0213_3120_14203_30241
Counting sequence:
1, 1, 2, 6, 22, 84, 320, 1202, 4438, 16114, 57658, 203842, 713874, 2482114, 8584162, 29572098, 101591106, 348317954, 1192620930, 4079631362, 13946390786, 47655791618, 162796314114, 556020211714, 1898812228610, 6483921522690, 22139624011778, 75594062970882, 258104419389442, 881245624188930, 3008808386813954, 10272817125261314, 35073812520255490, 119749960501624834, 408852954089750530, 1395913468387524610, 4765951315445088258, 16271985446061080578, 55556054263049093122, 189680278166170501122, 647609071827268403202, 2211075873913244221442, 7549085653402065043458, 25774191500474858864642, 87998596029902421491714, 300446003922414619066370, 1025786829512240841883650, 3502255322531858500026370, 11957447656910689243496450, 40825280036551866758201346, 139386224945152001090519042, 475894339942887720119959554, 1624804910372139237682184194, 5547430962625661575855341570, 18940114031888007501849821186, 64665594206731122989114327042, 220782148772358338190730330114, 753797406695102398001762533378, 2573625329275405657139742507010, 8786906503793797676939306074114, 30000375356795155891347628490754, 102427688419946830998238127980546, 349710002966929549711246830338050, 1193984635029340340396692917452802, 4076518534186637055735304026062850, 13918104866694346961003720749350914, 47519382398417499151212760438669314, 162241319860308940517152035591684098, 553926514644457801098858531422994434, 1891223418857330976694832174028816386, 6457040646140650879266180913873027074, 22045715746848441470439456836283269122, 75268781695113493894266636279396433922, 256983695286759212978738439915720146946, 877397217756814228183346469014970826754, 2995621480453747465175184552141405552642, 10227691486301379868786993290848466108418, 34919522984298062503179393365319281016834, 119222708964589568279193150920379831681026, 407051789889762308349753313683682155823106, 1389761741629870425895123479250847450267650, 4744943386739957762368288999310076856500226, 16200250063700091583867476954362789972934658, 55311113481320453654429089007342482381340674, 188843953797881637281839555941615488362086402, 644753588228885653774776401740459526529744898, 2201326445319779365040352858667140500688994306, 7515798604821346202820965771422421833593389058, 25660541528645826184048894694611139483599372290, 87610568904940612541158196419025033534424219650, 299121192562470798227686300594239204037708742658, 1021263632440001968710847943792016876283518517250, 3486812144635066280193554721277316227999029264386, 11904721313660261187045917104733163209590617145346, 40645260965370912195349850126077768129661416505346, 138771601234163126422750868284929865028831006425090, 473795883005910681331871243889341120865928860401666, 1617640329555316472546494770314744490291596590317570, 5522969552209444527654042545343088728063588194844674, 18856597549727145165792417744006964716898420327972866, 64380451094489691608411429333190675914365699937533954
Generating function in Maple syntax:
-(2*x^7-8*x^6+30*x^5-70*x^4+74*x^3-39*x^2+10*x-1)/(-1+x)/(2*x^2-4*x+1)/(2*x-1)^3
Generating function in latex syntax:
-\frac{2 x^{7}-8 x^{6}+30 x^{5}-70 x^{4}+74 x^{3}-39 x^{2}+10 x -1}{\left(-1+x \right) \left(2 x^{2}-4 x +1\right) \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(-2*x**7 + 8*x**6 - 30*x**5 + 70*x**4 - 74*x**3 + 39*x**2 - 10*x + 1)/((x - 1)*(2*x - 1)**3*(2*x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(-1+x)*(2*x^2-4*x+1)*(2*x-1)^3*F(x)+2*x^7-8*x^6+30*x^5-70*x^4+74*x^3-39*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+x \right) \left(2 x^{2}-4 x +1\right) \left(2 x -1\right)^{3} F \! \left(x \right)+2 x^{7}-8 x^{6}+30 x^{5}-70 x^{4}+74 x^{3}-39 x^{2}+10 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/32*(4*2^(1/2)+4)*(1-1/2*2^(1/2))^(-n)+1/32*(-4*2^(1/2)+4)*(1+1/2*2^(1/2))^(-n)+2+1/32*(-3*n^2+11*n-38)*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(4 \sqrt{2}+4\right) \left(1-\frac{\sqrt{2}}{2}\right)^{-n}}{32}+\frac{\left(-4 \sqrt{2}+4\right) \left(1+\frac{\sqrt{2}}{2}\right)^{-n}}{32}+2+\\\frac{\left(-3 n^{2}+11 n -38\right) 2^{n}}{32} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 84
a(6) = 320
a(7) = 1202
a(n+5) = 16*a(n)-56*a(n+1)+68*a(n+2)-38*a(n+3)+10*a(n+4)+2, n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 84
a \! \left(6\right) = 320
a \! \left(7\right) = 1202
a \! \left(n +5\right) = 16 a \! \left(n \right)-56 a \! \left(n +1\right)+68 a \! \left(n +2\right)-38 a \! \left(n +3\right)+10 a \! \left(n +4\right)+2, \quad n \geq 8
