02143_02413_02431_03214_03241_10243_10324_13024_30214_30241_31024
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, 1524831750, 8348277636, 45946421502, 254062504188, 1410766557732, 7863526070976, 43981872758514, 246769406256708, 1388526164228364, 7833576838654440, 44301614143740804, 251103453421282792, 1426226511474610404, 8116400731065294084, 46272243349012312565, 264245918837510282298, 1511402546925080517750, 8657528111737752337540, 49660504949699021334006, 285230998269767803566060, 1640282170384822387415908, 9443808789932257989919152, 54432148329534802223495814, 314064205693137675126104492, 1813898557618826325557820900, 10486190902491724502787091512, 60675436378907865063339251116, 351382410176828793703873494552, 2036582165232136621175037811632, 11813067174731004173699168460984, 68572075525046298167213706688962, 398328912948873194436373813364004, 2315438220925659971252689663664988, 13468186510699453005828960604579176, 78389532700704287810944844803094700, 456529890188743772629919482174967640, 2660310561188043024800231995384614696, 15510929214993194348328530173849912512, 90484994925655097164540888784573405508, 528128990887630970239817033058909030216, 3084040156569815828520111474896608657944, 18018097383148861855204782171555817396368, 105317233323857114456738711088347500853496, 615863762637233386715555713084167053445072, 3602948031641232601061546318620913454398604, 21086924778690136675179427684014256972751508, 123465174476725835448609474922307700037185621, 723179374040313046343580238862573886622028922, 4237527618702041852163369225462770551320341334, 24839272997664166834847468560120354233806095236, 145653242325277691004756433542158573215713107622, 854381232960312069250922270765573014105862069580, 5013361820960476584334403145829875971689244235300, 29427132047195323795774596447283237466973590810064, 172784302747517594798354287638767211430861346651262, 1014832067689881307099930810122312254203835807929116, 5962300855073194291165355182503867351817883813281140, 35039654096333817345139048747296727152265239440893080, 205981640083180381091607826711088610564009563803240572, 1211202305019883772438645560636651254084858129850721592, 7123955037726453146682377704304715649798400901501241920, 41912050499032522644688792149013223187147143851982688456, 246641968036519530489992834026955812570091732503116776982, 1451785848542283446363209056320847129677067259199464763148, 8547575466562250840489759821576835974411410249714267014196, 50336790803847017824337316476914472342928647325415877488504, 296502108672870791059842748031827489294577961345231033219588, 1746897045741607175694584569071557488098530074563953052272136, 10294417137284375104877952893270234000586989465418260450724152, 60677669351019158430352226420893116538424335977561872478849024, 357722720752362014444372372616372784920970864747123529589828348, 2109369045426169472922404646247334724655379144890147125092791096, 12440705134879612882577885305477278875510214009174624648857445672, 73387459591442332531927950929488870582012785685892063856577458864, 432993374803063562896494350407766468543979062444086650672384574456, 2555179183679798034048415442244727617696012582846175955974962597552, 15081356823959205426722816664736612385645656081234231377982262469960, 89030068132751292199060113717891274176879410324989281721142687873960, 525664413168816268379577242311109788452059485949159829480533300386914, 3104233822753861057747011550092834098292202313819210127721190198429412, 18334653346156182599330765168741568434730775512881764902537969968946556, 108308340899624625224190175279542858061954310688165737400342825828802920, 639912464528427363384713874312826141635485413486198251727484486574871740, 3781353591094030008664252738390183857043163609248437599225214167180067192, 22348104504712924163537883807639275463021957863337851229771407035834784040, 132098976270016990310621039686659940472332892107718287458165575876617774176
Specification 1
Strategy pack name: insertion_point_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/24242/
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[0,x]+F[5,x]
F[5,x] = F[51,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[27,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[18,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[20,x]+F[25,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[8,x]
F[21,x] = F[15,x]+F[22,x]
F[22,x] = F[19,x]+F[20,x]+F[23,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[15,x]+F[22,x]
F[25,x] = F[26,x]*F[8,x]
F[26,x] = F[14,x]
