01234_01243_01342_02134_02143_12034_12043
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3149, 17688, 102001, 600303, 3590921, 21768532, 133438243, 825696844, 5150735442, 32356470593, 204511706326, 1299656701871, 8299131182069, 53224431071103, 342671103498219, 2213972068163413, 14350163015085861, 93284901748124244, 608037623967390570, 3973026285497195222, 26019699731786911848, 170765455904355035040, 1122921736758291709193, 7397623439283332400981, 48817505031561978445909, 322665105173903932969897, 2135887434530690001822333, 14158441177626691512086291, 93978275090536216871715647, 624570877364819762382003846, 4155738591421682505671128894, 27682121234166383316172974775, 184590674644577123857192558221, 1232128301247363390522949370689, 8232205204373308791653617036225, 55051657091615808943755760430293, 368468076371578817141527931638093, 2468238991703214075625831845152531, 16546883572838235920493905147550215, 111012463805699756886816507992951441, 745314637907380593740292023985167725, 5007335496097423166238433100004882553, 33663590669102328508376759751871795161, 226458813004000215233814360306861745578, 1524340860213132968310989445121658687414, 10266648826535458276251573155661304464553, 69186178764083058272379252107165511691790, 466492668852950409396312007025163593576153, 3146998022390970263979340306269477096004739, 21240565998737195107267483763628211088234856, 143431951184993459557910585376643020364630823, 969010713391714684315446114512324661488658571, 6549484617881956681480664553837664754643641745, 44286863974594208613787545634040001617976708600, 299588882154067762800504138250045972998491557971, 2027465329734879720574181956360866106814201837052, 13726267739226722922272199494602902080877215563202, 92964546963175808882665527900357508999241409067279, 629858421739913239897432392319595927251715145652905, 4268981611062931897890652346269161291068766707450307, 28943875353416171675063115565875052616417848774526933, 196306928601081673773369989464365410076886753512504358, 1331854648657470105696311423835274780845384410458819499, 9038912325579591308216300031318066938060726503028480112, 61363443066354958823016600286893651243908015079674148754, 416709783087102823357769033424546290841478474057502949942, 2830639024350564728898945792994627218598073452265857846623, 19233513772747791249327457047554513008902571001372103195959, 130723238784744308979695787930774750443328743164115792050271, 888717630552636199250466952565921131301846471923182199895026, 6043500391703142059766994372437053014422474734334685801735046, 41107789789574928731976093563583321634295136481676793780389639, 279684035854616469283062344217061769774596987341145347959150981, 1903340458419225694847567659709764838442526799863226752549627719, 12955909493216289482798715334766989536866294902059152611169830309, 88210326122765450136016415725172117354896349637939848565613810629, 600715184104112448112373387192238541617394619093191329322115842097, 4091787796058501357536081056385716481827395373870347069742345705091, 27877295727430058265392234559936121825457994621451380969933699968893, 189967384371108325881504613204777851896815724453716422387538466901463, 1294780637900269649030481448930399092777816307872713397258789736427211, 8826734544296957980055668656754261561229047277932178065839306612977843, 60185058123529491188038630477323244229120508862668596763132628412627929, 410449896955257242270439461980029128340543282474774430646422911721749897, 2799707290638910253795274196775999713758735978129859693404615217634244073, 19100482533309832610539799454634802965949213453934825726599407003503346951, 130332751447819548230607648422293164996353365439011832220607233337061795911, 889485020549951540377328673171654101331772230326997423158509797934441136089, 6071527311532024095590297422500127090759179713371658136230780324925524490693, 41450516478581027987873161076523057368455294011876450497831037646868818878884, 283030414407011307461664908389599915388404137985572515608345320875648391512783, 1932884800943424879561877923427948761172573275953373084024707828775696105293506, 13202224624241163745693409953590838393620785003751211948619770700253943194592604, 90189331918881175829925895824296698086806206067377064077818830903281062674596079
Implicit equation for the generating function in Maple syntax:
(x-1)*F(x)^4+(-x+2)*F(x)^3+(-x-1)*F(x)^2+F(x)-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) F \! \left(x \right)^{4}+\left(-x +2\right) F \! \left(x \right)^{3}+\left(-x -1\right) F \! \left(x \right)^{2}+F \! \left(x \right)-1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 581
a(7) = 3149
a(8) = 17688
a(9) = 102001
a(10) = 600303
a(11) = 3590921
