02314_03124_03214_13042_20413_315042
Counting sequence:
1, 1, 2, 6, 24, 115, 607, 3370, 19235, 111571, 653603, 3853424, 22815443, 135482334, 806180411, 4804250596, 28660891938, 171120790746, 1022298997790, 6110152136891, 36532429252431, 218485628254633, 1306949786188459, 7819280602197891, 46787663410514384, 279988909890506863, 1675660680553158236, 10029053625856584172, 60028407810407594477, 359312427511673165299, 2150813016812764747934, 12874941136968887786232, 77072201023929236411537, 461379573452000908973855, 2762012159848006245147047, 16534773127364548039275570, 98986361016509064352162840, 592592505123430030846111972, 3547643606967373076092958217, 21238621406739357107918365985, 127149524317349028186459820696, 761210691151442717559226008710, 4557182806518358847938131187756, 27282817111176049306514979103149, 163336394643792878467313998271338, 977861945773398145972663937427352, 5854270922014627940572704787386721, 35048437807820141840267781958521028, 209828751652899432207641190219623082, 1256208516213792884481195792633742701, 7520709421629439402253483982307958342, 45025253829621540729352020858562274989, 269558958587193051927370128124308062999, 1613806911439611397407911508956183886361, 9661610863938419979203591135048165171870, 57842579847488609880212970860835059931561, 346294734519596843489864772870255325809721, 2073214428814421149316284612528419264821684, 12412025034935611922098055351076529986406530, 74308951813585412063087701429149269902937453, 444876728828905027851070086885288530002572550, 2663411642107931891034145608433978129164768262, 15945455963080889662969546058117443942873208996, 95463120867741724724521675137620414928861622474, 571523832487562348035749615491832547324000800869, 3421630343606252171650012682203888400485855679635, 20484805968218846579617406605912890942856226788560, 122639575832074966476042475130277896225855237707684, 734225461763607312778197285798821489551217726622038, 4395702138675901667649252494555254335618683006979773, 26316436595990547179778390795383533688573320440067285, 157552725160170568620804374482864371033882109293077935, 943245549116393716777416590115551061010090127284296675, 5647075794648297307497317640768842852181042895652284756, 33808233188934688234140272764093546019277596628437024003, 202405047603901714661041190084057642416393072714414593639, 1211770029037939364238966695378091254573488547002208442756, 7254693662065293756781822379829712312834673089804002676611, 43432812545717275786696064086846511513515329681092466279006, 260026033544215613126244789273179545637656802164161297373368, 1556738661882636630170714043889400899209888131224822922393553, 9319971694679599491431010518746408556455962211793109521829170, 55797337636862772296709500601549828575506340629559045783673606, 334050681670340401033189248037735768810780904483588452462282976, 1999913669155572998916785780234837670945157247097779915737490765, 11973197222079631712929751152692089454982878725104435032201102905, 71681820184441049346895475580076655501945696818939634385512095616, 429148811196794956076603815825323235537327332912724447407246320215, 2569252593715919199375379429699245465733402369843139328773652777215, 15381748071191730017332236135850350300526745390517398416499495887039, 92088327386250546835759570903028374160068541935099953342139794121570, 551319655581002255198947487075365519934507703496969205359507120751509, 3300671990726542295738921372004738915053346170893576770292735739879889, 19760651534274749098559949634888507761625006925507745353196251852192362, 118304196959955040410880412167152047003515476228082999208213761259182898, 708270322017717599606297562992296975813172467605389215528044033685614837, 4240313210861099498465931139435113180645990255630761013965211953150931500, 25386149290695793395146648768667101997053619650259860296535470289019036607, 151983248398898561780295627816903332087399209721132815950010566614415138733, 909901991660906118064467191643664632838721844980797714973136788922093899674, 5447453211749576791258916475746114151257833167652033933206076560138002179725
Implicit equation for the generating function in Maple syntax:
(13*x^9-69*x^8+162*x^7-115*x^6-496*x^5+1401*x^4-1415*x^3+637*x^2-97*x+4)*F(x)^3+(50*x^8-198*x^7+376*x^6+118*x^5-1794*x^4+2840*x^3-1676*x^2+281*x-12)*F(x)^2+(60*x^7-192*x^6+248*x^5+483*x^4-1743*x^3+1472*x^2-272*x+12)*F(x)+24*x^6-64*x^5+40*x^4+295*x^3-432*x^2+88*x-4 = 0
Implicit equation for the generating function in latex syntax:
\left(13 x^{9}-69 x^{8}+162 x^{7}-115 x^{6}-496 x^{5}+1401 x^{4}-1415 x^{3}+637 x^{2}-97 x +4\right) F \! \left(x \right)^{3}+\left(50 x^{8}-198 x^{7}+376 x^{6}+118 x^{5}-1794 x^{4}+2840 x^{3}-1676 x^{2}+281 x -12\right) F \! \left(x \right)^{2}+\left(60 x^{7}-192 x^{6}+248 x^{5}+483 x^{4}-1743 x^{3}+1472 x^{2}-272 x +12\right) F \! \left(x \right)+24 x^{6}-64 x^{5}+40 x^{4}+295 x^{3}-432 x^{2}+88 x -4 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 115
