01234_01243_02134_02143_12034_12043
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3298, 18944, 111778, 673220, 4121434, 25570144, 160415810, 1015899124, 6485782866, 41698225920, 269735407170, 1754332330244, 11465139694762, 75252567550880, 495851249128066, 3278760949419764, 21749946173057026, 144702650959854464, 965293531956318946, 6455267260210061252, 43267215303773301498, 290616713169640562400, 1955842939532896306242, 13186837427427729377140, 89061083165066292105266, 602460214294988929154560, 4081489885631942814133378, 27689799482394888480557060, 188103058780867095947509066, 1279422981542485152102130464, 8712537855174324458179510914, 59396365577313030020250046836, 405353865950223976265306597602, 2769137749970459872146687722624, 18935155951953525435331574989858, 129594679893784665321234844581316, 887729656841841390920561791180442, 6086002979537358565684736717352544, 41756612410330305422127709857802818, 286711352214032906274237870325256436, 1970048432205973994288160175106797842, 13545905820241381771524261324738157824, 93202145873849418994659446959437136578, 641680464123440535050565034146461781252, 4420544858704239651499333681057246054890, 30470988366870261681547342633881963697824, 210155763639575882582069602651517618518146, 1450210057895197163032562016833567785986548, 10012595969233063584443159124841622791243714, 69164054041360184493311740031171751476090240, 477996150950420152545811660237664391216173410, 3304998074771315154176041052211335695244378564, 22861983129995642615032150970590027836967770682, 158214340405283153118150996822815148710629757408, 1095369778433246271670572284476746508498351106626, 7586695356639126880179504880949533336407724621940, 52567318456841332350484923142132833155237810605042, 364371890007673543916695083008163914540654550367232, 2526588997930550584777966959273964470088093995907330, 17525890645272216710232261423694119191102435338872836, 121612060690424435218986105382568143889290018558503562, 844150248601158882028807422709158193643492993488074272, 5861450650905907547099701052882418666619391208175475842, 40712579030139625963940907187042108925432010157799209076, 282869628586154616847705155417553206381969938975974177954, 1965959007651756309830473984116295321473615447920725384832, 13667510411326515692512332241949828562677612548227184050850, 95044659585013244999971198098541117464514670007995364690884, 661128760308019381243461580025082735713723578746345155556826, 4600035800990808186317109315087861482583095780348239911713120, 32014751587183300184578494528012099548229690338568671978220610, 222869108354978009763247568402483063191367725363142777884161524, 1551878062812050733622625014240607778695164600280950772242634962, 10808627846524961754331066942684190544326962471113343162139200256, 75298471281955851424758655208161425064537427996000096297671743298, 524688869454857198133822579085506986889074654064256060124671408388, 3656917846055062044689328214088332785752779660365905788114570458922, 25493171537722910926338701972263260235716852228178500001173445357984, 177756536508382444752771748482544965857274420706406776311219987928706, 1239704430000057548684482645244234360766650962541406926628865376296180, 8647677393434997789997536636677901635799140340473665478866191277129602, 60334750737129294323085370021958479361979065211098899832021304722886528, 421037051523473386207222567924353841328367537582103725176856231230152674, 2938704765869125432543044244779551068683689276323819076930040785436867524, 20515051426301301148178774307974728261127950339595268723247382164624869754, 143241380067428793787482950024624829439280321349658364472819751479898051808, 1000326785203634791687643428076696635852909470746137731254994528907855484994, 6987006539187477328337598265028354790854126093722999830097517117460814270836, 48810655644086877788096715178734170897529874234545872967135272914283892559794, 341044313394054553433606768686920889837230452937349789668286303226540844874240, 2383296919602969628063478020065893651164536164957139168524004975831159156385154, 16657706052690300696952710271736931882862230307772599470856055957957510210887684, 116444912732089937096679992313352173035707782299420628109164473914508248858986442, 814128112348200011756490585504765286479707604273092790802853659252653429281601824
Implicit equation for the generating function in Maple syntax:
(2*x-1)*F(x)^3+(-3*x+1)*F(x)^2+2*F(x)-2 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) F \! \left(x \right)^{3}+\left(-3 x +1\right) F \! \left(x \right)^{2}+2 F \! \left(x \right)-2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(n+5) = 81*n*(2*n+1)/(n+5)/(n+4)*a(n)-9/2*(72*n^2+153*n+80)/(n+5)/(n+4)*a(n+1)+3/2*(n+2)*(167*n+300)/(n+5)/(n+4)*a(n+2)-1/2*(185*n^2+1021*n+1400)/(n+5)/(n+4)*a(n+3)+1/2*(32*n+105)/(n+5)*a(n+4), n >= 5
