x, k_0) + F_32(x, k_0) + F_35(x, k_0) + F_37(x) + F_99(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_31(x, k_0))
Eq(F_30(x, k_0), F_14(x) + F_26(x, k_0))
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x, k_0), F_17(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_13(x) + F_34(x, k_0))
Eq(F_34(x, k_0), F_26(x, k_0))
Eq(F_35(x, k_0), F_17(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_28(x, k_0) + F_28(x, 1))/(1 - k_0))
Eq(F_37(x), F_17(x)*F_38(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), F_1(x) + F_40(x, k_0) + F_41(x, k_0) + F_42(x, k_0) + F_44(x, k_0))
Eq(F_40(x, k_0), F_31(x, k_0)*F_39(x, k_0))
Eq(F_41(x, k_0), F_17(x)*F_28(x, k_0))
Eq(F_42(x, k_0), F_17(x)*F_43(x, k_0))
Eq(F_43(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_44(x, k_0), F_17(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_37(x) + F_46(x, k_0) + F_48(x, k_0) + F_78(x) + F_97(x, k_0))
Eq(F_46(x, k_0), F_31(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_1(x) + F_46(x, k_0) + F_48(x, k_0) + F_75(x) + F_95(x, k_0))
Eq(F_48(x, k_0), F_17(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0) + F_73(x) + F_75(x) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_0(x)*F_31(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0) + F_54(x, k_0) + F_89(x, k_0))
Eq(F_53(x, k_0), F_31(x, k_0)*F_52(x, k_0))
Eq(F_54(x, k_0), F_17(x)*F_55(x, k_0))
Eq(F_49(x, k_0), F_55(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x) + F_87(x, k_0))
Eq(F_57(x), F_58(x) + F_85(x))
Eq(F_58(x), F_59(x) - F_67(x))
Eq(F_59(x), F_1(x) + F_60(x) + F_73(x) + F_75(x))
Eq(F_60(x), F_17(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_0(x)*F_64(x))
Eq(F_64(x), F_11(x) + F_65(x) + F_70(x))
Eq(F_65(x), F_17(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_64(x) + F_68(x))
Eq(F_68(x), x*(x - 2)*F_68(x)**2 + (x + 2)*F_68(x) - 1)
Eq(F_69(x), F_64(x))
Eq(F_70(x), F_17(x)*F_71(x))
Eq(F_71(x), F_72(x, 1))
Eq(F_52(x, k_0), F_67(x) + F_72(x, k_0))
Eq(F_73(x), F_17(x)*F_74(x))
Eq(F_74(x), F_47(x, 1))
Eq(F_75(x), F_17(x)*F_76(x))
Eq(F_76(x), F_1(x) + F_37(x) + F_77(x) + F_78(x))
Eq(F_77(x), F_17(x)*F_76(x))
Eq(F_78(x), F_17(x)*F_79(x))
Eq(F_79(x), F_80(x, 1))
Eq(F_80(x, k_0), F_1(x) + F_42(x, k_0) + F_81(x, k_0) + F_82(x, k_0) + F_83(x, k_0))
Eq(F_81(x, k_0), F_31(x, k_0)*F_80(x, k_0))
Eq(F_82(x, k_0), F_17(x)*F_45(x, k_0))
Eq(F_83(x, k_0), F_17(x)*F_84(x, k_0))
Eq(F_84(x, k_0), (-k_0*F_80(x, k_0) + F_80(x, 1))/(1 - k_0))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_2(x)*F_64(x))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_2(x)*F_72(x, k_0))
Eq(F_89(x, k_0), F_17(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (-k_0*F_52(x, k_0) + F_52(x, 1))/(1 - k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_0(x)*F_17(x)*F_55(x, k_0))
Eq(F_93(x, k_0), F_17(x)*F_94(x, k_0))
Eq(F_94(x, k_0), (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Eq(F_95(x, k_0), F_17(x)*F_96(x, k_0))
Eq(F_96(x, k_0), (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_97(x, k_0), F_17(x)*F_98(x, k_0))
Eq(F_98(x, k_0), (-k_0*F_45(x, k_0) + F_45(x, 1))/(1 - k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_17(x))
Eq(F_100(x, k_0), F_1(x) + F_101(x) + F_37(x) + F_50(x, k_0) + F_78(x) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_101(x), F_102(x)*F_17(x))
Eq(F_102(x), F_45(x, 1))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_0(x)*F_17(x)*F_64(x))
Eq(F_105(x), F_106(x)*F_17(x))
Eq(F_106(x), F_1(x) + F_101(x) + F_37(x) + F_60(x) + F_78(x))
Eq(F_107(x), F_108(x)*F_17(x))
Eq(F_108(x), F_1(x) + F_109(x) + F_37(x) + F_78(x))
Eq(F_109(x), F_106(x)*F_17(x))
Pack JSON:
{"name": "point_and_col_placements_untracked_component_fusion_req_corrob", "initial_strats": [{"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.component", "strategy_class": "ComponentFusionFactory", "tracked": false, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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[0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 2], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[0, 3]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "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": []}, "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": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "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": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 2, 4], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": false}}, {"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"}}]}