a(6) = 607
a(7) = 3370
a(8) = 19235
a(9) = 111571
a(10) = 653603
a(11) = 3853424
a(12) = 22815443
a(13) = 135482334
a(14) = 806180411
a(15) = 4804250596
a(16) = 28660891938
a(17) = 171120790746
a(18) = 1022298997790
a(19) = 6110152136891
a(20) = 36532429252431
a(21) = 218485628254633
a(22) = 1306949786188459
a(23) = 7819280602197891
a(24) = 46787663410514384
a(25) = 279988909890506863
a(26) = 1675660680553158236
a(n+27) = -3/4*(2870*n^2+143228*n+1786491)/(2*n+53)/(n+26)*a(n+25)+3/4*(150*n^2+7639*n+97258)/(2*n+53)/(n+26)*a(n+26)-1/16*(24246610792*n^2+858496776663*n+7605196753667)/(2*n+53)/(n+26)*a(n+18)+1/16*(12483090055*n^2+460618546182*n+4250174677163)/(2*n+53)/(n+26)*a(n+19)-1/8*(2059267847*n^2+79071121917*n+758781691441)/(2*n+53)/(n+26)*a(n+20)+3/8*(141216301*n^2+5631113645*n+56078045437)/(2*n+53)/(n+26)*a(n+21)-1/8*(51035902*n^2+2101523442*n+21584384003)/(2*n+53)/(n+26)*a(n+22)+1/8*(2842105*n^2+117679806*n+1208358899)/(2*n+53)/(n+26)*a(n+23)+3/4*(9178*n^2+532642*n+7453545)/(2*n+53)/(n+26)*a(n+24)+1/16*(30721703953*n^2+1040895182118*n+8828090853959)/(2*n+53)/(n+26)*a(n+17)+1/32*(5234940499*n^2+131947290891*n+820854701750)/(2*n+53)/(n+26)*a(n+14)+1/16*(9580485722*n^2+302061226695*n+2378158241950)/(2*n+53)/(n+26)*a(n+15)-1/16*(24502373768*n^2+793768381311*n+6436861822186)/(2*n+53)/(n+26)*a(n+16)-3/32*(12072591*n^2+180302185*n+664492260)/(2*n+53)/(n+26)*a(n+6)+1/32*(168501335*n^2+2504088123*n+9161071858)/(2*n+53)/(n+26)*a(n+7)-3/32*(140883621*n^2+2177583625*n+8298517096)/(2*n+53)/(n+26)*a(n+8)+1/32*(529384081*n^2+8650037967*n+35244539990)/(2*n+53)/(n+26)*a(n+9)+1/16*(104225549*n^2+2780641806*n+17171348851)/(2*n+53)/(n+26)*a(n+10)-3/16*(427330215*n^2+10124230856*n+60248773028)/(2*n+53)/(n+26)*a(n+11)+1/16*(3683866163*n^2+93617955987*n+596768869546)/(2*n+53)/(n+26)*a(n+12)-3/32*(3935950077*n^2+104390310173*n+693195213084)/(2*n+53)/(n+26)*a(n+13)+3/32*(458405*n^2+2637517*n+3726348)/(2*n+53)/(n+26)*a(n+2)-1/32*(3773657*n^2+24614913*n+38867068)/(2*n+53)/(n+26)*a(n+3)+1/32*(7368883*n^2+60653781*n+129990848)/(2*n+53)/(n+26)*a(n+4)-1/16*(2179541*n^2+14707425*n+16019218)/(2*n+53)/(n+26)*a(n+5)+7917/8*(n+2)*(n+1)/(2*n+53)/(n+26)*a(n)-1/8*(75847*n+193159)*(n+2)/(2*n+53)/(n+26)*a(n+1), n >= 27
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) = 115
a \! \left(6\right) = 607
a \! \left(7\right) = 3370
a \! \left(8\right) = 19235
a \! \left(9\right) = 111571
a \! \left(10\right) = 653603
a \! \left(11\right) = 3853424
a \! \left(12\right) = 22815443
a \! \left(13\right) = 135482334
a \! \left(14\right) = 806180411
a \! \left(15\right) = 4804250596
a \! \left(16\right) = 28660891938
a \! \left(17\right) = 171120790746
a \! \left(18\right) = 1022298997790
a \! \left(19\right) = 6110152136891
a \! \left(20\right) = 36532429252431
a \! \left(21\right) = 218485628254633
a \! \left(22\right) = 1306949786188459
a \! \left(23\right) = 7819280602197891
a \! \left(24\right) = 46787663410514384
a \! \left(25\right) = 279988909890506863
a \! \left(26\right) = 1675660680553158236
a \! \left(n +27\right) = -\frac{3 \left(2870 n^{2}+143228 n +1786491\right) a \! \left(n +25\right)}{4 \left(2 n +53\right) \left(n +26\right)}+\frac{3 \left(150 n^{2}+7639 n +97258\right) a \! \left(n +26\right)}{4 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(24246610792 n^{2}+858496776663 n +7605196753667\right) a \! \left(n +18\right)}{16 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(12483090055 n^{2}+460618546182 n +4250174677163\right) a \! \left(n +19\right)}{16 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(2059267847 n^{2}+79071121917 n +758781691441\right) a \! \left(n +20\right)}{8 \left(2 n +53\right) \left(n +26\right)}+\frac{3 \left(141216301 n^{2}+5631113645 n +56078045437\right) a \! \left(n +21\right)}{8 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(51035902 n^{2}+2101523442 n +21584384003\right) a \! \left(n +22\right)}{8 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(2842105 n^{2}+117679806 n +1208358899\right) a \! \left(n +23\right)}{8 \left(2 n +53\right) \left(n +26\right)}+\frac{3 \left(9178 n^{2}+532642 n +7453545\right) a \! \left(n +24\right)}{4 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(30721703953 n^{2}+1040895182118 n +8828090853959\right) a \! \left(n +17\right)}{16 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(5234940499 n^{2}+131947290891 n +820854701750\right) a \! \left(n +14\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(9580485722 n^{2}+302061226695 n +2378158241950\right) a \! \left(n +15\right)}{16 