a(n+12) = 1600/8897*n*(n+1)*(2*n+1)/(n+10)/(n+12)/(n+11)*a(n)+40/8897*(n+1)*(1814*n^2+4123*n+2403)/(n+10)/(n+12)/(n+11)*a(n+1)-30/8897*(2178*n^3-12697*n^2-81881*n-96050)/(n+10)/(n+12)/(n+11)*a(n+2)+2/8897*(376384*n^3+3722439*n^2+12425549*n+13912914)/(n+10)/(n+12)/(n+11)*a(n+3)-12/8897*(532131*n^3+7201629*n^2+32240951*n+47807794)/(n+10)/(n+12)/(n+11)*a(n+4)+4/8897*(4749038*n^3+75272808*n^2+397041913*n+697149048)/(n+10)/(n+12)/(n+11)*a(n+5)-6/8897*(4978800*n^3+90328153*n^2+546634963*n+1103500758)/(n+10)/(n+12)/(n+11)*a(n+6)+1/8897*(28463783*n^3+583249173*n^2+3987133012*n+9093976596)/(n+10)/(n+12)/(n+11)*a(n+7)-1/8897*(17194963*n^3+393821559*n^2+3007073090*n+7655825904)/(n+10)/(n+12)/(n+11)*a(n+8)+2/8897*(3278329*n^3+83200071*n^2+703342100*n+1980771132)/(n+10)/(n+12)/(n+11)*a(n+9)-2/8897*(750095*n^2+13435303*n+60158832)/(n+12)/(n+11)*a(n+10)+1/8897*(182641*n+1732056)/(n+12)*a(n+11), n >= 12
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(5\right) = 113
a \! \left(6\right) = 581
a \! \left(7\right) = 3149
a \! \left(8\right) = 17688
a \! \left(9\right) = 102001
a \! \left(10\right) = 600303
a \! \left(11\right) = 3590921
a \! \left(n +12\right) = \frac{1600 n \left(n +1\right) \left(2 n +1\right) a \! \left(n \right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}+\frac{40 \left(n +1\right) \left(1814 n^{2}+4123 n +2403\right) a \! \left(n +1\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}-\frac{30 \left(2178 n^{3}-12697 n^{2}-81881 n -96050\right) a \! \left(n +2\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}+\frac{2 \left(376384 n^{3}+3722439 n^{2}+12425549 n +13912914\right) a \! \left(n +3\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}-\frac{12 \left(532131 n^{3}+7201629 n^{2}+32240951 n +47807794\right) a \! \left(n +4\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}+\frac{4 \left(4749038 n^{3}+75272808 n^{2}+397041913 n +697149048\right) a \! \left(n +5\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}-\frac{6 \left(4978800 n^{3}+90328153 n^{2}+546634963 n +1103500758\right) a \! \left(n +6\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}+\frac{\left(28463783 n^{3}+583249173 n^{2}+3987133012 n +9093976596\right) a \! \left(n +7\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}-\frac{\left(17194963 n^{3}+393821559 n^{2}+3007073090 n +7655825904\right) a \! \left(n +8\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}+\frac{2 \left(3278329 n^{3}+83200071 n^{2}+703342100 n +1980771132\right) a \! \left(n +9\right)}{8897 \left(n +10\right) \left(n +12\right) \left(n +11\right)}-\frac{2 \left(750095 n^{2}+13435303 n +60158832\right) a \! \left(n +10\right)}{8897 \left(n +12\right) \left(n +11\right)}+\frac{\left(182641 n +1732056\right) a \! \left(n +11\right)}{8897 n +106764}, \quad n \geq 12
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24129/
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[46,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[23,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,k[0]]
F[19,x,k[0]] = F[10,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[22,x,k[0]]
F[21,x,k[0]] = F[10,x,k[0]]
F[22,x,k[0]] = F[18,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[8,x,k[0]]
F[24,x,k[0]] = F[25,x]+F[26,x,k[0]]+F[42,x,k[0]]
F[25,x] = 0
F[26,x,k[0]] = F[10,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[31,x,k[0]]
F[28,x,k[0]] = F[10,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[19,x,k[0]]+F[25,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[34,x,k[0]]
F[32,x,k[0]] = F[25,x]+F[26,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[34,x,k[0]] = F[25,x]+F[35,x,k[0]]+F[36,x,k[0]]+F[41,x,k[0]]
F[35,x,k[0]] = 0
F[36,x,k[0]] = F[10,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = F[32,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[36,x,k[0]]
F[41,x,k[0]] = F[10,x,k[0]]*F[24,x,k[0]]
F[42,x,k[0]] = F[10,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[32,x,k[0]]+F[8,x,k[0]]
F[45,x,k[0]] = F[24,x,k[0]]+F[40,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[4,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[5,x]*F[7,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[10,x,k[0]]*F[130,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[7,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[63,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[10,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[10,x,k[0]]*F[57,x,k[0]]
F[60,x,k[0]] = F[54,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[10,x,k[0]]*F[60,x,k[0]]
F[63,x,k[0]] = F[25,x]+F[64,x,k[0]]+F[74,x,k[0]]
F[64,x,k[0]] = F[10,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[70,x,k[0]]