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 24
a \! \left(n +5\right) = \frac{81 n \left(2 n +1\right) a \! \left(n \right)}{\left(n +5\right) \left(n +4\right)}-\frac{9 \left(72 n^{2}+153 n +80\right) a \! \left(n +1\right)}{2 \left(n +5\right) \left(n +4\right)}+\frac{3 \left(n +2\right) \left(167 n +300\right) a \! \left(n +2\right)}{2 \left(n +5\right) \left(n +4\right)}-\frac{\left(185 n^{2}+1021 n +1400\right) a \! \left(n +3\right)}{2 \left(n +5\right) \left(n +4\right)}+\frac{\left(32 n +105\right) a \! \left(n +4\right)}{2 n +10}, \quad n \geq 5
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24088/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[44,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[1,x]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]+F[25,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[17,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[10,x,k[0]]
F[17,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x]+F[20,x,k[0]]+F[24,x,k[0]]
F[19,x] = 0
F[20,x,k[0]] = F[10,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[23,x,k[0]]
F[22,x,k[0]] = F[10,x,k[0]]
F[23,x,k[0]] = F[18,x,k[0]]
F[24,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[8,x,k[0]]
F[26,x,k[0]] = F[19,x]+F[27,x,k[0]]+F[40,x,k[0]]
F[27,x,k[0]] = F[10,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[10,x,k[0]]+F[18,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[33,x,k[0]]
F[31,x,k[0]] = F[19,x]+F[27,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[33,x,k[0]] = F[19,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[39,x,k[0]]
F[34,x,k[0]] = 0
F[35,x,k[0]] = F[10,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[38,x,k[0]]
F[37,x,k[0]] = F[31,x,k[0]]
F[38,x,k[0]] = F[33,x,k[0]]
F[39,x,k[0]] = F[10,x,k[0]]*F[26,x,k[0]]
F[40,x,k[0]] = F[10,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[43,x,k[0]]
F[42,x,k[0]] = F[31,x,k[0]]+F[8,x,k[0]]
F[43,x,k[0]] = F[26,x,k[0]]+F[33,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[48,x,k[0]]
F[47,x,k[0]] = F[5,x]*F[7,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[10,x,k[0]]*F[149,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[7,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[61,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[10,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[58,x,k[0]]
F[55,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[10,x,k[0]]*F[55,x,k[0]]
F[58,x,k[0]] = F[52,x,k[0]]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[10,x,k[0]]*F[58,x,k[0]]
F[61,x,k[0]] = F[105,x,k[0]]+F[19,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[10,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[78,x,k[0]]
F[64,x,k[0]] = F[13,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[10,x,k[0]]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[71,x,k[0]]
F[68,x,k[0]] = F[56,x,k[0]]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[10,x,k[0]]*F[56,x,k[0]]
F[71,x,k[0]] = F[65,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = 2*F[19,x]+F[73,x,k[0]]+F[77,x,k[0]]
F[73,x,k[0]] = F[10,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[69,x,k[0]]
F[76,x,k[0]] = F[72,x,k[0]]
F[77,x,k[0]] = F[10,x,k[0]]*F[65,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[92,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[10,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[82,x,k[0]] = F[52,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[10,x,k[0]]*F[52,x,k[0]]
F[85,x,k[0]] = F[79,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = 2*F[19,x]+F[87,x,k[0]]+F[91,x,k[0]]
F[87,x,k[0]] = F[10,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[90,x,k[0]]
F[89,x,k[0]] = F[83,x,k[0]]
F[90,x,k[0]] = F[86,x,k[0]]
F[91,x,k[0]] = F[10,x,k[0]]*F[79,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[10,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]+F[98,x,k[0]]
F[95,x,k[0]] = F[59,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[10,x,k[0]]*F[59,x,k[0]]
F[98,x,k[0]] = F[92,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = 3*F[19,x]+F[100,x,k[0]]+F[104,x,k[0]]
F[100,x,k[0]] = F[10,x,k[0]]*F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]
F[102,x,k[0]] = F[96,x,k[0]]
F[103,x,k[0]] = F[99,x,k[0]]
F[104,x,k[0]] = F[10,x,k[0]]*F[92,x,k[0]]
F[105,x,k[0]] = F[10,x,k[0]]*F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[125,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[52,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[113,x,k[0]]+F[19,x]
F[109,x,k[0]] = F[10,x,k[0]]*F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]
F[111,x,k[0]] = F[10,x,k[0]]+F[69,x,k[0]]
F[112,x,k[0]] = F[83,x,k[0]]+F[96,x,k[0]]