F[27,x] = F[28,x]+F[34,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[17,x]+F[31,x]
F[31,x] = F[28,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[8,x]
F[34,x] = F[19,x]+F[35,x]+F[45,x]
F[35,x] = F[36,x]*F[8,x]
F[36,x] = F[21,x]+F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[19,x]+F[35,x]+F[39,x]
F[39,x] = F[40,x]*F[8,x]
F[40,x] = F[28,x]+F[38,x]
F[41,x] = 2*F[19,x]+F[42,x]+F[43,x]
F[42,x] = F[37,x]*F[8,x]
F[43,x] = F[44,x]*F[8,x]
F[44,x] = F[32,x]+F[41,x]
F[45,x] = F[46,x]*F[8,x]
F[46,x] = F[27,x]+F[47,x]
F[47,x] = F[32,x]+F[48,x]
F[48,x] = 2*F[19,x]+F[42,x]+F[49,x]
F[49,x] = F[50,x]*F[8,x]
F[50,x] = F[47,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[8,x]
F[53,x] = F[122,x]+F[54,x]
F[54,x] = F[119,x]+F[55,x]
F[55,x] = F[28,x]+F[56,x]
F[56,x] = F[57,x,1]
F[57,x,k[0]] = F[2,x]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]*F[67,x,k[0]]*F[68,x,k[0]]
F[60,x,k[0]] = F[57,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[71,x,k[0]]
F[62,x,k[0]] = F[6,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[28,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]*F[67,x,k[0]]*F[68,x,k[0]]
F[66,x,k[0]] = F[1,x]+F[64,x,k[0]]
F[67,x,k[0]] = k[0]*x
F[68,x,k[0]] = F[1,x]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[67,x,k[0]]*F[68,x,k[0]]
F[71,x,k[0]] = F[51,x]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[8,x]
F[74,x,k[0]] = F[103,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[95,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[94,x,k[0]]
F[77,x,k[0]] = F[19,x]+F[78,x,k[0]]+F[89,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]*F[8,x]
F[79,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[80,x,k[0]] = F[69,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[8,x]*F[80,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[87,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[67,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[28,x]+F[84,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[8,x]*F[83,x,k[0]]
F[89,x,k[0]] = F[67,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[77,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[67,x,k[0]]*F[91,x,k[0]]
F[94,x,k[0]] = -k[0]*(F[58,x,1]-F[58,x,k[0]])/(-1+k[0])
F[95,x,k[0]] = F[102,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = (-F[97,x,1]*k[0]+F[97,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[28,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[67,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[69,x,k[0]]
F[101,x,k[0]] = F[64,x,k[0]]*F[68,x,k[0]]
F[102,x,k[0]] = -k[0]*(F[72,x,1]-F[72,x,k[0]])/(-1+k[0])
F[103,x,k[0]] = F[104,x,k[0]]+F[111,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]
F[105,x,k[0]] = (-F[106,x,1]*k[0]+F[106,x,k[0]])/(-1+k[0])
F[106,x,k[0]] = F[15,x]*F[98,x,k[0]]
F[107,x,k[0]] = -k[0]*(F[108,x,1]-F[108,x,k[0]])/(-1+k[0])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[8,x]
F[110,x,k[0]] = F[104,x,k[0]]+F[76,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[115,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = (-F[114,x,1]*k[0]+F[114,x,k[0]])/(-1+k[0])
F[114,x,k[0]] = F[15,x]*F[28,x]*F[98,x,k[0]]
F[115,x,k[0]] = -k[0]*(F[116,x,1]-F[116,x,k[0]])/(-1+k[0])
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[8,x]
F[118,x,k[0]] = F[111,x,k[0]]+F[95,x,k[0]]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[28,x]^2
F[121,x] = F[71,x,1]
F[122,x] = F[123,x]+F[129,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[15,x]*F[28,x]
F[125,x] = F[126,x]+F[51,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x,1]
F[128,x,k[0]] = F[108,x,k[0]]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]
F[131,x] = F[28,x]^2*F[15,x]
F[132,x] = F[133,x]+F[150,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[8,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[15,x]*F[55,x]
F[139,x] = F[119,x]*F[17,x]
F[140,x] = F[141,x]+F[147,x]
F[141,x] = F[142,x]*F[15,x]
F[142,x] = F[124,x]+F[143,x]
F[143,x] = F[126,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[8,x]
F[146,x] = F[142,x]+F[55,x]
F[147,x] = F[148,x]*F[17,x]
F[148,x] = F[130,x]+F[149,x]
F[149,x] = F[134,x]+F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x,1]
F[152,x,k[0]] = F[116,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{51}\! \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_{27}\! \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_{18}\! \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_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{34}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{8}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{45}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{8}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{37}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{8}\! \left(x \right)