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(24502373768 n^{2}+793768381311 n +6436861822186\right) a \! \left(n +16\right)}{16 \left(2 n +53\right) \left(n +26\right)}-\frac{3 \left(12072591 n^{2}+180302185 n +664492260\right) a \! \left(n +6\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(168501335 n^{2}+2504088123 n +9161071858\right) a \! \left(n +7\right)}{32 \left(2 n +53\right) \left(n +26\right)}-\frac{3 \left(140883621 n^{2}+2177583625 n +8298517096\right) a \! \left(n +8\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(529384081 n^{2}+8650037967 n +35244539990\right) a \! \left(n +9\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(104225549 n^{2}+2780641806 n +17171348851\right) a \! \left(n +10\right)}{16 \left(2 n +53\right) \left(n +26\right)}-\frac{3 \left(427330215 n^{2}+10124230856 n +60248773028\right) a \! \left(n +11\right)}{16 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(3683866163 n^{2}+93617955987 n +596768869546\right) a \! \left(n +12\right)}{16 \left(2 n +53\right) \left(n +26\right)}-\frac{3 \left(3935950077 n^{2}+104390310173 n +693195213084\right) a \! \left(n +13\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{3 \left(458405 n^{2}+2637517 n +3726348\right) a \! \left(n +2\right)}{32 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(3773657 n^{2}+24614913 n +38867068\right) a \! \left(n +3\right)}{32 \left(2 n +53\right) \left(n +26\right)}+\frac{\left(7368883 n^{2}+60653781 n +129990848\right) a \! \left(n +4\right)}{32 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(2179541 n^{2}+14707425 n +16019218\right) a \! \left(n +5\right)}{16 \left(2 n +53\right) \left(n +26\right)}+\frac{7917 \left(n +2\right) \left(n +1\right) a \! \left(n \right)}{8 \left(2 n +53\right) \left(n +26\right)}-\frac{\left(75847 n +193159\right) \left(n +2\right) a \! \left(n +1\right)}{8 \left(2 n +53\right) \left(n +26\right)}, \quad n \geq 27
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/24107/
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[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[34,x]+F[9,x]
F[9,x] = F[0,x]*F[10,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[10,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[11,x]*F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]^2*F[20,x]*F[4,x]
F[23,x] = F[24,x]+F[32,x]
F[24,x] = F[25,x]+F[30,x]
F[25,x] = F[26,x]+F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[12,x]+F[29,x]
F[29,x] = F[11,x]*F[12,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[14,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[10,x]*F[21,x]*F[4,x]
F[34,x] = F[145,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]*F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[73,x]
F[38,x] = F[0,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[11,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[11,x]*F[39,x]*F[4,x]
F[43,x] = F[44,x]+F[62,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[57,x]
F[47,x] = F[48,x]+F[55,x]
F[48,x] = F[44,x]+F[49,x]
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[49,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[49,x]^2*F[4,x]*F[52,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[48,x]*F[49,x]*F[52,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[49,x]*F[52,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[44,x]*F[52,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[44,x]*F[64,x]
F[64,x] = F[40,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[17,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[17,x]*F[39,x]*F[4,x]
F[71,x] = F[72,x]
F[72,x] = F[10,x]*F[4,x]*F[64,x]
F[73,x] = F[140,x]+F[74,x]
F[74,x] = F[105,x]+F[75,x]
F[75,x] = F[6,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[103,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[48,x]*F[81,x]
F[81,x] = F[100,x]+F[82,x]
F[82,x] = F[0,x]*F[83,x]
F[83,x] = F[84,x]+F[97,x]
F[84,x] = F[11,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[11,x]*F[4,x]*F[87,x]
F[87,x] = F[48,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[48,x]*F[90,x]
F[90,x] = F[84,x]+F[91,x]
F[91,x] = F[92,x]+F[94,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[49,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[90,x]*F[96,x]
F[96,x] = F[29,x]+F[93,x]
F[97,x] = F[14,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[14,x]*F[4,x]*F[87,x]
F[100,x] = F[101,x]+F[34,x]
F[101,x] = F[102,x]
F[102,x] = F[34,x]*F[4,x]*F[87,x]
F[103,x] = F[104,x]
F[104,x] = F[4,x]*F[8,x]*F[87,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[132,x]
F[108,x] = F[109,x]+F[130,x]
F[109,x] = F[110,x]+F[74,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]*F[49,x]