Specification 5
Strategy pack name: insertion_row_placements_tracked_fusion_tracked_component_fusion_req_corrob
Tree: http://permpal.com/tree/25976/
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[8,x]
F[4,x] = F[43,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[18,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[10,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[8,x]
F[17,x] = F[1,x]+F[15,x]
F[18,x] = F[19,x]+F[31,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[8,x]
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[8,x]
F[29,x] = F[15,x]+F[26,x]
F[30,x] = F[22,x]*F[8,x]
F[31,x] = F[27,x]+F[32,x]+F[39,x]
F[32,x] = F[33,x]*F[8,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[11,x]
F[35,x] = F[36,x]
F[36,x] = F[27,x]+F[37,x]+F[39,x]
F[37,x] = F[38,x]*F[8,x]
F[38,x] = F[11,x]+F[36,x]
F[39,x] = F[40,x]*F[8,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[23,x]+F[36,x]
F[42,x] = F[26,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[45,x,1]
F[45,x,k[0]] = F[27,x]+F[46,x,k[0]]+F[85,x,k[0]]
F[46,x,k[0]] = -k[0]*(F[47,x,1]-F[47,x,k[0]])/(-1+k[0])
F[47,x,k[0]] = F[48,x,k[0]]*F[8,x]
F[48,x,k[0]] = F[45,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]*F[52,x,k[0]]
F[51,x,k[0]] = k[0]*x
F[52,x,k[0]] = F[53,x,k[0]]+F[61,x,k[0]]
F[53,x,k[0]] = F[1,x]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[51,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[53,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[51,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[1,x]+F[58,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[73,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[51,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[60,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[51,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[1,x]+F[66,x,k[0]]
F[69,x,k[0]] = F[27,x]+F[70,x,k[0]]+F[72,x,k[0]]
F[70,x,k[0]] = F[51,x,k[0]]*F[71,x,k[0]]
F[71,x,k[0]] = F[58,x,k[0]]+F[69,x,k[0]]
F[72,x,k[0]] = F[51,x,k[0]]*F[65,x,k[0]]
F[73,x,k[0]] = F[27,x]+F[74,x,k[0]]+F[81,x,k[0]]
F[74,x,k[0]] = F[51,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[77,x,k[0]]
F[76,x,k[0]] = F[54,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[27,x]+F[79,x,k[0]]+F[81,x,k[0]]
F[79,x,k[0]] = F[51,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[54,x,k[0]]+F[78,x,k[0]]
F[81,x,k[0]] = F[51,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[84,x,k[0]]
F[83,x,k[0]] = F[66,x,k[0]]+F[78,x,k[0]]
F[84,x,k[0]] = F[69,x,k[0]]
F[85,x,k[0]] = F[51,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[198,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[2,x]+F[88,x,k[0]]
F[88,x,k[0]] = F[194,x,k[0]]+F[27,x]+F[89,x,k[0]]
F[89,x,k[0]] = F[8,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[105,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[54,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[27,x]+F[93,x,k[0]]+F[99,x,k[0]]
F[93,x,k[0]] = -k[0]*(F[94,x,1]-F[94,x,k[0]])/(-1+k[0])
F[94,x,k[0]] = F[8,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[54,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[27,x]+F[93,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[51,x,k[0]]*F[60,x,k[0]]*F[8,x]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[51,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[104,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[6,x]
F[103,x,k[0]] = F[1,x]+F[51,x,k[0]]
F[104,x,k[0]] = F[58,x,k[0]]*F[8,x]
F[105,x,k[0]] = F[106,x,k[0]]+F[88,x,k[0]]
F[106,x,k[0]] = F[107,x,1,k[0]]
F[107,x,k[0],k[1]] = F[108,x,k[0],k[1]]+F[124,x,k[0],k[1]]+F[187,x,k[0],k[1]]+F[27,x]
F[108,x,k[0],k[1]] = -k[0]*(F[109,x,1,k[1]]-F[109,x,k[0],k[1]])/(-1+k[0])
F[109,x,k[0],k[1]] = F[110,x,k[0],k[1]]*F[8,x]
F[110,x,k[0],k[1]] = F[107,x,k[0],k[1]]+F[111,x,k[0],k[1]]
F[111,x,k[0],k[1]] = F[112,x,k[0],k[1]]+F[119,x,k[0],k[1]]+F[27,x]
F[112,x,k[0],k[1]] = k[1]*(F[113,x,k[0],1]-F[113,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[113,x,k[0],k[1]] = F[114,x,k[0],k[1]]*F[51,x,k[0]]
F[114,x,k[0],k[1]] = F[115,x,k[0],k[1]]+F[54,x,k[0]*k[1]]
F[115,x,k[0],k[1]] = F[116,x,k[0],k[0]*k[1]]
F[116,x,k[0],k[1]] = F[112,x,k[0],k[1]]+F[117,x,k[0],k[1]]+F[27,x]
F[117,x,k[0],k[1]] = F[118,x,k[0],k[1]]
F[118,x,k[0],k[1]] = F[51,x,k[0]]*F[51,x,k[1]]*F[60,x,k[1]]
F[119,x,k[0],k[1]] = F[120,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]*F[51,x,k[1]]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[122,x,k[0],k[1]] = F[103,x,k[1]]*F[49,x,k[0]]