F_{46}\! \left(x \right) = F_{27}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{122}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{119}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{28}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{57}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = y x
F_{68}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{51}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{y \left(F_{58}\! \left(x , 1\right)-F_{58}\! \left(x , y\right)\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = -\frac{F_{97}\! \left(x , 1\right) y -F_{97}\! \left(x , y\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = -\frac{y \left(F_{72}\! \left(x , 1\right)-F_{72}\! \left(x , y\right)\right)}{-1+y}
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = -\frac{F_{106}\! \left(x , 1\right) y -F_{106}\! \left(x , y\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = -\frac{y \left(F_{108}\! \left(x , 1\right)-F_{108}\! \left(x , y\right)\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = -\frac{F_{114}\! \left(x , 1\right) y -F_{114}\! \left(x , y\right)}{-1+y}
F_{114}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = -\frac{y \left(F_{116}\! \left(x , 1\right)-F_{116}\! \left(x , y\right)\right)}{-1+y}
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{28} \left(x \right)^{2}
F_{121}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{129}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{51}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x , 1\right)
F_{128}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{150}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{8}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{139}\! \left(x \right) = F_{119}\! \left(x \right) F_{17}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{147}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right)
F_{142}\! \left(x \right) = F_{124}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{126}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{8}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right)+F_{55}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{17}\! \left(x \right)
F_{148}\! \left(x \right) = F_{130}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{134}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x , 1\right)
F_{152}\! \left(x , y\right) = F_{116}\! \left(x , y\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_0(x) + F_5(x))
Eq(F_5(x), F_51(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_27(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) + F_18(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_20(x) + F_25(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_8(x))
Eq(F_21(x), F_15(x) + F_22(x))
Eq(F_22(x), F_19(x) + F_20(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_15(x) + F_22(x))
Eq(F_25(x), F_26(x)*F_8(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_28(x) + F_34(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_17(x) + F_31(x))
Eq(F_31(x), F_28(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_8(x))
Eq(F_34(x), F_19(x) + F_35(x) + F_45(x))
Eq(F_35(x), F_36(x)*F_8(x))
Eq(F_36(x), F_21(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_19(x) + F_35(x) + F_39(x))
Eq(F_39(x), F_40(x)*F_8(x))
Eq(F_40(x), F_28(x) + F_38(x))
Eq(F_41(x), 2*F_19(x) + F_42(x) + F_43(x))
Eq(F_42(x), F_37(x)*F_8(x))
Eq(F_43(x), F_44(x)*F_8(x))
Eq(F_44(x), F_32(x) + F_41(x))
Eq(F_45(x), F_46(x)*F_8(x))
Eq(F_46(x), F_27(x) + F_47(x))
Eq(F_47(x), F_32(x) + F_48(x))
Eq(F_48(x), 2*F_19(x) + F_42(x) + F_49(x))
Eq(F_49(x), F_50(x)*F_8(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_8(x))
Eq(F_53(x), F_122(x) + F_54(x))
Eq(F_54(x), F_119(x) + F_55(x))
Eq(F_55(x), F_28(x) + F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_57(x, k_0), F_2(x) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0)*F_67(x, k_0)*F_68(x, k_0))
Eq(F_60(x, k_0), F_57(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_71(x, k_0))
Eq(F_62(x, k_0), F_6(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_28(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0)*F_67(x, k_0)*F_68(x, k_0))
Eq(F_66(x, k_0), F_1(x) + F_64(x, k_0))
Eq(F_67(x, k_0), k_0*x)
Eq(F_68(x, k_0), F_1(x) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_67(x, k_0)*F_68(x, k_0))
