01342_02341_03241_04231_12340_13240_14230_23140_24130_34120
Counting sequence:
1, 1, 2, 6, 24, 110, 530, 2597, 12796, 63156, 311826, 1539461, 7598492, 37496186, 184997956, 912625066, 4501830916, 22206530636, 109543668026, 540413135951, 2666309305376, 13156864704526, 64932244378096, 320509876116426, 1582342892961624, 7813430487947280, 38589353188263380, 190624850409535707, 941843407407450186, 4654417403633826236, 23005896125557032326, 113736415850679118421, 562400260350340160020, 2781479482703559155956, 13759072809304051165594, 68074408669597991270375, 336866883568898672559440, 1667288475660201478265702, 8253523102353254385219456, 40864140007366113834041076, 202356840086837891594805876, 1002222418567751365567002676, 4964542284671298559538126296, 24595824819872912307388460251, 121873384563999688219746430006, 603976328989877406032408515816, 2993593503003172125702771572866, 14839727961137007883363684203961, 73572859466807868261876579231376, 364809669220661267948369162858776, 1809133122407273373217635074626876, 8972814783758993999623796369874301, 44508138942675608378773012072259182, 220801147070572126781414946276540056, 1095501614386220341388525985854369594, 5435922004307259042406897607202588470, 26976191991481836306523591769147813390, 133885664546171870932844803929566364262, 664557152390208652606201842589548377446, 3298938903652030310361720046549458569931, 16377921273051490596832528000572268092576, 81317643743218639373773814389383257321886, 403786000961773491229530326639257219327692, 2005197685871651521752108590519619365958586, 9958676581187744113282730051965371079213876, 49463361070591868012719390972171392240885076, 245698370249057997923843188041484455207936826, 1220553189046130440445492510633613237779051551, 6063816903667916361472726520668227073319661376, 30127948872346196972652359819143651562857279126, 149701577380948796186261351068476723789001239376, 743902031902888225732600994311180427999975808876, 3696893409108206226881269859196379143904950055476, 18373386455476180155556709504559984521250964965876, 91321259328232856687301864400010172510782513066856, 453925207638276886750935215416125500331573181138291, 2256450361680479703331590104191027291945821842718166, 11217490462236718310589993735140846101795710797972936, 55769077669292615747071164326935902260829090889852226, 277279938445458465064686049215171641703056799579936851, 1378701008786976878718355864900170619724454401762398876, 6855637350168521530993722715482565992826677958275635076, 34091894447589147847292601893250740897589089079247557216, 169542844020002305686717741043288031535668116640713402301, 843203328243948404249223489332692617759107961835612610906, 4193814178340069177538294191716747122669888092570686501916, 20859773919877054789965169535355532704624215056825591862566, 103760745955615580402265993707964830146301682898862791824586, 516153876996812750683225580229736416079972210720050440278426, 2567718921478086309835055476987921581412858582888210831464626, 12774312002746262921852784380087911153174961228811774178650626, 63554878156590436772837112345243599803213419512741367209148251, 316214069731206325600605671487827757232657410884850759290816676, 1573381439562752895449919275844939488465639699709256192365295626, 7829012854020592688972873950849961721917457991472109920312040576, 38958279302554985775844472885127442625598885960112859835008571226, 193870594410617184537321772651222986778986209868559068568107486976, 964813069377104711096483999975924537814416755666394476858729079776, 4801679080013120445352954564442231555026955304221912042015002366876, 23897994971084485237474932892034075347355270578400654254776531148501, 118945456060545843547475918214673337517166028994930337045482806728126
Implicit equation for the generating function in Maple syntax:
x^2*(5*x-1)^2*(x-1)^6*F(x)^4+4*x^2*(5*x-1)^2*(x-1)^5*F(x)^3+(5*x-1)*(10*x^5-29*x^4+50*x^3-44*x^2+12*x-1)*(x-1)^3*F(x)^2+2*(5*x-1)*(10*x^5-49*x^4+74*x^3-48*x^2+12*x-1)*(x-1)^2*F(x)+25*x^8-295*x^6+724*x^5-778*x^4+434*x^3-126*x^2+18*x-1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(5 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{4}+4 x^{2} \left(5 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)^{3}+\left(5 x -1\right) \left(10 x^{5}-29 x^{4}+50 x^{3}-44 x^{2}+12 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)^{2}+2 \left(5 x -1\right) \left(10 x^{5}-49 x^{4}+74 x^{3}-48 x^{2}+12 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+25 x^{8}-295 x^{6}+724 x^{5}-778 x^{4}+434 x^{3}-126 x^{2}+18 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(n+5) = 350/3*(n+1)*(2*n+1)/(n+6)/(n+3)*a(n)-5/3*(283*n^2+661*n+346)/(n+6)/(n+3)*a(n+1)+10/3*(99*n^2+382*n+309)/(n+6)/(n+3)*a(n+2)-2/3*(161*n^2+898*n+1082)/(n+6)/(n+3)*a(n+3)+2/3*(25*n^2+183*n+296)/(n+6)/(n+3)*a(n+4)-4*(9*n+7)/(n+6)/(n+3), n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a{\left(n + 5 \right)} = \frac{350 \left(n + 1\right) \left(2 n + 1\right) a{\left(n \right)}}{3 \left(n + 3\right) \left(n + 6\right)} - \frac{4 \left(9 n + 7\right)}{\left(n + 3\right) \left(n + 6\right)} + \frac{2 \left(25 n^{2} + 183 n + 296\right) a{\left(n + 4 \right)}}{3 \left(n + 3\right) \left(n + 6\right)} + \frac{10 \left(99 n^{2} + 382 n + 309\right) a{\left(n + 2 \right)}}{3 \left(n + 3\right) \left(n + 6\right)} - \frac{2 \left(161 n^{2} + 898 n + 1082\right) a{\left(n + 3 \right)}}{3 \left(n + 3\right) \left(n + 6\right)} - \frac{5 \left(283 n^{2} + 661 n + 346\right) a{\left(n + 1 \right)}}{3 \left(n + 3\right) \left(n + 6\right)}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24505/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[20,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[11,x]*F[14,x]*F[17,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[14,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[114,x]+F[23,x]