F[112,x] = F[113,x]+F[74,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[119,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[48,x]*F[8,x]
F[118,x] = F[10,x]*F[74,x]
F[119,x] = F[120,x]
F[120,x] = F[11,x]*F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[124,x]
F[122,x] = F[116,x]+F[123,x]
F[123,x] = F[10,x]*F[113,x]
F[124,x] = F[125,x]*F[48,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[116,x]+F[128,x]
F[128,x] = F[129,x]
F[129,x] = F[121,x]*F[4,x]*F[49,x]
F[130,x] = F[131,x]
F[131,x] = F[109,x]*F[4,x]*F[49,x]*F[52,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[138,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[46,x]*F[81,x]
F[137,x] = F[108,x]*F[83,x]
F[138,x] = F[139,x]
F[139,x] = F[121,x]*F[4,x]*F[84,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[4,x]*F[74,x]
F[142,x] = F[143,x]+F[40,x]
F[143,x] = F[144,x]
F[144,x] = F[4,x]*F[67,x]
F[145,x] = F[146,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[155,x]
F[148,x] = F[149,x]+F[153,x]
F[149,x] = F[150,x]+F[34,x]
F[150,x] = F[151,x]
F[151,x] = F[11,x]*F[152,x]*F[4,x]
F[152,x] = F[125,x]+F[34,x]
F[153,x] = F[154,x]
F[154,x] = F[11,x]*F[149,x]*F[20,x]*F[4,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[161,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[16,x]*F[37,x]
F[160,x] = F[148,x]*F[39,x]
F[161,x] = F[162,x]
F[162,x] = F[121,x]*F[4,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{34}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right) F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{145}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{73}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{62}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{49}\! \left(x \right) F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right) F_{52}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{52}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{40}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{17}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{73}\! \left(x \right) = F_{140}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{105}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{6}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{103}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{100}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{0}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{97}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{48}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{84}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{29}\! \left(x \right)+F_{93}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{34}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right) F_{87}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{132}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{130}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{74}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{74}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{118}\! \left(x \right) = F_{10}\! \left(x \right) F_{74}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{11}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{124}\! \left(x \right)
F_{122}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{10}\! \left(x \right) F_{113}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{48}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{116}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right) F_{52}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{138}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{46}\! \left(x \right) F_{81}\! \left(x \right)
F_{137}\! \left(x \right) = F_{108}\! \left(x \right) F_{83}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{40}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{155}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{34}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{125}\! \left(x \right)+F_{34}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{11}\! \left(x \right) F_{149}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{161}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{16}\! \left(x \right) F_{37}\! \left(x \right)
F_{160}\! \left(x \right) = F_{148}\! \left(x \right) F_{39}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_34(x) + F_9(x))
Eq(F_9(x), F_0(x)*F_10(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_10(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_11(x)*F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)**2*F_20(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_32(x))
Eq(F_24(x), F_25(x) + F_30(x))
Eq(F_25(x), F_26(x) + F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_12(x) + F_29(x))