F[113,x,k[0]] = F[10,x,k[0]]*F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[117,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[52,x,k[0]]
F[116,x,k[0]] = F[109,x,k[0]]+F[19,x]+F[84,x,k[0]]
F[117,x,k[0]] = F[108,x,k[0]]+F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]+F[124,x,k[0]]+F[19,x]
F[119,x,k[0]] = 0
F[120,x,k[0]] = F[10,x,k[0]]*F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[123,x,k[0]]
F[122,x,k[0]] = F[116,x,k[0]]
F[123,x,k[0]] = F[118,x,k[0]]
F[124,x,k[0]] = F[10,x,k[0]]*F[108,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[61,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[131,x,k[0]]+F[145,x,k[0]]+F[19,x]
F[127,x,k[0]] = F[10,x,k[0]]*F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[130,x,k[0]]
F[129,x,k[0]] = F[18,x,k[0]]+F[72,x,k[0]]
F[130,x,k[0]] = F[86,x,k[0]]+F[99,x,k[0]]
F[131,x,k[0]] = F[10,x,k[0]]*F[132,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[134,x,k[0]]
F[133,x,k[0]] = F[116,x,k[0]]+F[118,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]+F[137,x,k[0]]
F[135,x,k[0]] = F[127,x,k[0]]+F[131,x,k[0]]+F[136,x,k[0]]+F[19,x]
F[136,x,k[0]] = F[10,x,k[0]]*F[61,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]+F[139,x,k[0]]+F[140,x,k[0]]+F[144,x,k[0]]+F[19,x]
F[138,x,k[0]] = 0
F[139,x,k[0]] = 0
F[140,x,k[0]] = F[10,x,k[0]]*F[141,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[143,x,k[0]]
F[142,x,k[0]] = F[135,x,k[0]]
F[143,x,k[0]] = F[137,x,k[0]]
F[144,x,k[0]] = F[10,x,k[0]]*F[126,x,k[0]]
F[145,x,k[0]] = F[10,x,k[0]]*F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[147,x,k[0]] = F[135,x,k[0]]+F[61,x,k[0]]
F[148,x,k[0]] = F[126,x,k[0]]+F[137,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[150,x,k[0]]*k[0]-F[150,x,1])
F[151,x,k[0]] = F[10,x,k[0]]*F[150,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]
F[6,x,k[0]] = F[0,x]+F[152,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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = 0
F_{35}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{149}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{56}\! \left(x , y\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_{10}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{79}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = 3 F_{19}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{113}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{124}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{119}\! \left(x , y\right) = 0
F_{120}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{108}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{145}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{139}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{138}\! \left(x , y\right) = 0
F_{139}\! \left(x , y\right) = 0
F_{140}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{137}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{126}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{150}\! \left(x , y\right)+F_{150}\! \left(x , 1\right)}{-1+y}
F_{151}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{150}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{152}\! \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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_44(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_1(x) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0) + F_25(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_17(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_10(x, k_0))
Eq(F_17(x, k_0), F_13(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x) + F_20(x, k_0) + F_24(x, k_0))
Eq(F_19(x), 0)
Eq(F_20(x, k_0), F_10(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_23(x, k_0))
Eq(F_22(x, k_0), F_10(x, k_0))
Eq(F_23(x, k_0), F_18(x, k_0))
Eq(F_24(x, k_0), F_10(x, k_0)*F_13(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_8(x, k_0))
Eq(F_26(x, k_0), F_19(x) + F_27(x, k_0) + F_40(x, k_0))
Eq(F_27(x, k_0), F_10(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_10(x, k_0) + F_18(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_33(x, k_0))
Eq(F_31(x, k_0), F_19(x) + F_27(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_33(x, k_0), F_19(x) + F_34(x, k_0) + F_35(x, k_0) + F_39(x, k_0))
Eq(F_34(x, k_0), 0)
Eq(F_35(x, k_0), F_10(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_38(x, k_0))
Eq(F_37(x, k_0), F_31(x, k_0))
Eq(F_38(x, k_0), F_33(x, k_0))
Eq(F_39(x, k_0), F_10(x, k_0)*F_26(x, k_0))
Eq(F_40(x, k_0), F_10(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_43(x, k_0))
Eq(F_42(x, k_0), F_31(x, k_0) + F_8(x, k_0))
Eq(F_43(x, k_0), F_26(x, k_0) + F_33(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_48(x, k_0))