F[23,x] = F[24,x]*F[90,x]
F[24,x] = 1/F[14,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[10,x]+F[27,x]
F[27,x] = 1/F[89,x]*F[28,x]
F[28,x] = -F[80,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = 1/F[14,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[44,x]
F[35,x] = F[18,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[14,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[14,x]+F[39,x]
F[43,x] = F[12,x]*F[14,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[74,x]
F[47,x] = F[48,x]*F[64,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[14,x]*F[51,x]
F[51,x] = 1/F[48,x]*F[52,x]
F[52,x] = -F[57,x]+F[53,x]
F[53,x] = 1/F[11,x]/F[14,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[14,x]*F[29,x]
F[57,x] = -F[63,x]+F[58,x]
F[58,x] = 1/F[11,x]/F[14,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[55,x]
F[61,x] = F[62,x]
F[62,x] = F[48,x]^2*F[11,x]*F[14,x]
F[63,x] = F[49,x]*F[51,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[48,x]+F[67,x]
F[67,x] = F[42,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[48,x]*F[67,x]
F[72,x] = F[48,x]*F[67,x]
F[73,x] = F[17,x]*F[34,x]
F[74,x] = F[67,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[18,x]*F[48,x]
F[77,x] = F[17,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[24,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[11,x]/F[14,x]*F[82,x]
F[82,x] = F[60,x]
F[83,x] = F[27,x]*F[84,x]
F[84,x] = F[12,x]+F[85,x]
F[85,x] = F[40,x]+F[86,x]+F[87,x]
F[86,x] = F[14,x]*F[84,x]
F[87,x] = F[14,x]*F[88,x]
F[88,x] = F[12,x]+F[85,x]
F[89,x] = F[11,x]+F[88,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = 1/F[10,x]*F[92,x]
F[92,x] = -F[112,x]+F[93,x]
F[93,x] = 1/F[14,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[111,x]+F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = -F[109,x]+F[99,x]
F[99,x] = 1/F[14,x]/F[48,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[11,x]*F[14,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[17,x]*F[51,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[14,x]*F[17,x]
F[106,x] = 1/F[11,x]/F[14,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[14,x]*F[51,x]*F[99,x]
F[109,x] = F[110,x]
F[110,x] = F[10,x]*F[14,x]*F[98,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]
F[113,x] = F[26,x]*F[48,x]
F[114,x] = F[115,x]*F[48,x]
F[115,x] = -F[24,x]+F[29,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \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_{20}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \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_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \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_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{114}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{90}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{89}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \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) = \frac{F_{33}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{44}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{64}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{48}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{48} \left(x \right)^{2} F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{48}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{60}\! \left(x \right)
F_{83}\! \left(x \right) = F_{27}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{111}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{14}\! \left(x \right) F_{48}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{17}\! \left(x \right) F_{51}\! \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_{17}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{26}\! \left(x \right) F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{48}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{29}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(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_20(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_11(x)*F_14(x)*F_17(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_14(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_114(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_90(x))
Eq(F_24(x), F_25(x)/F_14(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_10(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_89(x))
Eq(F_28(x), F_29(x) - F_80(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x)/F_14(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_44(x))