Eq(F_29(x), F_11(x)*F_12(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_14(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_10(x)*F_21(x)*F_4(x))
Eq(F_34(x), F_145(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_73(x))
Eq(F_38(x), F_0(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_11(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_11(x)*F_39(x)*F_4(x))
Eq(F_43(x), F_44(x) + F_62(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_57(x))
Eq(F_47(x), F_48(x) + F_55(x))
Eq(F_48(x), F_44(x) + F_49(x))
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_49(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_49(x)**2*F_52(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_48(x)*F_49(x)*F_52(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_49(x)*F_52(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_44(x)*F_52(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_44(x)*F_64(x))
Eq(F_64(x), F_40(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_17(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_17(x)*F_39(x)*F_4(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_10(x)*F_4(x)*F_64(x))
Eq(F_73(x), F_140(x) + F_74(x))
Eq(F_74(x), F_105(x) + F_75(x))
Eq(F_75(x), F_6(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_103(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_48(x)*F_81(x))
Eq(F_81(x), F_100(x) + F_82(x))
Eq(F_82(x), F_0(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_97(x))
Eq(F_84(x), F_11(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_11(x)*F_4(x)*F_87(x))
Eq(F_87(x), F_48(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_48(x)*F_90(x))
Eq(F_90(x), F_84(x) + F_91(x))
Eq(F_91(x), F_92(x) + F_94(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_49(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_90(x)*F_96(x))
Eq(F_96(x), F_29(x) + F_93(x))
Eq(F_97(x), F_14(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_14(x)*F_4(x)*F_87(x))
Eq(F_100(x), F_101(x) + F_34(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_34(x)*F_4(x)*F_87(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_4(x)*F_8(x)*F_87(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_132(x))
Eq(F_108(x), F_109(x) + F_130(x))
Eq(F_109(x), F_110(x) + F_74(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x)*F_49(x))
Eq(F_112(x), F_113(x) + F_74(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_119(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_48(x)*F_8(x))
Eq(F_118(x), F_10(x)*F_74(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_11(x)*F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_124(x))
Eq(F_122(x), F_116(x) + F_123(x))
Eq(F_123(x), F_10(x)*F_113(x))
Eq(F_124(x), F_125(x)*F_48(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_116(x) + F_128(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_121(x)*F_4(x)*F_49(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_109(x)*F_4(x)*F_49(x)*F_52(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_138(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_46(x)*F_81(x))
Eq(F_137(x), F_108(x)*F_83(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_121(x)*F_4(x)*F_84(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_4(x)*F_74(x))
Eq(F_142(x), F_143(x) + F_40(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_4(x)*F_67(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_155(x))
Eq(F_148(x), F_149(x) + F_153(x))
Eq(F_149(x), F_150(x) + F_34(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_11(x)*F_152(x)*F_4(x))
Eq(F_152(x), F_125(x) + F_34(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_11(x)*F_149(x)*F_20(x)*F_4(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_161(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_16(x)*F_37(x))
Eq(F_160(x), F_148(x)*F_39(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_121(x)*F_4(x)*F_40(x))
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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}], "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 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{"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}], "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, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_untracked_fusion
Tree: http://permpal.com/tree/24108/
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[14,x]*F[4,x]
F[4,x] = F[21,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[14,x]
F[12,x] = F[13,x]+F[15,x]
F[13,x] = F[14,x]*F[8,x]
F[14,x] = x
F[15,x] = F[16,x]+F[18,x]
F[16,x] = F[17,x]
F[17,x] = F[8,x]^2*F[14,x]*F[5,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]*F[8,x]
F[20,x] = F[6,x]+F[9,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = F[27,x]+F[34,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[14,x]*F[30,x]