Eq(F_47(x, k_0), F_5(x)*F_7(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_10(x, k_0)*F_149(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_7(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_61(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_10(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_58(x, k_0))
Eq(F_55(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_10(x, k_0)*F_55(x, k_0))
Eq(F_58(x, k_0), F_52(x, k_0) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_10(x, k_0)*F_58(x, k_0))
Eq(F_61(x, k_0), F_105(x, k_0) + F_19(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_10(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_78(x, k_0))
Eq(F_64(x, k_0), F_13(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x, k_0)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_71(x, k_0))
Eq(F_68(x, k_0), F_56(x, k_0) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_10(x, k_0)*F_56(x, k_0))
Eq(F_71(x, k_0), F_65(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), 2*F_19(x) + F_73(x, k_0) + F_77(x, k_0))
Eq(F_73(x, k_0), F_10(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_69(x, k_0))
Eq(F_76(x, k_0), F_72(x, k_0))
Eq(F_77(x, k_0), F_10(x, k_0)*F_65(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_92(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_10(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_82(x, k_0), F_52(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_10(x, k_0)*F_52(x, k_0))
Eq(F_85(x, k_0), F_79(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), 2*F_19(x) + F_87(x, k_0) + F_91(x, k_0))
Eq(F_87(x, k_0), F_10(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_90(x, k_0))
Eq(F_89(x, k_0), F_83(x, k_0))
Eq(F_90(x, k_0), F_86(x, k_0))
Eq(F_91(x, k_0), F_10(x, k_0)*F_79(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_10(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0) + F_98(x, k_0))
Eq(F_95(x, k_0), F_59(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_10(x, k_0)*F_59(x, k_0))
Eq(F_98(x, k_0), F_92(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_104(x, k_0) + 3*F_19(x))
Eq(F_100(x, k_0), F_10(x, k_0)*F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0))
Eq(F_102(x, k_0), F_96(x, k_0))
Eq(F_103(x, k_0), F_99(x, k_0))
Eq(F_104(x, k_0), F_10(x, k_0)*F_92(x, k_0))
Eq(F_105(x, k_0), F_10(x, k_0)*F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_125(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_52(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_113(x, k_0) + F_19(x))
Eq(F_109(x, k_0), F_10(x, k_0)*F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0))
Eq(F_111(x, k_0), F_10(x, k_0) + F_69(x, k_0))
Eq(F_112(x, k_0), F_83(x, k_0) + F_96(x, k_0))
Eq(F_113(x, k_0), F_10(x, k_0)*F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_117(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_52(x, k_0))
Eq(F_116(x, k_0), F_109(x, k_0) + F_19(x) + F_84(x, k_0))
Eq(F_117(x, k_0), F_108(x, k_0) + F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0) + F_124(x, k_0) + F_19(x))
Eq(F_119(x, k_0), 0)
Eq(F_120(x, k_0), F_10(x, k_0)*F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_123(x, k_0))
Eq(F_122(x, k_0), F_116(x, k_0))
Eq(F_123(x, k_0), F_118(x, k_0))
Eq(F_124(x, k_0), F_10(x, k_0)*F_108(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_61(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_131(x, k_0) + F_145(x, k_0) + F_19(x))
Eq(F_127(x, k_0), F_10(x, k_0)*F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_130(x, k_0))
Eq(F_129(x, k_0), F_18(x, k_0) + F_72(x, k_0))
Eq(F_130(x, k_0), F_86(x, k_0) + F_99(x, k_0))
Eq(F_131(x, k_0), F_10(x, k_0)*F_132(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_134(x, k_0))
Eq(F_133(x, k_0), F_116(x, k_0) + F_118(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_137(x, k_0))
Eq(F_135(x, k_0), F_127(x, k_0) + F_131(x, k_0) + F_136(x, k_0) + F_19(x))
Eq(F_136(x, k_0), F_10(x, k_0)*F_61(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_139(x, k_0) + F_140(x, k_0) + F_144(x, k_0) + F_19(x))
Eq(F_138(x, k_0), 0)
Eq(F_139(x, k_0), 0)
Eq(F_140(x, k_0), F_10(x, k_0)*F_141(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_143(x, k_0))
Eq(F_142(x, k_0), F_135(x, k_0))
Eq(F_143(x, k_0), F_137(x, k_0))
Eq(F_144(x, k_0), F_10(x, k_0)*F_126(x, k_0))
Eq(F_145(x, k_0), F_10(x, k_0)*F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_147(x, k_0), F_135(x, k_0) + F_61(x, k_0))
Eq(F_148(x, k_0), F_126(x, k_0) + F_137(x, k_0))
Eq(F_149(x, k_0), (k_0*F_150(x, k_0) - F_150(x, 1))/(k_0 - 1))