Eq(F_35(x), F_18(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_14(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_39(x))
Eq(F_43(x), F_12(x)*F_14(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_74(x))
Eq(F_47(x), F_48(x)*F_64(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_14(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_48(x))
Eq(F_52(x), F_53(x) - F_57(x))
Eq(F_53(x), F_54(x)/(F_11(x)*F_14(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_14(x)*F_29(x))
Eq(F_57(x), F_58(x) - F_63(x))
Eq(F_58(x), F_59(x)/(F_11(x)*F_14(x)))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_55(x) - F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_14(x)*F_48(x)**2)
Eq(F_63(x), F_49(x)*F_51(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_48(x) + F_67(x))
Eq(F_67(x), F_42(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_48(x)*F_67(x))
Eq(F_72(x), F_48(x)*F_67(x))
Eq(F_73(x), F_17(x)*F_34(x))
Eq(F_74(x), F_67(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_18(x)*F_48(x))
Eq(F_77(x), F_17(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_24(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/(F_11(x)*F_14(x)))
Eq(F_82(x), F_60(x))
Eq(F_83(x), F_27(x)*F_84(x))
Eq(F_84(x), F_12(x) + F_85(x))
Eq(F_85(x), F_40(x) + F_86(x) + F_87(x))
Eq(F_86(x), F_14(x)*F_84(x))
Eq(F_87(x), F_14(x)*F_88(x))
Eq(F_88(x), F_12(x) + F_85(x))
Eq(F_89(x), F_11(x) + F_88(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_10(x))
Eq(F_92(x), -F_112(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_14(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_111(x) + F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), -F_109(x) + F_99(x))
Eq(F_99(x), F_100(x)/(F_14(x)*F_48(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_11(x)*F_14(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_17(x)*F_51(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_14(x)*F_17(x))
Eq(F_106(x), F_107(x)/(F_11(x)*F_14(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_14(x)*F_51(x)*F_99(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_10(x)*F_14(x)*F_98(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_26(x)*F_48(x))
Eq(F_114(x), F_115(x)*F_48(x))
Eq(F_115(x), -F_24(x) + F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0], "pos": [[6, 2], [6, 2], [6, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25096/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[20,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[11,x]*F[14,x]*F[17,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[14,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[114,x]+F[23,x]
F[23,x] = F[24,x]*F[90,x]
F[24,x] = 1/F[14,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[10,x]+F[27,x]
F[27,x] = 1/F[89,x]*F[28,x]
F[28,x] = -F[80,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = 1/F[14,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[44,x]
F[35,x] = F[18,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[14,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[14,x]+F[39,x]
F[43,x] = F[12,x]*F[14,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[74,x]
F[47,x] = F[48,x]*F[64,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[14,x]*F[51,x]
F[51,x] = 1/F[48,x]*F[52,x]
F[52,x] = -F[57,x]+F[53,x]
F[53,x] = 1/F[11,x]/F[14,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[14,x]*F[29,x]
F[57,x] = -F[63,x]+F[58,x]
F[58,x] = 1/F[11,x]/F[14,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[55,x]
F[61,x] = F[62,x]
F[62,x] = F[48,x]^2*F[11,x]*F[14,x]
F[63,x] = F[49,x]*F[51,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[48,x]+F[67,x]
F[67,x] = F[42,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[48,x]*F[67,x]
F[72,x] = F[48,x]*F[67,x]
F[73,x] = F[17,x]*F[34,x]
F[74,x] = F[67,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[18,x]*F[48,x]
F[77,x] = F[17,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[24,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[11,x]/F[14,x]*F[82,x]
F[82,x] = F[60,x]
F[83,x] = F[27,x]*F[84,x]
F[84,x] = F[12,x]+F[85,x]
F[85,x] = F[40,x]+F[86,x]+F[87,x]
F[86,x] = F[14,x]*F[84,x]
F[87,x] = F[14,x]*F[88,x]
F[88,x] = F[12,x]+F[85,x]
F[89,x] = F[11,x]+F[88,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = 1/F[10,x]*F[92,x]
F[92,x] = -F[112,x]+F[93,x]
F[93,x] = 1/F[14,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[111,x]+F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = -F[109,x]+F[99,x]
F[99,x] = 1/F[14,x]/F[48,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[11,x]*F[14,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[17,x]*F[51,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[14,x]*F[17,x]
F[106,x] = 1/F[11,x]/F[14,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[14,x]*F[51,x]*F[99,x]
F[109,x] = F[110,x]
F[110,x] = F[10,x]*F[14,x]*F[98,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]
F[113,x] = F[26,x]*F[48,x]
F[114,x] = F[115,x]*F[48,x]