F[30,x] = F[27,x]+F[31,x]
F[31,x] = F[14,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[28,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = F[36,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[38,x]+F[40,x]
F[38,x] = F[34,x]*F[39,x]
F[39,x] = F[1,x]+F[14,x]
F[40,x] = F[41,x]+F[43,x]
F[41,x] = F[42,x]
F[42,x] = F[14,x]*F[26,x]*F[5,x]*F[8,x]
F[43,x] = F[44,x]
F[44,x] = F[14,x]*F[20,x]*F[26,x]
F[45,x] = F[139,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[14,x]*F[48,x]*F[5,x]
F[48,x] = F[49,x]+F[74,x]
F[49,x] = F[0,x]*F[50,x]
F[50,x] = F[51,x]+F[69,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[14,x]*F[51,x]
F[55,x] = F[56,x]
F[56,x] = F[14,x]*F[57,x]
F[57,x] = F[58,x]+F[64,x]
F[58,x] = F[51,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[14,x]*F[51,x]*F[52,x]*F[61,x]
F[61,x] = F[52,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[14,x]*F[57,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[14,x]*F[51,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[51,x]*F[68,x]
F[68,x] = F[53,x]+F[62,x]
F[69,x] = F[70,x]
F[70,x] = F[14,x]*F[51,x]*F[71,x]
F[71,x] = F[72,x]+F[8,x]
F[72,x] = F[73,x]
F[73,x] = F[14,x]*F[50,x]*F[8,x]
F[74,x] = F[137,x]+F[75,x]
F[75,x] = F[76,x]+F[96,x]
F[76,x] = F[77,x]
F[77,x] = F[14,x]*F[52,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = F[45,x]+F[80,x]
F[80,x] = F[0,x]*F[26,x]
F[81,x] = F[82,x]
F[82,x] = F[14,x]*F[79,x]*F[83,x]
F[83,x] = F[84,x]+F[90,x]
F[84,x] = F[52,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[14,x]*F[52,x]*F[87,x]
F[87,x] = F[26,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[14,x]*F[26,x]*F[83,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[5,x]*F[53,x]
F[92,x] = F[93,x]
F[93,x] = F[14,x]*F[83,x]*F[94,x]
F[94,x] = F[91,x]+F[95,x]
F[95,x] = F[52,x]*F[53,x]
F[96,x] = F[97,x]
F[97,x] = F[14,x]*F[98,x]
F[98,x] = F[123,x]+F[99,x]
F[99,x] = F[100,x]+F[121,x]
F[100,x] = F[101,x]+F[75,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[14,x]*F[52,x]
F[103,x] = F[104,x]+F[75,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[14,x]
F[106,x] = F[107,x]+F[110,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[51,x]*F[79,x]
F[109,x] = F[26,x]*F[75,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[14,x]*F[5,x]
F[112,x] = F[113,x]+F[120,x]
F[113,x] = F[107,x]+F[114,x]
F[114,x] = F[115,x]*F[51,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[14,x]
F[117,x] = F[107,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[112,x]*F[14,x]*F[52,x]
F[120,x] = F[104,x]*F[26,x]
F[121,x] = F[122,x]
F[122,x] = F[100,x]*F[14,x]*F[52,x]*F[61,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[14,x]
F[125,x] = F[126,x]+F[135,x]
F[126,x] = F[127,x]+F[134,x]
F[127,x] = F[128,x]*F[78,x]
F[128,x] = F[129,x]+F[58,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]
F[131,x] = F[14,x]*F[52,x]*F[61,x]
F[132,x] = F[133,x]
F[133,x] = F[14,x]*F[55,x]*F[61,x]
F[134,x] = F[87,x]*F[99,x]
F[135,x] = F[136,x]
F[136,x] = F[112,x]*F[14,x]*F[84,x]
F[137,x] = F[138,x]
F[138,x] = F[14,x]*F[71,x]*F[75,x]
F[139,x] = F[140,x]
F[140,x] = F[14,x]*F[141,x]
F[141,x] = F[142,x]+F[150,x]
F[142,x] = F[143,x]+F[146,x]
F[143,x] = F[144,x]
F[144,x] = F[14,x]*F[145,x]*F[48,x]
F[145,x] = F[26,x]+F[41,x]
F[146,x] = F[147,x]
F[147,x] = F[14,x]*F[148,x]*F[26,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[48,x]*F[8,x]
F[150,x] = F[151,x]+F[158,x]
F[151,x] = F[152,x]+F[156,x]
F[152,x] = F[153,x]+F[45,x]
F[153,x] = F[154,x]
F[154,x] = F[14,x]*F[155,x]*F[5,x]
F[155,x] = F[115,x]+F[45,x]
F[156,x] = F[157,x]
F[157,x] = F[14,x]*F[152,x]*F[5,x]*F[8,x]
F[158,x] = F[159,x]
F[159,x] = F[14,x]*F[160,x]
F[160,x] = F[161,x]+F[162,x]
F[161,x] = F[151,x]*F[50,x]
F[162,x] = F[163,x]
F[163,x] = F[112,x]*F[14,x]*F[164,x]
F[164,x] = F[165,x]+F[5,x]
F[165,x] = F[166,x]
F[166,x] = F[14,x]*F[167,x]*F[5,x]
F[167,x] = F[164,x]+F[168,x]
F[168,x] = F[169,x]+F[91,x]
F[169,x] = F[170,x]
F[170,x] = F[14,x]*F[167,x]*F[171,x]
F[171,x] = F[172,x]+F[91,x]
F[172,x] = F[52,x]*F[53,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{15}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{20}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{45}\! \left(x \right) = F_{139}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{69}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{14}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{52}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{52}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{57}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{137}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{96}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{45}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{26}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{79}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{90}\! \left(x \right)