F[123,x,k[0],k[1]] = F[51,x,k[0]]*F[58,x,k[1]]
F[124,x,k[0],k[1]] = k[1]*(F[125,x,k[0],1]-F[125,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[51,x,k[0]]
F[126,x,k[0],k[1]] = F[127,x,k[0],k[1]]+F[88,x,k[0]*k[1]]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[0]*k[1]]
F[128,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[129,x,k[0],k[1]]+F[185,x,k[0],k[1]]+F[27,x]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]*F[8,x]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[158,x,k[0],k[1]]
F[131,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[132,x,k[0],k[1]]
F[132,x,k[0],k[1]] = F[133,x,k[0],k[1]]+F[151,x,k[0],k[1]]+F[156,x,k[0],k[1]]+F[27,x]
F[133,x,k[0],k[1]] = F[134,x,1,k[0],k[1]]
F[134,x,k[0],k[1],k[2]] = F[135,x,k[0],k[0]*k[1],k[2]]
F[135,x,k[0],k[1],k[2]] = k[1]*(F[136,x,k[0],1,k[2]]-F[136,x,k[0],k[1]/k[0],k[2]])/(-k[1]+k[0])
F[136,x,k[0],k[1],k[2]] = F[137,x,k[0],k[1],k[2]]*F[51,x,k[0]]
F[137,x,k[0],k[1],k[2]] = F[138,x,k[0]*k[1],k[2]]+F[147,x,k[0],k[1],k[2]]
F[138,x,k[0],k[1]] = F[117,x,k[0],k[1]]+F[139,x,k[0],k[1]]+F[27,x]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]*F[51,x,k[0]]
F[140,x,k[0],k[1]] = F[141,x,k[0],k[1]]+F[142,x,k[0],k[1]]
F[141,x,k[0],k[1]] = F[138,x,k[0],k[1]]+F[54,x,k[1]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]+F[144,x,k[0],k[1]]
F[143,x,k[0],k[1]] = F[117,x,k[0],k[1]]
F[144,x,k[0],k[1]] = F[145,x,k[0],k[1]]
F[145,x,k[0],k[1]] = F[146,x,k[0],k[1]]*F[51,x,k[0]]
F[146,x,k[0],k[1]] = F[142,x,k[0],k[1]]
F[147,x,k[0],k[1],k[2]] = F[134,x,k[0],k[1],k[2]]+F[148,x,k[0],k[1],k[2]]+F[150,x,k[0],k[1],k[2]]+F[27,x]
F[148,x,k[0],k[1],k[2]] = F[149,x,k[0],k[1],k[2]]
F[149,x,k[0],k[1],k[2]] = F[51,x,k[0]]*F[51,x,k[1]]*F[58,x,k[2]]*F[60,x,k[1]]
F[150,x,k[0],k[1],k[2]] = 0
F[151,x,k[0],k[1]] = F[152,x,1,k[0],k[1]]
F[152,x,k[0],k[1],k[2]] = -k[0]*(F[153,x,1,k[1],k[2]]-F[153,x,k[0]/k[1],k[1],k[2]])/(-k[1]+k[0])
F[153,x,k[0],k[1],k[2]] = F[154,x,k[0],k[1],k[2]]*F[51,x,k[1]]
F[154,x,k[0],k[1],k[2]] = k[2]*(F[155,x,k[0],k[1],1]-F[155,x,k[0],k[1],k[2]/k[1]])/(-k[2]+k[1])
F[155,x,k[0],k[1],k[2]] = F[116,x,k[0]*k[1],k[1]*k[2]]
F[156,x,k[0],k[1]] = F[157,x,k[0],k[1]]
F[157,x,k[0],k[1]] = F[51,x,k[0]]*F[51,x,k[1]]*F[6,x]
F[158,x,k[0],k[1]] = F[128,x,k[0],k[1]]+F[159,x,k[0],k[1]]
F[159,x,k[0],k[1]] = F[160,x,1,k[0],k[1]]
F[160,x,k[0],k[1],k[2]] = F[161,x,k[0],k[1],k[2]]+F[167,x,k[0],k[1],k[2]]+F[179,x,k[0],k[1],k[2]]+F[183,x,k[0],k[1],k[2]]+F[27,x]
F[161,x,k[0],k[1],k[2]] = -k[0]*(F[162,x,1,k[1],k[2]]-F[162,x,k[0],k[1],k[2]])/(-1+k[0])
F[162,x,k[0],k[1],k[2]] = F[163,x,k[0],k[1],k[2]]*F[8,x]
F[163,x,k[0],k[1],k[2]] = F[160,x,k[0],k[1],k[2]]+F[164,x,k[0],k[1],k[2]]
F[164,x,k[0],k[1],k[2]] = F[135,x,k[0],k[1],k[2]]+F[152,x,k[0],k[1],k[2]]+F[165,x,k[0],k[1],k[2]]+F[27,x]
F[165,x,k[0],k[1],k[2]] = F[166,x,k[0],k[1],k[2]]
F[166,x,k[0],k[1],k[2]] = F[49,x,k[0]]*F[51,x,k[1]]*F[51,x,k[2]]
F[167,x,k[0],k[1],k[2]] = k[1]*(F[168,x,k[0],1,k[2]]-F[168,x,k[0],k[1]/k[0],k[2]])/(-k[1]+k[0])
F[168,x,k[0],k[1],k[2]] = F[169,x,k[0],k[1],k[2]]*F[51,x,k[0]]
F[169,x,k[0],k[1],k[2]] = F[170,x,k[0]*k[1],k[2]]+F[175,x,k[0],k[1],k[2]]
F[170,x,k[0],k[1]] = (F[171,x,k[0]]*k[1]-F[171,x,k[1]]*k[0])/(-k[1]+k[0])
F[172,x,k[0]] = (-F[171,x,1]*k[0]+F[171,x,k[0]])/(-1+k[0])
F[173,x,k[0]] = F[172,x,k[0]]+F[174,x]
F[173,x,k[0]] = (F[88,x,k[0]]-F[88,x,1])/(-1+k[0])
F[174,x] = F[88,x,1]
F[175,x,k[0],k[1],k[2]] = (-F[176,x,k[0],k[2]/k[0]]*k[0]*k[1]+F[176,x,k[0],k[1]]*k[2])/(k[0]*k[1]-k[2])
F[177,x,k[0],k[1]] = (-F[176,x,k[0],1]*k[1]+F[176,x,k[0],k[1]])/(-1+k[1])
F[178,x,k[0],k[1]] = F[127,x,k[0],k[1]]+F[177,x,k[0],k[1]]
F[178,x,k[0],k[1]] = -k[1]*(F[127,x,k[0],1]-F[127,x,k[0],k[1]])/(-1+k[1])
F[179,x,k[0],k[1],k[2]] = -k[0]*(F[180,x,1,k[1],k[2]]-F[180,x,k[0]/k[1],k[1],k[2]])/(-k[1]+k[0])
F[180,x,k[0],k[1],k[2]] = F[181,x,k[0],k[1],k[2]]*F[51,x,k[1]]
F[181,x,k[0],k[1],k[2]] = k[2]*(F[182,x,k[0],k[1],1]-F[182,x,k[0],k[1],k[2]/k[1]])/(-k[2]+k[1])
F[182,x,k[0],k[1],k[2]] = F[128,x,k[0]*k[1],k[1]*k[2]]
F[183,x,k[0],k[1],k[2]] = F[184,x,k[0],k[1],k[2]]
F[184,x,k[0],k[1],k[2]] = F[45,x,k[0]]*F[51,x,k[1]]*F[51,x,k[2]]
F[185,x,k[0],k[1]] = F[186,x,k[0],k[1]]
F[186,x,k[0],k[1]] = F[2,x]*F[51,x,k[0]]*F[51,x,k[1]]*F[60,x,k[1]]
F[187,x,k[0],k[1]] = F[188,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1]]*F[51,x,k[1]]
F[189,x,k[0],k[1]] = F[190,x,k[0],k[1]]+F[193,x,k[0],k[1]]
F[190,x,k[0],k[1]] = F[191,x,k[0],k[1]]+F[45,x,k[0]]
F[191,x,k[0],k[1]] = F[192,x,k[0],k[1]]
F[192,x,k[0],k[1]] = F[2,x]*F[51,x,k[0]]*F[58,x,k[1]]