F[115,x] = -F[24,x]+F[29,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \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_{20}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \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_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \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_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{114}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{90}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{89}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \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) = \frac{F_{33}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{44}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{64}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{48}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{48} \left(x \right)^{2} F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{48}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{60}\! \left(x \right)
F_{83}\! \left(x \right) = F_{27}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{111}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{14}\! \left(x \right) F_{48}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{17}\! \left(x \right) F_{51}\! \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_{17}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{26}\! \left(x \right) F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{48}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{29}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(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_20(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_11(x)*F_14(x)*F_17(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_14(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_114(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_90(x))
Eq(F_24(x), F_25(x)/F_14(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_10(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_89(x))
Eq(F_28(x), F_29(x) - F_80(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x)/F_14(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_44(x))
Eq(F_35(x), F_18(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_14(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_39(x))
Eq(F_43(x), F_12(x)*F_14(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_74(x))
Eq(F_47(x), F_48(x)*F_64(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_14(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_48(x))
Eq(F_52(x), F_53(x) - F_57(x))
Eq(F_53(x), F_54(x)/(F_11(x)*F_14(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_14(x)*F_29(x))
Eq(F_57(x), F_58(x) - F_63(x))
Eq(F_58(x), F_59(x)/(F_11(x)*F_14(x)))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_55(x) - F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_14(x)*F_48(x)**2)
Eq(F_63(x), F_49(x)*F_51(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_48(x) + F_67(x))
Eq(F_67(x), F_42(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_48(x)*F_67(x))
Eq(F_72(x), F_48(x)*F_67(x))
Eq(F_73(x), F_17(x)*F_34(x))
Eq(F_74(x), F_67(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_18(x)*F_48(x))
Eq(F_77(x), F_17(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_24(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/(F_11(x)*F_14(x)))
Eq(F_82(x), F_60(x))
Eq(F_83(x), F_27(x)*F_84(x))
Eq(F_84(x), F_12(x) + F_85(x))
Eq(F_85(x), F_40(x) + F_86(x) + F_87(x))
Eq(F_86(x), F_14(x)*F_84(x))
Eq(F_87(x), F_14(x)*F_88(x))
Eq(F_88(x), F_12(x) + F_85(x))
Eq(F_89(x), F_11(x) + F_88(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_10(x))
Eq(F_92(x), -F_112(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_14(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_111(x) + F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), -F_109(x) + F_99(x))
Eq(F_99(x), F_100(x)/(F_14(x)*F_48(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_11(x)*F_14(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_17(x)*F_51(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_14(x)*F_17(x))
Eq(F_106(x), F_107(x)/(F_11(x)*F_14(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_14(x)*F_51(x)*F_99(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_10(x)*F_14(x)*F_98(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_26(x)*F_48(x))
Eq(F_114(x), F_115(x)*F_48(x))
Eq(F_115(x), -F_24(x) + F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 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, 2, 3, 4, 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"inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25152/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[20,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[11,x]*F[14,x]*F[17,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[14,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[114,x]+F[23,x]
F[23,x] = F[24,x]*F[90,x]
F[24,x] = 1/F[14,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[10,x]+F[27,x]
F[27,x] = 1/F[89,x]*F[28,x]
F[28,x] = -F[80,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = 1/F[14,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[44,x]
F[35,x] = F[18,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[14,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[14,x]+F[39,x]
F[43,x] = F[12,x]*F[14,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[74,x]