F_{84}\! \left(x \right) = F_{52}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{26}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right) F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{5}\! \left(x \right) F_{53}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right) F_{83}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{52}\! \left(x \right) F_{53}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{123}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{121}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{75}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{75}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{14}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{110}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{51}\! \left(x \right) F_{79}\! \left(x \right)
F_{109}\! \left(x \right) = F_{26}\! \left(x \right) F_{75}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{120}\! \left(x \right)
F_{113}\! \left(x \right) = F_{107}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{51}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{117}\! \left(x \right) = F_{107}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{112}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{120}\! \left(x \right) = F_{104}\! \left(x \right) F_{26}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{100}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{61}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{14}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{135}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{134}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{78}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{58}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{61}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right) F_{61}\! \left(x \right)
F_{134}\! \left(x \right) = F_{87}\! \left(x \right) F_{99}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{112}\! \left(x \right) F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right) F_{75}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{14}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{150}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{14}\! \left(x \right) F_{145}\! \left(x \right) F_{48}\! \left(x \right)
F_{145}\! \left(x \right) = F_{26}\! \left(x \right)+F_{41}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{14}\! \left(x \right) F_{148}\! \left(x \right) F_{26}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{158}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{156}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{45}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{14}\! \left(x \right) F_{155}\! \left(x \right) F_{5}\! \left(x \right)
F_{155}\! \left(x \right) = F_{115}\! \left(x \right)+F_{45}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{14}\! \left(x \right) F_{152}\! \left(x \right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{14}\! \left(x \right) F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{162}\! \left(x \right)
F_{161}\! \left(x \right) = F_{151}\! \left(x \right) F_{50}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{112}\! \left(x \right) F_{14}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{5}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{14}\! \left(x \right) F_{167}\! \left(x \right) F_{5}\! \left(x \right)
F_{167}\! \left(x \right) = F_{164}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{91}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{14}\! \left(x \right) F_{167}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{91}\! \left(x \right)
F_{172}\! \left(x \right) = F_{52}\! \left(x \right) F_{53}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_14(x)*F_4(x))
Eq(F_4(x), F_21(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_14(x))
Eq(F_12(x), F_13(x) + F_15(x))
Eq(F_13(x), F_14(x)*F_8(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x) + F_18(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_5(x)*F_8(x)**2)
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x)*F_8(x))
Eq(F_20(x), F_6(x) + F_9(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_34(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_14(x)*F_30(x))
Eq(F_30(x), F_27(x) + F_31(x))
Eq(F_31(x), F_14(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_28(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_40(x))
Eq(F_38(x), F_34(x)*F_39(x))
Eq(F_39(x), F_1(x) + F_14(x))