Eq(F_71(x, k_0), F_51(x) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_8(x))
Eq(F_74(x, k_0), F_103(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_95(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_94(x, k_0))
Eq(F_77(x, k_0), F_19(x) + F_78(x, k_0) + F_89(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0)*F_8(x))
Eq(F_79(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_80(x, k_0), F_69(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_8(x)*F_80(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_87(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_67(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_28(x) + F_84(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_8(x)*F_83(x, k_0))
Eq(F_89(x, k_0), F_67(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_77(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_67(x, k_0)*F_91(x, k_0))
Eq(F_94(x, k_0), -F_58(x, 1) + (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_95(x, k_0), F_102(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), -F_97(x, 1) - F_97(x, k_0) + (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_28(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_67(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_69(x, k_0))
Eq(F_101(x, k_0), F_64(x, k_0)*F_68(x, k_0))
Eq(F_102(x, k_0), -F_72(x, 1) + (k_0*F_72(x, k_0) - F_72(x, 1))/(k_0 - 1))
Eq(F_103(x, k_0), F_104(x, k_0) + F_111(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_107(x, k_0))
Eq(F_105(x, k_0), -F_106(x, 1) - F_106(x, k_0) + (k_0*F_106(x, k_0) - F_106(x, 1))/(k_0 - 1))
Eq(F_106(x, k_0), F_15(x)*F_98(x, k_0))
Eq(F_107(x, k_0), -F_108(x, 1) + (k_0*F_108(x, k_0) - F_108(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_8(x))
Eq(F_110(x, k_0), F_104(x, k_0) + F_76(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_115(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), -F_114(x, 1) - F_114(x, k_0) + (k_0*F_114(x, k_0) - F_114(x, 1))/(k_0 - 1))
Eq(F_114(x, k_0), F_15(x)*F_28(x)*F_98(x, k_0))
Eq(F_115(x, k_0), -F_116(x, 1) + (k_0*F_116(x, k_0) - F_116(x, 1))/(k_0 - 1))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_8(x))
Eq(F_118(x, k_0), F_111(x, k_0) + F_95(x, k_0))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_28(x)**2)
Eq(F_121(x), F_71(x, 1))
Eq(F_122(x), F_123(x) + F_129(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_15(x)*F_28(x))
Eq(F_125(x), F_126(x) + F_51(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x, 1))
Eq(F_128(x, k_0), F_108(x, k_0))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_15(x)*F_28(x)**2)
Eq(F_132(x), F_133(x) + F_150(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_8(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_15(x)*F_55(x))
Eq(F_139(x), F_119(x)*F_17(x))
Eq(F_140(x), F_141(x) + F_147(x))
Eq(F_141(x), F_142(x)*F_15(x))
Eq(F_142(x), F_124(x) + F_143(x))
Eq(F_143(x), F_126(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_8(x))
Eq(F_146(x), F_142(x) + F_55(x))
Eq(F_147(x), F_148(x)*F_17(x))
Eq(F_148(x), F_130(x) + F_149(x))
Eq(F_149(x), F_134(x) + F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x, 1))
Eq(F_152(x, k_0), F_116(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion_isolated", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
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"obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24243/
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[9,x]
F[3,x] = F[1,x]+F[4,x]+F[47,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[46,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0]]*F[13,x,k[1]]*F[16,x,k[1]]*F[17,x,k[1]]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = (F[17,x,k[0]]*k[0]-F[17,x,k[1]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[13,x,k[0]]*F[16,x,k[0]]*F[18,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[12,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[9,x]
F[23,x,k[0],k[1]] = (F[24,x,k[0]]*k[0]-F[24,x,k[1]]*k[1])/(-k[1]+k[0])
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[27,x,k[0]]+F[44,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[20,x,k[0],1]
F[27,x,k[0]] = F[28,x,k[0]]*F[9,x]
F[29,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[29,x,k[0]] = F[30,x,k[0],1]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[31,x,k[0],k[1]]*k[0]-F[31,x,1,k[1]])
F[31,x,k[0],k[1]] = F[1,x]+F[32,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[37,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[13,x,k[0]]*F[16,x,k[0]]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = (F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])/(-1+k[0])