F[47,x] = F[48,x]*F[64,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[14,x]*F[51,x]
F[51,x] = 1/F[48,x]*F[52,x]
F[52,x] = -F[57,x]+F[53,x]
F[53,x] = 1/F[11,x]/F[14,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[14,x]*F[29,x]
F[57,x] = -F[63,x]+F[58,x]
F[58,x] = 1/F[11,x]/F[14,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[55,x]
F[61,x] = F[62,x]
F[62,x] = F[48,x]^2*F[11,x]*F[14,x]
F[63,x] = F[49,x]*F[51,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[48,x]+F[67,x]
F[67,x] = F[42,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[48,x]*F[67,x]
F[72,x] = F[48,x]*F[67,x]
F[73,x] = F[17,x]*F[34,x]
F[74,x] = F[67,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[18,x]*F[48,x]
F[77,x] = F[17,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[24,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[11,x]/F[14,x]*F[82,x]
F[82,x] = F[60,x]
F[83,x] = F[27,x]*F[84,x]
F[84,x] = F[12,x]+F[85,x]
F[85,x] = F[40,x]+F[86,x]+F[87,x]
F[86,x] = F[14,x]*F[84,x]
F[87,x] = F[14,x]*F[88,x]
F[88,x] = F[12,x]+F[85,x]
F[89,x] = F[11,x]+F[88,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = 1/F[10,x]*F[92,x]
F[92,x] = -F[112,x]+F[93,x]
F[93,x] = 1/F[14,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[111,x]+F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = -F[109,x]+F[99,x]
F[99,x] = 1/F[14,x]/F[48,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[11,x]*F[14,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[17,x]*F[51,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[14,x]*F[17,x]
F[106,x] = 1/F[11,x]/F[14,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[14,x]*F[51,x]*F[99,x]
F[109,x] = F[110,x]
F[110,x] = F[10,x]*F[14,x]*F[98,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]
F[113,x] = F[26,x]*F[48,x]
F[114,x] = F[115,x]*F[48,x]
F[115,x] = -F[24,x]+F[29,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \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_{20}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \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_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \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_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{114}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{90}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{89}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \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) = \frac{F_{33}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{44}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{64}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{48}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{48} \left(x \right)^{2} F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{48}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{60}\! \left(x \right)
F_{83}\! \left(x \right) = F_{27}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{111}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{14}\! \left(x \right) F_{48}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{17}\! \left(x \right) F_{51}\! \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_{17}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{26}\! \left(x \right) F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{48}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{29}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(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_20(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_11(x)*F_14(x)*F_17(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_14(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_114(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_90(x))
Eq(F_24(x), F_25(x)/F_14(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_10(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_89(x))
Eq(F_28(x), F_29(x) - F_80(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x)/F_14(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_44(x))
Eq(F_35(x), F_18(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_14(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_39(x))
Eq(F_43(x), F_12(x)*F_14(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_74(x))
Eq(F_47(x), F_48(x)*F_64(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_14(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_48(x))
Eq(F_52(x), F_53(x) - F_57(x))
Eq(F_53(x), F_54(x)/(F_11(x)*F_14(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_14(x)*F_29(x))
Eq(F_57(x), F_58(x) - F_63(x))
Eq(F_58(x), F_59(x)/(F_11(x)*F_14(x)))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_55(x) - F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_14(x)*F_48(x)**2)
Eq(F_63(x), F_49(x)*F_51(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_48(x) + F_67(x))
Eq(F_67(x), F_42(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_48(x)*F_67(x))
Eq(F_72(x), F_48(x)*F_67(x))
Eq(F_73(x), F_17(x)*F_34(x))
Eq(F_74(x), F_67(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_18(x)*F_48(x))
Eq(F_77(x), F_17(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_24(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/(F_11(x)*F_14(x)))
Eq(F_82(x), F_60(x))