Eq(F_40(x), F_41(x) + F_43(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_14(x)*F_26(x)*F_5(x)*F_8(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_14(x)*F_20(x)*F_26(x))
Eq(F_45(x), F_139(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_14(x)*F_48(x)*F_5(x))
Eq(F_48(x), F_49(x) + F_74(x))
Eq(F_49(x), F_0(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_69(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_14(x)*F_51(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_14(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_64(x))
Eq(F_58(x), F_51(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_14(x)*F_51(x)*F_52(x)*F_61(x))
Eq(F_61(x), F_52(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_14(x)*F_57(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_14(x)*F_51(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_51(x)*F_68(x))
Eq(F_68(x), F_53(x) + F_62(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_14(x)*F_51(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_8(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_14(x)*F_50(x)*F_8(x))
Eq(F_74(x), F_137(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_96(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_14(x)*F_52(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_45(x) + F_80(x))
Eq(F_80(x), F_0(x)*F_26(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_14(x)*F_79(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_90(x))
Eq(F_84(x), F_52(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_14(x)*F_52(x)*F_87(x))
Eq(F_87(x), F_26(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_14(x)*F_26(x)*F_83(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_5(x)*F_53(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_14(x)*F_83(x)*F_94(x))
Eq(F_94(x), F_91(x) + F_95(x))
Eq(F_95(x), F_52(x)*F_53(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_14(x)*F_98(x))
Eq(F_98(x), F_123(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_121(x))
Eq(F_100(x), F_101(x) + F_75(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_14(x)*F_52(x))
Eq(F_103(x), F_104(x) + F_75(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_14(x))
Eq(F_106(x), F_107(x) + F_110(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_51(x)*F_79(x))
Eq(F_109(x), F_26(x)*F_75(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_14(x)*F_5(x))
Eq(F_112(x), F_113(x) + F_120(x))
Eq(F_113(x), F_107(x) + F_114(x))
Eq(F_114(x), F_115(x)*F_51(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_14(x))
Eq(F_117(x), F_107(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_112(x)*F_14(x)*F_52(x))
Eq(F_120(x), F_104(x)*F_26(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_100(x)*F_14(x)*F_52(x)*F_61(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_14(x))
Eq(F_125(x), F_126(x) + F_135(x))
Eq(F_126(x), F_127(x) + F_134(x))
Eq(F_127(x), F_128(x)*F_78(x))
Eq(F_128(x), F_129(x) + F_58(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_14(x)*F_52(x)*F_61(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_14(x)*F_55(x)*F_61(x))
Eq(F_134(x), F_87(x)*F_99(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_112(x)*F_14(x)*F_84(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_14(x)*F_71(x)*F_75(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_14(x)*F_141(x))
Eq(F_141(x), F_142(x) + F_150(x))
Eq(F_142(x), F_143(x) + F_146(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_14(x)*F_145(x)*F_48(x))
Eq(F_145(x), F_26(x) + F_41(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_14(x)*F_148(x)*F_26(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_48(x)*F_8(x))
Eq(F_150(x), F_151(x) + F_158(x))
Eq(F_151(x), F_152(x) + F_156(x))
Eq(F_152(x), F_153(x) + F_45(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_14(x)*F_155(x)*F_5(x))
Eq(F_155(x), F_115(x) + F_45(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_14(x)*F_152(x)*F_5(x)*F_8(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_14(x)*F_160(x))
Eq(F_160(x), F_161(x) + F_162(x))
Eq(F_161(x), F_151(x)*F_50(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_112(x)*F_14(x)*F_164(x))
Eq(F_164(x), F_165(x) + F_5(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_14(x)*F_167(x)*F_5(x))
Eq(F_167(x), F_164(x) + F_168(x))
Eq(F_168(x), F_169(x) + F_91(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_14(x)*F_167(x)*F_171(x))
Eq(F_171(x), F_172(x) + F_91(x))
Eq(F_172(x), F_52(x)*F_53(x))
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.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": false}], "iterative": false, "name": "point_placements_untracked_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, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": 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