F[193,x,k[0],k[1]] = F[45,x,k[0]]*F[51,x,k[1]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[2,x]*F[51,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[53,x,k[0]]
F[197,x,k[0]] = F[51,x,k[0]]*F[60,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[45,x,k[0]]
F[199,x,k[0]] = F[127,x,k[0],1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{43}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{39}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{42}\! \left(x \right) = F_{26}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{45}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{48}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{52}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = y_{0} x
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)+F_{61}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{58}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)+F_{73}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{66}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{70}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{71}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{65}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{74}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{79}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{83}\! \left(x , y_{0}\right)+F_{84}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{198}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{88}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{194}\! \left(x , y_{0}\right)+F_{27}\! \left(x \right)+F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{8}\! \left(x \right) F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{93}\! \left(x , y_{0}\right)+F_{99}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{94}\! \left(x , 1\right)-F_{94}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{94}\! \left(x , y_{0}\right) = F_{8}\! \left(x \right) F_{95}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right)+F_{93}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{99}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)+F_{104}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{6}\! \left(x \right)
F_{103}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{51}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x , 1, y_{0}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , y_{0}, y_{1}\right)+F_{187}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{109}\! \left(x , 1, y_{1}\right)-F_{109}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{109}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{110}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}, y_{1}\right)+F_{111}\! \left(x , y_{0}, y_{1}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x , y_{0}, y_{1}\right)+F_{119}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)
F_{112}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{113}\! \left(x , y_{0}, 1\right)-F_{113}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{0}, y_{1}\right)+F_{54}\! \left(x , y_{0} y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x , y_{0}, y_{1}\right)+F_{117}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \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_{51}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{60}\! \left(x , y_{1}\right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{120}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{1}\right)
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{103}\! \left(x , y_{1}\right) F_{49}\! \left(x , y_{0}\right)
F_{123}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{1}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{125}\! \left(x , y_{0}, 1\right)-F_{125}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{88}\! \left(x , y_{0} y_{1}\right)
F_{127}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{128}\! \left(x , y_{0}, y_{1}\right) = F_{124}\! \left(x , y_{0}, y_{1}\right)+F_{129}\! \left(x , y_{0}, y_{1}\right)+F_{185}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = F_{130}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{158}\! \left(x , y_{0}, y_{1}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)+F_{132}\! \left(x , y_{0}, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}\right) = F_{133}\! \left(x , y_{0}, y_{1}\right)+F_{151}\! \left(x , y_{0}, y_{1}\right)+F_{156}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , 1, y_{0}, y_{1}\right)