F[66,x,k[0]] = F[58,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[10,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[58,x,k[0]]+F[67,x,k[0]]
F[70,x,k[0]] = F[61,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[10,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = F[61,x,k[0]]+F[71,x,k[0]]
F[74,x,k[0]] = F[10,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[98,x,k[0]]
F[76,x,k[0]] = F[54,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[25,x]+F[78,x,k[0]]+F[88,x,k[0]]
F[78,x,k[0]] = F[10,x,k[0]]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[83,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[82,x,k[0]] = F[10,x,k[0]]*F[58,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[10,x,k[0]]*F[54,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[10,x,k[0]]*F[61,x,k[0]]
F[88,x,k[0]] = F[10,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[54,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[25,x]+F[78,x,k[0]]+F[85,x,k[0]]
F[92,x,k[0]] = F[77,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[10,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[91,x,k[0]]
F[97,x,k[0]] = F[93,x,k[0]]
F[98,x,k[0]] = F[63,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]+F[126,x,k[0]]+F[25,x]
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[105,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[81,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[10,x,k[0]]*F[67,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[86,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[10,x,k[0]]*F[71,x,k[0]]
F[108,x,k[0]] = F[10,x,k[0]]*F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[114,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[91,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[113,x,k[0]]+F[25,x]+F[94,x,k[0]]
F[112,x,k[0]] = 0
F[113,x,k[0]] = F[10,x,k[0]]*F[77,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[117,x,k[0]]
F[115,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]+F[116,x,k[0]]+F[25,x]
F[116,x,k[0]] = F[10,x,k[0]]*F[63,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]+F[120,x,k[0]]+F[125,x,k[0]]+F[25,x]
F[118,x,k[0]] = 0
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[115,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[120,x,k[0]]
F[125,x,k[0]] = F[10,x,k[0]]*F[99,x,k[0]]
F[126,x,k[0]] = F[10,x,k[0]]*F[127,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[129,x,k[0]]
F[128,x,k[0]] = F[115,x,k[0]]+F[63,x,k[0]]
F[129,x,k[0]] = F[124,x,k[0]]+F[99,x,k[0]]
F[130,x,k[0]] = 1/(-1+k[0])*(F[131,x,k[0]]*k[0]-F[131,x,1])
F[132,x,k[0]] = F[10,x,k[0]]*F[131,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]
F[6,x,k[0]] = F[0,x]+F[133,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_{46}\! \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_{23}\! \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 , y\right)
F_{19}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{25}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = 0
F_{36}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{130}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{1}\! \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_{10}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{79}\! \left(x , y\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_{10}\! \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_{10}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{25}\! \left(x \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_{105}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)+F_{25}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = 0
F_{113}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{77}\! \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_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{25}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{25}\! \left(x \right)
F_{118}\! \left(x , y\right) = 0
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_{115}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = -\frac{-y F_{131}\! \left(x , y\right)+F_{131}\! \left(x , 1\right)}{-1+y}
F_{132}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{131}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{133}\! \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_46(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_23(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, k_0))
Eq(F_19(x, k_0), F_10(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_22(x, k_0))
Eq(F_21(x, k_0), F_10(x, k_0))
Eq(F_22(x, k_0), F_18(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_8(x, k_0))
Eq(F_24(x, k_0), F_25(x) + F_26(x, k_0) + F_42(x, k_0))
Eq(F_25(x), 0)
Eq(F_26(x, k_0), F_10(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_31(x, k_0))