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]*F[9,x]
F[36,x,k[0],k[1]] = 1/(-1+k[1])*(F[31,x,k[0],k[1]]*k[1]-F[31,x,k[0],1])
F[37,x,k[0],k[1]] = F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[13,x,k[0]]*F[13,x,k[1]]*F[16,x,k[1]]*F[17,x,k[1]]*F[39,x]
F[39,x] = F[1,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[39,x]*F[9,x]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]*F[9,x]
F[43,x,k[0],k[1]] = (F[23,x,k[0],k[1]]*k[0]-F[23,x,1,k[1]])/(-1+k[0])
F[44,x,k[0]] = F[45,x,k[0]]*F[9,x]
F[45,x,k[0]] = (F[24,x,k[0]]*k[0]-F[24,x,1])/(-1+k[0])
F[46,x,k[0]] = F[22,x,1,k[0]]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = F[24,x,k[0]]*F[9,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{47}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{13}\! \left(x , z\right) F_{16}\! \left(x , z\right) F_{17}\! \left(x , z\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = \frac{y F_{17}\! \left(x , y\right)-z F_{17}\! \left(x , z\right)}{-z +y}
F_{18}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{18}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{23}\! \left(x , y , z\right) = \frac{y F_{24}\! \left(x , y\right)-z F_{24}\! \left(x , z\right)}{-z +y}
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{20}\! \left(x , y , 1\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{29}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y , 1\right)
F_{30}\! \left(x , y , z\right) = -\frac{-y F_{31}\! \left(x , y , z\right)+F_{31}\! \left(x , 1, z\right)}{-1+y}
F_{31}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)+F_{42}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{36}\! \left(x , y , z\right) = -\frac{-z F_{31}\! \left(x , y , z\right)+F_{31}\! \left(x , y , 1\right)}{-1+z}
F_{37}\! \left(x , y , z\right) = F_{38}\! \left(x , y , z\right)
F_{38}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{13}\! \left(x , z\right) F_{16}\! \left(x , z\right) F_{17}\! \left(x , z\right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right) F_{9}\! \left(x \right)
F_{42}\! \left(x , y , z\right) = F_{43}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{43}\! \left(x , y , z\right) = -\frac{-y F_{23}\! \left(x , y , z\right)+F_{23}\! \left(x , 1, z\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{22}\! \left(x , 1, y\right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{9}\! \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)*F_9(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_47(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_46(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0)*F_13(x, k_1)*F_16(x, k_1)*F_17(x, k_1))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_13(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), (-k_0*F_17(x, k_0) + k_1*F_17(x, k_1))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_13(x, k_0)*F_16(x, k_0)*F_18(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_12(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_9(x))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0) + k_1*F_24(x, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_27(x, k_0) + F_44(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_20(x, k_0, 1))
Eq(F_27(x, k_0), F_28(x, k_0)*F_9(x))
Eq(F_29(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_30(x, k_0, 1))
Eq(F_30(x, k_0, k_1), (k_0*F_31(x, k_0, k_1) - F_31(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_1(x) + F_32(x, k_0, k_1) + F_35(x, k_0, k_1) + F_37(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_13(x, k_0)*F_16(x, k_0)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (-k_0*F_18(x, k_0, k_1) + F_18(x, 1, k_1))/(1 - k_0))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1)*F_9(x))
Eq(F_36(x, k_0, k_1), (k_1*F_31(x, k_0, k_1) - F_31(x, k_0, 1))/(k_1 - 1))
Eq(F_37(x, k_0, k_1), F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_13(x, k_0)*F_13(x, k_1)*F_16(x, k_1)*F_17(x, k_1)*F_39(x))
Eq(F_39(x), F_1(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_39(x)*F_9(x))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1)*F_9(x))
Eq(F_43(x, k_0, k_1), (-k_0*F_23(x, k_0, k_1) + F_23(x, 1, k_1))/(1 - k_0))
Eq(F_44(x, k_0), F_45(x, k_0)*F_9(x))