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{135}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} \left(F_{136}\! \left(x , y_{0}, 1, y_{2}\right)-F_{136}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)\right)}{-y_{1}+y_{0}}
F_{136}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{51}\! \left(x , y_{0}\right)
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{138}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{138}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{1}\right)+F_{139}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x \right)
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{140}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{0}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{142}\! \left(x , y_{0}, y_{1}\right)
F_{141}\! \left(x , y_{0}, y_{1}\right) = F_{138}\! \left(x , y_{0}, y_{1}\right)+F_{54}\! \left(x , y_{1}\right)
F_{142}\! \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_{143}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{1}\right)
F_{144}\! \left(x , y_{0}, y_{1}\right) = F_{145}\! \left(x , y_{0}, y_{1}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = F_{146}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{0}\right)
F_{146}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , y_{0}, y_{1}\right)
F_{147}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{148}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x \right)
F_{148}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{51}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{58}\! \left(x , y_{2}\right) F_{60}\! \left(x , y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 0
F_{151}\! \left(x , y_{0}, y_{1}\right) = F_{152}\! \left(x , 1, y_{0}, y_{1}\right)
F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{153}\! \left(x , 1, y_{1}, y_{2}\right)-F_{153}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)\right)}{-y_{1}+y_{0}}
F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{51}\! \left(x , y_{1}\right)
F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} \left(F_{155}\! \left(x , y_{0}, y_{1}, 1\right)-F_{155}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)\right)}{-y_{2}+y_{1}}
F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{116}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{0}, y_{1}\right)
F_{157}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{6}\! \left(x \right)
F_{158}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{159}\! \left(x , y_{0}, y_{1}\right)
F_{159}\! \left(x , y_{0}, y_{1}\right) = F_{160}\! \left(x , 1, y_{0}, y_{1}\right)
F_{160}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{161}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{179}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{183}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x \right)
F_{161}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{162}\! \left(x , 1, y_{1}, y_{2}\right)-F_{162}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{162}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{163}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{163}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{160}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{164}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{164}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{165}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x \right)
F_{165}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{166}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{166}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{49}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{51}\! \left(x , y_{2}\right)
F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} \left(F_{168}\! \left(x , y_{0}, 1, y_{2}\right)-F_{168}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)\right)}{-y_{1}+y_{0}}
F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{51}\! \left(x , y_{0}\right)
F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{170}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{171}\! \left(x , y_{0}\right) y_{1}-F_{171}\! \left(x , y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{172}\! \left(x , y_{0}\right) = -\frac{F_{171}\! \left(x , 1\right) y_{0}-F_{171}\! \left(x , y_{0}\right)}{-1+y_{0}}
F_{173}\! \left(x , y_{0}\right) = F_{172}\! \left(x , y_{0}\right)+F_{174}\! \left(x \right)
F_{173}\! \left(x , y_{0}\right) = -\frac{-F_{88}\! \left(x , y_{0}\right)+F_{88}\! \left(x , 1\right)}{-1+y_{0}}
F_{174}\! \left(x \right) = F_{88}\! \left(x , 1\right)