Eq(F_151(x, k_0), F_10(x, k_0)*F_150(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_6(x, k_0), F_0(x) + F_152(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"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.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": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, 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2], "pos": [[1, 1], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 3], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 5]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 4], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 1], [1, 5], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 3]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 4]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 0], [1, 1], [1, 5]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 3]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 4]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 5]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 0], [1, 5], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 4]]}], [{"patt": [0], "pos": [[1, 5]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"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": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}], [{"patt": [0], "pos": [[1, 5]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"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": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 4], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24089/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[27,x,k[0]]+F[29,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]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[26,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[9,x,k[0]]
F[17,x,k[0],k[1]] = F[1,x]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[25,x,k[1],k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]*F[3,x]
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[17,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[25,x,k[0],k[1]] = F[10,x,k[1]]*F[9,x,k[0]]
F[26,x,k[0],k[1]] = F[5,x,k[1]]*F[9,x,k[0]]
F[27,x,k[0]] = F[28,x,1,k[0]]
F[28,x,k[0],k[1]] = F[16,x,k[0]*k[1],k[1]]
F[29,x,k[0]] = F[30,x,k[0]]*F[9,x,k[0]]
F[30,x,k[0]] = F[31,x,1,k[0]]
F[31,x,k[0],k[1]] = F[17,x,k[0]*k[1],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{29}\! \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 z , z\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y , z\right) = -\frac{-y F_{15}\! \left(x , y , z\right)+F_{15}\! \left(x , 1, z\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{26}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{25}\! \left(x , z , y\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y , z\right) = \frac{y F_{20}\! \left(x , y , 1\right)-z F_{20}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{20}\! \left(x , y , z\right) = F_{14}\! \left(x , y , y z \right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{22}\! \left(x , y , z\right) = \frac{y F_{23}\! \left(x , y , 1\right)-z F_{23}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , y , y z \right)
F_{24}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{25}\! \left(x , y , z\right) = F_{10}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y , z\right) = F_{5}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , 1, y\right)
F_{28}\! \left(x , y , z\right) = F_{16}\! \left(x , y z , z\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , 1, y\right)
F_{31}\! \left(x , y , z\right) = F_{17}\! \left(x , y z , z\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_27(x, k_0) + F_29(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*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_26(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_9(x, k_0))
Eq(F_17(x, k_0, k_1), F_1(x) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_25(x, k_1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1)*F_3(x))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_17(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_25(x, k_0, k_1), F_10(x, k_1)*F_9(x, k_0))
Eq(F_26(x, k_0, k_1), F_5(x, k_1)*F_9(x, k_0))
Eq(F_27(x, k_0), F_28(x, 1, k_0))
Eq(F_28(x, k_0, k_1), F_16(x, k_0*k_1, k_1))
Eq(F_29(x, k_0), F_30(x, k_0)*F_9(x, k_0))
Eq(F_30(x, k_0), F_31(x, 1, k_0))
Eq(F_31(x, k_0, k_1), F_17(x, k_0*k_1, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "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": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "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, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"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": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 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[1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 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