Eq(F_45(x, k_0), (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), F_22(x, 1, k_0))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), F_24(x, k_0)*F_9(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, 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0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 1, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "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]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"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, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 3
Strategy pack name: insertion_partial_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/24244/
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[0,x]+F[5,x]
F[5,x] = F[51,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[27,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[18,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[20,x]+F[25,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[8,x]
F[21,x] = F[15,x]+F[22,x]
F[22,x] = F[19,x]+F[20,x]+F[23,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[15,x]+F[22,x]
F[25,x] = F[26,x]*F[8,x]
F[26,x] = F[14,x]
F[27,x] = F[28,x]+F[34,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[17,x]+F[31,x]
F[31,x] = F[28,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[8,x]
F[34,x] = F[19,x]+F[35,x]+F[45,x]
F[35,x] = F[36,x]*F[8,x]
F[36,x] = F[21,x]+F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[19,x]+F[35,x]+F[39,x]
F[39,x] = F[40,x]*F[8,x]
F[40,x] = F[28,x]+F[38,x]
F[41,x] = 2*F[19,x]+F[42,x]+F[43,x]
F[42,x] = F[37,x]*F[8,x]
F[43,x] = F[44,x]*F[8,x]
F[44,x] = F[32,x]+F[41,x]
F[45,x] = F[46,x]*F[8,x]
F[46,x] = F[27,x]+F[47,x]
F[47,x] = F[32,x]+F[48,x]
F[48,x] = 2*F[19,x]+F[42,x]+F[49,x]
F[49,x] = F[50,x]*F[8,x]
F[50,x] = F[47,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[8,x]
F[53,x] = F[122,x]+F[54,x]
F[54,x] = F[119,x]+F[55,x]
F[55,x] = F[28,x]+F[56,x]
F[56,x] = F[57,x,1]
F[57,x,k[0]] = F[2,x]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]*F[67,x,k[0]]*F[68,x,k[0]]
F[60,x,k[0]] = F[57,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[71,x,k[0]]
F[62,x,k[0]] = F[6,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[28,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]*F[67,x,k[0]]*F[68,x,k[0]]
F[66,x,k[0]] = F[1,x]+F[64,x,k[0]]
F[67,x,k[0]] = k[0]*x
F[68,x,k[0]] = F[1,x]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[67,x,k[0]]*F[68,x,k[0]]
F[71,x,k[0]] = F[51,x]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[8,x]
F[74,x,k[0]] = F[103,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[95,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[94,x,k[0]]
F[77,x,k[0]] = F[19,x]+F[78,x,k[0]]+F[89,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]*F[8,x]
F[79,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[80,x,k[0]] = F[69,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[8,x]*F[80,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[87,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[67,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[28,x]+F[84,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[8,x]*F[83,x,k[0]]
F[89,x,k[0]] = F[67,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[77,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[67,x,k[0]]*F[91,x,k[0]]
F[94,x,k[0]] = -k[0]*(F[58,x,1]-F[58,x,k[0]])/(-1+k[0])
F[95,x,k[0]] = F[102,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = (-F[97,x,1]*k[0]+F[97,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[28,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[67,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[69,x,k[0]]
F[101,x,k[0]] = F[64,x,k[0]]*F[68,x,k[0]]
F[102,x,k[0]] = -k[0]*(F[72,x,1]-F[72,x,k[0]])/(-1+k[0])
F[103,x,k[0]] = F[104,x,k[0]]+F[111,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[107,x,k[0]]
F[105,x,k[0]] = (-F[106,x,1]*k[0]+F[106,x,k[0]])/(-1+k[0])
F[106,x,k[0]] = F[15,x]*F[98,x,k[0]]
F[107,x,k[0]] = -k[0]*(F[108,x,1]-F[108,x,k[0]])/(-1+k[0])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[8,x]
F[110,x,k[0]] = F[104,x,k[0]]+F[76,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[115,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = (-F[114,x,1]*k[0]+F[114,x,k[0]])/(-1+k[0])
F[114,x,k[0]] = F[15,x]*F[28,x]*F[98,x,k[0]]
F[115,x,k[0]] = -k[0]*(F[116,x,1]-F[116,x,k[0]])/(-1+k[0])
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[8,x]
F[118,x,k[0]] = F[111,x,k[0]]+F[95,x,k[0]]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[28,x]^2
F[121,x] = F[71,x,1]
F[122,x] = F[123,x]+F[129,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[15,x]*F[28,x]
F[125,x] = F[126,x]+F[51,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x,1]
F[128,x,k[0]] = F[108,x,k[0]]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]