F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-F_{176}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right) y_{0} y_{1}+F_{176}\! \left(x , y_{0}, y_{1}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{177}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{176}\! \left(x , y_{0}, 1\right) y_{1}-F_{176}\! \left(x , y_{0}, y_{1}\right)}{-1+y_{1}}
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{127}\! \left(x , y_{0}, y_{1}\right)+F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{127}\! \left(x , y_{0}, 1\right)-F_{127}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{179}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{180}\! \left(x , 1, y_{1}, y_{2}\right)-F_{180}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)\right)}{-y_{1}+y_{0}}
F_{180}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{181}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{51}\! \left(x , y_{1}\right)
F_{181}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} \left(F_{182}\! \left(x , y_{0}, y_{1}, 1\right)-F_{182}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)\right)}{-y_{2}+y_{1}}
F_{182}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{128}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{183}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{184}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{184}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{45}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{51}\! \left(x , y_{2}\right)
F_{185}\! \left(x , y_{0}, y_{1}\right) = F_{186}\! \left(x , y_{0}, y_{1}\right)
F_{186}\! \left(x , y_{0}, y_{1}\right) = F_{2}\! \left(x \right) F_{51}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{1}\right) F_{60}\! \left(x , y_{1}\right)
F_{187}\! \left(x , y_{0}, y_{1}\right) = F_{188}\! \left(x , y_{0}, y_{1}\right)
F_{188}\! \left(x , y_{0}, y_{1}\right) = F_{189}\! \left(x , y_{0}, y_{1}\right) F_{51}\! \left(x , y_{1}\right)
F_{189}\! \left(x , y_{0}, y_{1}\right) = F_{190}\! \left(x , y_{0}, y_{1}\right)+F_{193}\! \left(x , y_{0}, y_{1}\right)
F_{190}\! \left(x , y_{0}, y_{1}\right) = F_{191}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}\right)
F_{191}\! \left(x , y_{0}, y_{1}\right) = F_{192}\! \left(x , y_{0}, y_{1}\right)
F_{192}\! \left(x , y_{0}, y_{1}\right) = F_{2}\! \left(x \right) F_{51}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{1}\right)
F_{193}\! \left(x , y_{0}, y_{1}\right) = F_{45}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{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_{2}\! \left(x \right) F_{51}\! \left(x , y_{0}\right)
F_{196}\! \left(x , y_{0}\right) = F_{197}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{197}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}\right)
F_{198}\! \left(x , y_{0}\right) = F_{199}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{199}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}, 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_43(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_18(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_10(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_8(x))
Eq(F_17(x), F_1(x) + F_15(x))
Eq(F_18(x), F_19(x) + F_31(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_8(x))
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_8(x))
Eq(F_29(x), F_15(x) + F_26(x))
Eq(F_30(x), F_22(x)*F_8(x))
Eq(F_31(x), F_27(x) + F_32(x) + F_39(x))
Eq(F_32(x), F_33(x)*F_8(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_11(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_27(x) + F_37(x) + F_39(x))
Eq(F_37(x), F_38(x)*F_8(x))
Eq(F_38(x), F_11(x) + F_36(x))
Eq(F_39(x), F_40(x)*F_8(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_23(x) + F_36(x))
Eq(F_42(x), F_26(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_45(x, 1))
Eq(F_45(x, k_0), F_27(x) + F_46(x, k_0) + F_85(x, k_0))
Eq(F_46(x, k_0), -F_47(x, 1) + (k_0*F_47(x, k_0) - F_47(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), F_48(x, k_0)*F_8(x))
Eq(F_48(x, k_0), F_45(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0)*F_52(x, k_0))
Eq(F_51(x, k_0), k_0*x)
Eq(F_52(x, k_0), F_53(x, k_0) + F_61(x, k_0))
Eq(F_53(x, k_0), F_1(x) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_51(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_53(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_51(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_1(x) + F_58(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_73(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_51(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_60(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_51(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_1(x) + F_66(x, k_0))