Eq(F_83(x), F_27(x)*F_84(x))
Eq(F_84(x), F_12(x) + F_85(x))
Eq(F_85(x), F_40(x) + F_86(x) + F_87(x))
Eq(F_86(x), F_14(x)*F_84(x))
Eq(F_87(x), F_14(x)*F_88(x))
Eq(F_88(x), F_12(x) + F_85(x))
Eq(F_89(x), F_11(x) + F_88(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_10(x))
Eq(F_92(x), -F_112(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_14(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_111(x) + F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), -F_109(x) + F_99(x))
Eq(F_99(x), F_100(x)/(F_14(x)*F_48(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_11(x)*F_14(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_17(x)*F_51(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_14(x)*F_17(x))
Eq(F_106(x), F_107(x)/(F_11(x)*F_14(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_14(x)*F_51(x)*F_99(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_10(x)*F_14(x)*F_98(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_26(x)*F_48(x))
Eq(F_114(x), F_115(x)*F_48(x))
Eq(F_115(x), -F_24(x) + F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 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[1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0], "pos": [[6, 2], [6, 2], [6, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25295/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[20,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[11,x]*F[14,x]*F[17,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[14,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[114,x]+F[23,x]
F[23,x] = F[24,x]*F[90,x]
F[24,x] = 1/F[14,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[10,x]+F[27,x]
F[27,x] = 1/F[89,x]*F[28,x]
F[28,x] = -F[80,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = 1/F[14,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[44,x]
F[35,x] = F[18,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[14,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[14,x]+F[39,x]
F[43,x] = F[12,x]*F[14,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[74,x]
F[47,x] = F[48,x]*F[64,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]*F[14,x]*F[51,x]
F[51,x] = 1/F[48,x]*F[52,x]
F[52,x] = -F[57,x]+F[53,x]
F[53,x] = 1/F[11,x]/F[14,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[14,x]*F[29,x]
F[57,x] = -F[63,x]+F[58,x]
F[58,x] = 1/F[11,x]/F[14,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[55,x]
F[61,x] = F[62,x]
F[62,x] = F[48,x]^2*F[11,x]*F[14,x]
F[63,x] = F[49,x]*F[51,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[48,x]+F[67,x]
F[67,x] = F[42,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[48,x]*F[67,x]
F[72,x] = F[48,x]*F[67,x]
F[73,x] = F[17,x]*F[34,x]
F[74,x] = F[67,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[18,x]*F[48,x]
F[77,x] = F[17,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[24,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[11,x]/F[14,x]*F[82,x]
F[82,x] = F[60,x]
F[83,x] = F[27,x]*F[84,x]
F[84,x] = F[12,x]+F[85,x]
F[85,x] = F[40,x]+F[86,x]+F[87,x]
F[86,x] = F[14,x]*F[84,x]
F[87,x] = F[14,x]*F[88,x]
F[88,x] = F[12,x]+F[85,x]
F[89,x] = F[11,x]+F[88,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = 1/F[10,x]*F[92,x]
F[92,x] = -F[112,x]+F[93,x]
F[93,x] = 1/F[14,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[111,x]+F[97,x]
F[97,x] = F[18,x]*F[98,x]
F[98,x] = -F[109,x]+F[99,x]
F[99,x] = 1/F[14,x]/F[48,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[11,x]*F[14,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[17,x]*F[51,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[14,x]*F[17,x]
F[106,x] = 1/F[11,x]/F[14,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[14,x]*F[51,x]*F[99,x]
F[109,x] = F[110,x]
F[110,x] = F[10,x]*F[14,x]*F[98,x]
F[111,x] = F[108,x]
F[112,x] = F[113,x]
F[113,x] = F[26,x]*F[48,x]
F[114,x] = F[115,x]*F[48,x]
F[115,x] = -F[24,x]+F[29,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \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_{20}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \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_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \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_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{114}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{90}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{89}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \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) = \frac{F_{33}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{44}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{64}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{48}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{48} \left(x \right)^{2} F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{63}\! \left(x \right) = F_{49}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right) F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{34}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{48}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{60}\! \left(x \right)