F[131,x] = F[28,x]^2*F[15,x]
F[132,x] = F[133,x]+F[150,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[8,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[15,x]*F[55,x]
F[139,x] = F[119,x]*F[17,x]
F[140,x] = F[141,x]+F[147,x]
F[141,x] = F[142,x]*F[15,x]
F[142,x] = F[124,x]+F[143,x]
F[143,x] = F[126,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[8,x]
F[146,x] = F[142,x]+F[55,x]
F[147,x] = F[148,x]*F[17,x]
F[148,x] = F[130,x]+F[149,x]
F[149,x] = F[134,x]+F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x,1]
F[152,x,k[0]] = F[116,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{51}\! \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_{27}\! \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_{18}\! \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_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{34}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{8}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{45}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{8}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{37}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{8}\! \left(x \right)
F_{46}\! \left(x \right) = F_{27}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{122}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{119}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{28}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{57}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{6}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = y x
F_{68}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{51}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{y \left(F_{58}\! \left(x , 1\right)-F_{58}\! \left(x , y\right)\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = -\frac{F_{97}\! \left(x , 1\right) y -F_{97}\! \left(x , y\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = -\frac{y \left(F_{72}\! \left(x , 1\right)-F_{72}\! \left(x , y\right)\right)}{-1+y}
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = -\frac{F_{106}\! \left(x , 1\right) y -F_{106}\! \left(x , y\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = -\frac{y \left(F_{108}\! \left(x , 1\right)-F_{108}\! \left(x , y\right)\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = -\frac{F_{114}\! \left(x , 1\right) y -F_{114}\! \left(x , y\right)}{-1+y}
F_{114}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = -\frac{y \left(F_{116}\! \left(x , 1\right)-F_{116}\! \left(x , y\right)\right)}{-1+y}
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{28} \left(x \right)^{2}
F_{121}\! \left(x \right) = F_{71}\! \left(x , 1\right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{129}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{51}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x , 1\right)
F_{128}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{150}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{8}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{139}\! \left(x \right) = F_{119}\! \left(x \right) F_{17}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{147}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right)
F_{142}\! \left(x \right) = F_{124}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{126}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{8}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right)+F_{55}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{17}\! \left(x \right)
F_{148}\! \left(x \right) = F_{130}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{134}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x , 1\right)
F_{152}\! \left(x , y\right) = F_{116}\! \left(x , y\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_0(x) + F_5(x))
Eq(F_5(x), F_51(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_27(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) + F_18(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_20(x) + F_25(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_8(x))
Eq(F_21(x), F_15(x) + F_22(x))
Eq(F_22(x), F_19(x) + F_20(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_15(x) + F_22(x))
Eq(F_25(x), F_26(x)*F_8(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_28(x) + F_34(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_17(x) + F_31(x))
Eq(F_31(x), F_28(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_8(x))
Eq(F_34(x), F_19(x) + F_35(x) + F_45(x))
Eq(F_35(x), F_36(x)*F_8(x))
Eq(F_36(x), F_21(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_19(x) + F_35(x) + F_39(x))
Eq(F_39(x), F_40(x)*F_8(x))