Eq(F_69(x, k_0), F_27(x) + F_70(x, k_0) + F_72(x, k_0))
Eq(F_70(x, k_0), F_51(x, k_0)*F_71(x, k_0))
Eq(F_71(x, k_0), F_58(x, k_0) + F_69(x, k_0))
Eq(F_72(x, k_0), F_51(x, k_0)*F_65(x, k_0))
Eq(F_73(x, k_0), F_27(x) + F_74(x, k_0) + F_81(x, k_0))
Eq(F_74(x, k_0), F_51(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_77(x, k_0))
Eq(F_76(x, k_0), F_54(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_27(x) + F_79(x, k_0) + F_81(x, k_0))
Eq(F_79(x, k_0), F_51(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_54(x, k_0) + F_78(x, k_0))
Eq(F_81(x, k_0), F_51(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_84(x, k_0))
Eq(F_83(x, k_0), F_66(x, k_0) + F_78(x, k_0))
Eq(F_84(x, k_0), F_69(x, k_0))
Eq(F_85(x, k_0), F_51(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_198(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_2(x) + F_88(x, k_0))
Eq(F_88(x, k_0), F_194(x, k_0) + F_27(x) + F_89(x, k_0))
Eq(F_89(x, k_0), F_8(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_105(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_54(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_27(x) + F_93(x, k_0) + F_99(x, k_0))
Eq(F_93(x, k_0), -F_94(x, 1) + (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_94(x, k_0), F_8(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_54(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_27(x) + F_93(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_51(x, k_0)*F_60(x, k_0)*F_8(x))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_51(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_104(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_6(x))
Eq(F_103(x, k_0), F_1(x) + F_51(x, k_0))
Eq(F_104(x, k_0), F_58(x, k_0)*F_8(x))
Eq(F_105(x, k_0), F_106(x, k_0) + F_88(x, k_0))
Eq(F_106(x, k_0), F_107(x, 1, k_0))
Eq(F_107(x, k_0, k_1), F_108(x, k_0, k_1) + F_124(x, k_0, k_1) + F_187(x, k_0, k_1) + F_27(x))
Eq(F_108(x, k_0, k_1), -F_109(x, 1, k_1) + (k_0*F_109(x, k_0, k_1) - F_109(x, 1, k_1))/(k_0 - 1))
Eq(F_109(x, k_0, k_1), F_110(x, k_0, k_1)*F_8(x))
Eq(F_110(x, k_0, k_1), F_107(x, k_0, k_1) + F_111(x, k_0, k_1))
Eq(F_111(x, k_0, k_1), F_112(x, k_0, k_1) + F_119(x, k_0, k_1) + F_27(x))
Eq(F_112(x, k_0, k_1), -F_113(x, k_0, 1) + (-k_0*F_113(x, k_0, 1) + k_1*F_113(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_113(x, k_0, k_1), F_114(x, k_0, k_1)*F_51(x, k_0))
Eq(F_114(x, k_0, k_1), F_115(x, k_0, k_1) + F_54(x, k_0*k_1))
Eq(F_115(x, k_0, k_1), F_116(x, k_0, k_0*k_1))
Eq(F_116(x, k_0, k_1), F_112(x, k_0, k_1) + F_117(x, k_0, k_1) + F_27(x))
Eq(F_117(x, k_0, k_1), F_118(x, k_0, k_1))
Eq(F_118(x, k_0, k_1), F_51(x, k_0)*F_51(x, k_1)*F_60(x, k_1))
Eq(F_119(x, k_0, k_1), F_120(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1)*F_51(x, k_1))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_122(x, k_0, k_1), F_103(x, k_1)*F_49(x, k_0))
Eq(F_123(x, k_0, k_1), F_51(x, k_0)*F_58(x, k_1))
Eq(F_124(x, k_0, k_1), -F_125(x, k_0, 1) + (-k_0*F_125(x, k_0, 1) + k_1*F_125(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1)*F_51(x, k_0))
Eq(F_126(x, k_0, k_1), F_127(x, k_0, k_1) + F_88(x, k_0*k_1))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_0*k_1))
Eq(F_128(x, k_0, k_1), F_124(x, k_0, k_1) + F_129(x, k_0, k_1) + F_185(x, k_0, k_1) + F_27(x))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1)*F_8(x))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1) + F_158(x, k_0, k_1))
Eq(F_131(x, k_0, k_1), F_116(x, k_0, k_1) + F_132(x, k_0, k_1))
Eq(F_132(x, k_0, k_1), F_133(x, k_0, k_1) + F_151(x, k_0, k_1) + F_156(x, k_0, k_1) + F_27(x))
Eq(F_133(x, k_0, k_1), F_134(x, 1, k_0, k_1))
Eq(F_134(x, k_0, k_1, k_2), F_135(x, k_0, k_0*k_1, k_2))
Eq(F_135(x, k_0, k_1, k_2), -F_136(x, k_0, 1, k_2) + (-k_0*F_136(x, k_0, 1, k_2) + k_1*F_136(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_136(x, k_0, k_1, k_2), F_137(x, k_0, k_1, k_2)*F_51(x, k_0))
Eq(F_137(x, k_0, k_1, k_2), F_138(x, k_0*k_1, k_2) + F_147(x, k_0, k_1, k_2))
Eq(F_138(x, k_0, k_1), F_117(x, k_0, k_1) + F_139(x, k_0, k_1) + F_27(x))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1)*F_51(x, k_0))
Eq(F_140(x, k_0, k_1), F_141(x, k_0, k_1) + F_142(x, k_0, k_1))
Eq(F_141(x, k_0, k_1), F_138(x, k_0, k_1) + F_54(x, k_1))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1) + F_144(x, k_0, k_1))