F_{83}\! \left(x \right) = F_{27}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{111}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{14}\! \left(x \right) F_{48}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{17}\! \left(x \right) F_{51}\! \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_{17}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{11}\! \left(x \right) F_{14}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right) F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{26}\! \left(x \right) F_{48}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{48}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{29}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(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_20(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_11(x)*F_14(x)*F_17(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_14(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_114(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_90(x))
Eq(F_24(x), F_25(x)/F_14(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_10(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_89(x))
Eq(F_28(x), F_29(x) - F_80(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x)/F_14(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_44(x))
Eq(F_35(x), F_18(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_14(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_39(x))
Eq(F_43(x), F_12(x)*F_14(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_74(x))
Eq(F_47(x), F_48(x)*F_64(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x)*F_14(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_48(x))
Eq(F_52(x), F_53(x) - F_57(x))
Eq(F_53(x), F_54(x)/(F_11(x)*F_14(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_14(x)*F_29(x))
Eq(F_57(x), F_58(x) - F_63(x))
Eq(F_58(x), F_59(x)/(F_11(x)*F_14(x)))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_55(x) - F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x)*F_14(x)*F_48(x)**2)
Eq(F_63(x), F_49(x)*F_51(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_48(x) + F_67(x))
Eq(F_67(x), F_42(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_48(x)*F_67(x))
Eq(F_72(x), F_48(x)*F_67(x))
Eq(F_73(x), F_17(x)*F_34(x))
Eq(F_74(x), F_67(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_18(x)*F_48(x))
Eq(F_77(x), F_17(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_24(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/(F_11(x)*F_14(x)))
Eq(F_82(x), F_60(x))
Eq(F_83(x), F_27(x)*F_84(x))
Eq(F_84(x), F_12(x) + F_85(x))
Eq(F_85(x), F_40(x) + F_86(x) + F_87(x))
Eq(F_86(x), F_14(x)*F_84(x))
Eq(F_87(x), F_14(x)*F_88(x))
Eq(F_88(x), F_12(x) + F_85(x))
Eq(F_89(x), F_11(x) + F_88(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_10(x))
Eq(F_92(x), -F_112(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_14(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_111(x) + F_97(x))
Eq(F_97(x), F_18(x)*F_98(x))
Eq(F_98(x), -F_109(x) + F_99(x))
Eq(F_99(x), F_100(x)/(F_14(x)*F_48(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_11(x)*F_14(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_17(x)*F_51(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_14(x)*F_17(x))
Eq(F_106(x), F_107(x)/(F_11(x)*F_14(x)))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_14(x)*F_51(x)*F_99(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_10(x)*F_14(x)*F_98(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_26(x)*F_48(x))
Eq(F_114(x), F_115(x)*F_48(x))
Eq(F_115(x), -F_24(x) + F_29(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 4, 2, 3, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [1, 4, 2, 3, 0], [2, 3, 1, 4, 0], [2, 4, 1, 3, 0], [3, 4, 1, 2, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 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, 2, 3, 4, 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"inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/25763/
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[11,x,1,k[0]]
F[11,x,k[0],k[1]] = (F[12,x,k[0]*k[1]]*k[0]-F[12,x,k[1]])/(-1+k[0])
F[12,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[13,x,k[0]]^2*F[9,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_{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{-F_{5}\! \left(x , y\right) y +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_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = -\frac{-F_{12}\! \left(x , y z \right) y +F_{12}\! \left(x , z\right)}{-1+y}
F_{12}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{13}\! \left(x , y\right)^{2} F_{9}\! \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)*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_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), (-k_0*k_1*F_12(x, k_0*k_1) + k_1*F_12(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_12(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_13(x, k_0)**2*F_9(x, k_0))
Pack JSON:
{"name": "col_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [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, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 4, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [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], 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