Eq(F_40(x), F_28(x) + F_38(x))
Eq(F_41(x), 2*F_19(x) + F_42(x) + F_43(x))
Eq(F_42(x), F_37(x)*F_8(x))
Eq(F_43(x), F_44(x)*F_8(x))
Eq(F_44(x), F_32(x) + F_41(x))
Eq(F_45(x), F_46(x)*F_8(x))
Eq(F_46(x), F_27(x) + F_47(x))
Eq(F_47(x), F_32(x) + F_48(x))
Eq(F_48(x), 2*F_19(x) + F_42(x) + F_49(x))
Eq(F_49(x), F_50(x)*F_8(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_8(x))
Eq(F_53(x), F_122(x) + F_54(x))
Eq(F_54(x), F_119(x) + F_55(x))
Eq(F_55(x), F_28(x) + F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_57(x, k_0), F_2(x) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0)*F_67(x, k_0)*F_68(x, k_0))
Eq(F_60(x, k_0), F_57(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_71(x, k_0))
Eq(F_62(x, k_0), F_6(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_28(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0)*F_67(x, k_0)*F_68(x, k_0))
Eq(F_66(x, k_0), F_1(x) + F_64(x, k_0))
Eq(F_67(x, k_0), k_0*x)
Eq(F_68(x, k_0), F_1(x) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_67(x, k_0)*F_68(x, k_0))
Eq(F_71(x, k_0), F_51(x) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_8(x))
Eq(F_74(x, k_0), F_103(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_95(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_94(x, k_0))
Eq(F_77(x, k_0), F_19(x) + F_78(x, k_0) + F_89(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0)*F_8(x))
Eq(F_79(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_80(x, k_0), F_69(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_8(x)*F_80(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_87(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_67(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_28(x) + F_84(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_8(x)*F_83(x, k_0))
Eq(F_89(x, k_0), F_67(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_77(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_67(x, k_0)*F_91(x, k_0))
Eq(F_94(x, k_0), -F_58(x, 1) + (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_95(x, k_0), F_102(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), -F_97(x, 1) - F_97(x, k_0) + (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_28(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_67(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_69(x, k_0))
Eq(F_101(x, k_0), F_64(x, k_0)*F_68(x, k_0))
Eq(F_102(x, k_0), -F_72(x, 1) + (k_0*F_72(x, k_0) - F_72(x, 1))/(k_0 - 1))
Eq(F_103(x, k_0), F_104(x, k_0) + F_111(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_107(x, k_0))
Eq(F_105(x, k_0), -F_106(x, 1) - F_106(x, k_0) + (k_0*F_106(x, k_0) - F_106(x, 1))/(k_0 - 1))
Eq(F_106(x, k_0), F_15(x)*F_98(x, k_0))
Eq(F_107(x, k_0), -F_108(x, 1) + (k_0*F_108(x, k_0) - F_108(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_8(x))
Eq(F_110(x, k_0), F_104(x, k_0) + F_76(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_115(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), -F_114(x, 1) - F_114(x, k_0) + (k_0*F_114(x, k_0) - F_114(x, 1))/(k_0 - 1))
Eq(F_114(x, k_0), F_15(x)*F_28(x)*F_98(x, k_0))
Eq(F_115(x, k_0), -F_116(x, 1) + (k_0*F_116(x, k_0) - F_116(x, 1))/(k_0 - 1))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_8(x))
Eq(F_118(x, k_0), F_111(x, k_0) + F_95(x, k_0))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_28(x)**2)
Eq(F_121(x), F_71(x, 1))
Eq(F_122(x), F_123(x) + F_129(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_15(x)*F_28(x))
Eq(F_125(x), F_126(x) + F_51(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x, 1))
Eq(F_128(x, k_0), F_108(x, k_0))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_15(x)*F_28(x)**2)
Eq(F_132(x), F_133(x) + F_150(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_8(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_15(x)*F_55(x))
Eq(F_139(x), F_119(x)*F_17(x))
Eq(F_140(x), F_141(x) + F_147(x))
Eq(F_141(x), F_142(x)*F_15(x))
Eq(F_142(x), F_124(x) + F_143(x))
Eq(F_143(x), F_126(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_8(x))
Eq(F_146(x), F_142(x) + F_55(x))
Eq(F_147(x), F_148(x)*F_17(x))
Eq(F_148(x), F_130(x) + F_149(x))
Eq(F_149(x), F_134(x) + F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x, 1))
Eq(F_152(x, k_0), F_116(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": true, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": true, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_partial_col_placements_tracked_fusion_isolated", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 2], [0, 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