Eq(F_28(x, k_0), F_10(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_19(x, k_0) + F_25(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_10(x, k_0)*F_13(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_34(x, k_0))
Eq(F_32(x, k_0), F_25(x) + F_26(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_34(x, k_0), F_25(x) + F_35(x, k_0) + F_36(x, k_0) + F_41(x, k_0))
Eq(F_35(x, k_0), 0)
Eq(F_36(x, k_0), F_10(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), F_32(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_36(x, k_0))
Eq(F_41(x, k_0), F_10(x, k_0)*F_24(x, k_0))
Eq(F_42(x, k_0), F_10(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_32(x, k_0) + F_8(x, k_0))
Eq(F_45(x, k_0), F_24(x, k_0) + F_40(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_4(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_5(x)*F_7(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_10(x, k_0)*F_130(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_7(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_63(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_10(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_10(x, k_0)*F_57(x, k_0))
Eq(F_60(x, k_0), F_54(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_10(x, k_0)*F_60(x, k_0))
Eq(F_63(x, k_0), F_25(x) + F_64(x, k_0) + F_74(x, k_0))
Eq(F_64(x, k_0), F_10(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_70(x, k_0))
Eq(F_66(x, k_0), F_58(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_10(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_58(x, k_0) + F_67(x, k_0))
Eq(F_70(x, k_0), F_61(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_10(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), F_61(x, k_0) + F_71(x, k_0))
Eq(F_74(x, k_0), F_10(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_98(x, k_0))
Eq(F_76(x, k_0), F_54(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_25(x) + F_78(x, k_0) + F_88(x, k_0))
Eq(F_78(x, k_0), F_10(x, k_0)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_83(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))
Eq(F_82(x, k_0), F_10(x, k_0)*F_58(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_10(x, k_0)*F_54(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_10(x, k_0)*F_61(x, k_0))
Eq(F_88(x, k_0), F_10(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_54(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_25(x) + F_78(x, k_0) + F_85(x, k_0))
Eq(F_92(x, k_0), F_77(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_10(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_91(x, k_0))
Eq(F_97(x, k_0), F_93(x, k_0))
Eq(F_98(x, k_0), F_63(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_108(x, k_0) + F_126(x, k_0) + F_25(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_105(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_81(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_10(x, k_0)*F_67(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_86(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_10(x, k_0)*F_71(x, k_0))
Eq(F_108(x, k_0), F_10(x, k_0)*F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_114(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_91(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_113(x, k_0) + F_25(x) + F_94(x, k_0))
Eq(F_112(x, k_0), 0)
Eq(F_113(x, k_0), F_10(x, k_0)*F_77(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_100(x, k_0) + F_108(x, k_0) + F_116(x, k_0) + F_25(x))
Eq(F_116(x, k_0), F_10(x, k_0)*F_63(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0) + F_120(x, k_0) + F_125(x, k_0) + F_25(x))
Eq(F_118(x, k_0), 0)
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_115(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_120(x, k_0))
Eq(F_125(x, k_0), F_10(x, k_0)*F_99(x, k_0))
Eq(F_126(x, k_0), F_10(x, k_0)*F_127(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_129(x, k_0))
Eq(F_128(x, k_0), F_115(x, k_0) + F_63(x, k_0))
Eq(F_129(x, k_0), F_124(x, k_0) + F_99(x, k_0))
Eq(F_130(x, k_0), (k_0*F_131(x, k_0) - F_131(x, 1))/(k_0 - 1))