Eq(F_143(x, k_0, k_1), F_117(x, k_0, k_1))
Eq(F_144(x, k_0, k_1), F_145(x, k_0, k_1))
Eq(F_145(x, k_0, k_1), F_146(x, k_0, k_1)*F_51(x, k_0))
Eq(F_146(x, k_0, k_1), F_142(x, k_0, k_1))
Eq(F_147(x, k_0, k_1, k_2), F_134(x, k_0, k_1, k_2) + F_148(x, k_0, k_1, k_2) + F_150(x, k_0, k_1, k_2) + F_27(x))
Eq(F_148(x, k_0, k_1, k_2), F_149(x, k_0, k_1, k_2))
Eq(F_149(x, k_0, k_1, k_2), F_51(x, k_0)*F_51(x, k_1)*F_58(x, k_2)*F_60(x, k_1))
Eq(F_150(x, k_0, k_1, k_2), 0)
Eq(F_151(x, k_0, k_1), F_152(x, 1, k_0, k_1))
Eq(F_152(x, k_0, k_1, k_2), -F_153(x, 1, k_1, k_2) + (-k_0*F_153(x, k_0/k_1, k_1, k_2) + k_1*F_153(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_153(x, k_0, k_1, k_2), F_154(x, k_0, k_1, k_2)*F_51(x, k_1))
Eq(F_154(x, k_0, k_1, k_2), -F_155(x, k_0, k_1, 1) + (-k_1*F_155(x, k_0, k_1, 1) + k_2*F_155(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_155(x, k_0, k_1, k_2), F_116(x, k_0*k_1, k_1*k_2))
Eq(F_156(x, k_0, k_1), F_157(x, k_0, k_1))
Eq(F_157(x, k_0, k_1), F_51(x, k_0)*F_51(x, k_1)*F_6(x))
Eq(F_158(x, k_0, k_1), F_128(x, k_0, k_1) + F_159(x, k_0, k_1))
Eq(F_159(x, k_0, k_1), F_160(x, 1, k_0, k_1))
Eq(F_160(x, k_0, k_1, k_2), F_161(x, k_0, k_1, k_2) + F_167(x, k_0, k_1, k_2) + F_179(x, k_0, k_1, k_2) + F_183(x, k_0, k_1, k_2) + F_27(x))
Eq(F_161(x, k_0, k_1, k_2), -F_162(x, 1, k_1, k_2) + (k_0*F_162(x, k_0, k_1, k_2) - F_162(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_162(x, k_0, k_1, k_2), F_163(x, k_0, k_1, k_2)*F_8(x))
Eq(F_163(x, k_0, k_1, k_2), F_160(x, k_0, k_1, k_2) + F_164(x, k_0, k_1, k_2))
Eq(F_164(x, k_0, k_1, k_2), F_135(x, k_0, k_1, k_2) + F_152(x, k_0, k_1, k_2) + F_165(x, k_0, k_1, k_2) + F_27(x))
Eq(F_165(x, k_0, k_1, k_2), F_166(x, k_0, k_1, k_2))
Eq(F_166(x, k_0, k_1, k_2), F_49(x, k_0)*F_51(x, k_1)*F_51(x, k_2))
Eq(F_167(x, k_0, k_1, k_2), -F_168(x, k_0, 1, k_2) + (-k_0*F_168(x, k_0, 1, k_2) + k_1*F_168(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_168(x, k_0, k_1, k_2), F_169(x, k_0, k_1, k_2)*F_51(x, k_0))
Eq(F_169(x, k_0, k_1, k_2), F_170(x, k_0*k_1, k_2) + F_175(x, k_0, k_1, k_2))
Eq(F_170(x, k_0, k_1), -F_171(x, k_0) - F_171(x, k_1) + (-k_0*F_171(x, k_0) + k_1*F_171(x, k_1))/(-k_0 + k_1))
Eq(F_172(x, k_0), -F_171(x, 1) - F_171(x, k_0) + (-k_0*F_171(x, k_0) + F_171(x, 1))/(1 - k_0))
Eq(F_173(x, k_0), F_172(x, k_0) + F_174(x))
Eq(F_173(x, k_0), -F_88(x, k_0) + (-k_0*F_88(x, k_0) + F_88(x, 1))/(1 - k_0))
Eq(F_174(x), F_88(x, 1))
Eq(F_175(x, k_0, k_1, k_2), -F_176(x, k_0, k_1) - F_176(x, k_0, k_2/k_0) + (-k_0*k_1*F_176(x, k_0, k_1) + k_2*F_176(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_177(x, k_0, k_1), -F_176(x, k_0, 1) - F_176(x, k_0, k_1) + (k_1*F_176(x, k_0, k_1) - F_176(x, k_0, 1))/(k_1 - 1))
Eq(F_178(x, k_0, k_1), F_127(x, k_0, k_1) + F_177(x, k_0, k_1))
Eq(F_178(x, k_0, k_1), -F_127(x, k_0, 1) + (k_1*F_127(x, k_0, k_1) - F_127(x, k_0, 1))/(k_1 - 1))
Eq(F_179(x, k_0, k_1, k_2), -F_180(x, 1, k_1, k_2) + (-k_0*F_180(x, k_0/k_1, k_1, k_2) + k_1*F_180(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_180(x, k_0, k_1, k_2), F_181(x, k_0, k_1, k_2)*F_51(x, k_1))
Eq(F_181(x, k_0, k_1, k_2), -F_182(x, k_0, k_1, 1) + (-k_1*F_182(x, k_0, k_1, 1) + k_2*F_182(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_182(x, k_0, k_1, k_2), F_128(x, k_0*k_1, k_1*k_2))
Eq(F_183(x, k_0, k_1, k_2), F_184(x, k_0, k_1, k_2))
Eq(F_184(x, k_0, k_1, k_2), F_45(x, k_0)*F_51(x, k_1)*F_51(x, k_2))
Eq(F_185(x, k_0, k_1), F_186(x, k_0, k_1))
Eq(F_186(x, k_0, k_1), F_2(x)*F_51(x, k_0)*F_51(x, k_1)*F_60(x, k_1))
Eq(F_187(x, k_0, k_1), F_188(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1)*F_51(x, k_1))
Eq(F_189(x, k_0, k_1), F_190(x, k_0, k_1) + F_193(x, k_0, k_1))
Eq(F_190(x, k_0, k_1), F_191(x, k_0, k_1) + F_45(x, k_0))
Eq(F_191(x, k_0, k_1), F_192(x, k_0, k_1))
Eq(F_192(x, k_0, k_1), F_2(x)*F_51(x, k_0)*F_58(x, k_1))
Eq(F_193(x, k_0, k_1), F_45(x, k_0)*F_51(x, k_1))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_2(x)*F_51(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_53(x, k_0))
Eq(F_197(x, k_0), F_51(x, k_0)*F_60(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_45(x, k_0))
Eq(F_199(x, k_0), F_127(x, k_0, 1))
Pack JSON:
{"name": "insertion_row_placements_tracked_fusion_tracked_component_fusion_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"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.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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