Eq(F_132(x, k_0), F_10(x, k_0)*F_131(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_6(x, k_0), F_0(x) + F_133(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, 1, 3, 4, 2], "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, 1, 3, 4, 2], "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": [0, 2, 3, 1], "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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": 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"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": [0, 2, 3, 1], "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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "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": [0, 2, 1], "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, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 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": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [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], 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"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, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 3], [1, 5]]}, {"patt": [0, 1, 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": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 5], [1, 3]]}, {"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, 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": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"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, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [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": [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": [], "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"}}, {"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, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 4]]}, {"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, 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, 0], [1, 0]]}, {"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]]}]]}, "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": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 0], "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": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 2, 3, 1], "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/24130/
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[30,x,k[0]]+F[32,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[28,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[29,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[25,x,k[0],k[1]]*F[9,x,k[0]]
F[25,x,k[0],k[1]] = (F[26,x,k[0],1]*k[0]-F[26,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[27,x,k[0],k[0]*k[1]]
F[27,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[28,x,k[1],k[0]]
F[28,x,k[0],k[1]] = F[5,x,k[1]]*F[9,x,k[0]]
F[29,x,k[0],k[1]] = F[10,x,k[1]]*F[9,x,k[0]]
F[30,x,k[0]] = F[31,x,1,k[0]]
F[31,x,k[0],k[1]] = F[16,x,k[0]*k[1],k[1]]
F[32,x,k[0]] = F[33,x,k[0]]*F[9,x,k[0]]
F[33,x,k[0]] = F[26,x,k[0],1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{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_{30}\! \left(x , y\right)+F_{32}\! \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_{28}\! \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_{29}\! \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_{25}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{25}\! \left(x , y , z\right) = \frac{y F_{26}\! \left(x , y , 1\right)-z F_{26}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , y z \right)
F_{27}\! \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_{28}\! \left(x , z , y\right)
F_{28}\! \left(x , y , z\right) = F_{5}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{29}\! \left(x , y , z\right) = F_{10}\! \left(x , z\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_{16}\! \left(x , y z , z\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{26}\! \left(x , y , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*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_30(x, k_0) + F_32(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_28(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_29(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_25(x, k_0, k_1)*F_9(x, k_0))
Eq(F_25(x, k_0, k_1), (-k_0*F_26(x, k_0, 1) + k_1*F_26(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_0*k_1))
Eq(F_27(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_28(x, k_1, k_0))
Eq(F_28(x, k_0, k_1), F_5(x, k_1)*F_9(x, k_0))
Eq(F_29(x, k_0, k_1), F_10(x, k_1)*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_16(x, k_0*k_1, k_1))
Eq(F_32(x, k_0), F_33(x, k_0)*F_9(x, k_0))
Eq(F_33(x, k_0), F_26(x, k_0, 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, 1, 3, 4, 2], "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": [0, 2, 3, 1], "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, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "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, 1, 3, 4, 2], "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": [0, 2, 3, 1], "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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "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], 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