Specification 1
Strategy pack name: point_and_row_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24043/
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[16,x]*F[4,x]
F[4,x] = F[31,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]*F[26,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[16,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[16,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[16,x]*F[24,x]
F[24,x] = F[14,x]+F[21,x]
F[25,x] = F[16,x]*F[17,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[16,x]*F[29,x]
F[29,x] = F[26,x]+F[30,x]
F[30,x] = F[27,x]
F[31,x] = F[132,x]+F[22,x]+F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[49,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[47,x]
F[36,x] = F[37,x]*F[46,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[13,x]+F[41,x]
F[41,x] = F[18,x]+F[42,x]
F[42,x] = F[22,x]+F[43,x]+F[45,x]
F[43,x] = F[16,x]*F[44,x]
F[44,x] = F[14,x]+F[42,x]
F[45,x] = F[16,x]*F[41,x]
F[46,x] = F[1,x]+F[10,x]
F[47,x] = F[48,x]
F[48,x] = F[10,x]*F[13,x]*F[16,x]*F[38,x]
F[49,x] = F[50,x]+F[99,x]
F[50,x] = F[22,x]+F[51,x]+F[52,x]
F[51,x] = F[16,x]*F[49,x]
F[52,x] = F[16,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[8,x]
F[55,x] = F[31,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[16,x]*F[58,x]
F[58,x] = F[59,x]+F[89,x]
F[59,x] = F[26,x]*F[60,x]
F[60,x] = F[22,x]+F[61,x]+F[87,x]
F[61,x] = F[62,x]
F[62,x] = F[16,x]*F[63,x]
F[63,x] = F[35,x]+F[64,x]
F[64,x] = F[37,x]*F[65,x]
F[65,x] = F[10,x]+F[66,x]
F[66,x] = F[22,x]+F[67,x]+F[77,x]
F[67,x] = F[16,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[14,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[16,x]*F[69,x]
F[72,x] = F[21,x]+F[73,x]
F[73,x] = 2*F[22,x]+F[74,x]+F[76,x]
F[74,x] = F[16,x]*F[75,x]
F[75,x] = F[70,x]+F[73,x]
F[76,x] = F[16,x]*F[72,x]
F[77,x] = F[16,x]*F[78,x]
F[78,x] = F[17,x]+F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]
F[81,x] = F[16,x]*F[82,x]
F[82,x] = F[18,x]+F[80,x]
F[83,x] = 2*F[22,x]+F[84,x]+F[86,x]
F[84,x] = F[16,x]*F[85,x]
F[85,x] = F[21,x]+F[83,x]
F[86,x] = F[16,x]*F[79,x]
F[87,x] = F[88,x]
F[88,x] = F[16,x]*F[60,x]
F[89,x] = F[131,x]*F[90,x]
F[90,x] = F[130,x]+F[22,x]+F[91,x]
F[91,x] = F[16,x]*F[92,x]
F[92,x] = F[93,x]+F[95,x]
F[93,x] = F[94,x]
F[94,x] = F[20,x]*F[37,x]
F[95,x] = 1/F[125,x]*F[96,x]
F[96,x] = -F[128,x]+F[97,x]
F[97,x] = 1/F[16,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[16,x]
F[101,x] = F[102,x]+F[110,x]
F[102,x] = F[103,x]*F[37,x]
F[103,x] = F[104,x]+F[106,x]+F[22,x]
F[104,x] = F[105,x]
F[105,x] = F[103,x]*F[16,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[16,x]
F[108,x] = F[109,x]+F[8,x]
F[109,x] = F[26,x]*F[65,x]
F[110,x] = F[111,x]*F[126,x]
F[111,x] = F[112,x]+F[113,x]+F[22,x]
F[112,x] = F[16,x]*F[95,x]
F[113,x] = F[114,x]*F[16,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]
F[116,x] = F[13,x]*F[26,x]
F[117,x] = 1/F[125,x]*F[118,x]
F[118,x] = -F[121,x]+F[119,x]
F[119,x] = 1/F[16,x]*F[120,x]
F[120,x] = F[56,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[13,x]*F[26,x]
F[123,x] = F[124,x]
F[124,x] = F[16,x]*F[35,x]
F[125,x] = F[10,x]+F[46,x]
F[126,x] = F[10,x]+F[127,x]
F[127,x] = F[46,x]+F[65,x]
F[128,x] = F[129,x]
F[129,x] = F[20,x]*F[37,x]*F[6,x]
F[130,x] = F[117,x]*F[16,x]
F[131,x] = F[125,x]+F[65,x]
F[132,x] = F[16,x]*F[55,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{31}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{26}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{132}\! \left(x \right)+F_{22}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{49}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{47}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{46}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{38}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{99}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{16}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{31}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{89}\! \left(x \right)
F_{59}\! \left(x \right) = F_{26}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{61}\! \left(x \right)+F_{87}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{35}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{37}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{10}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)+F_{77}\! \left(x \right)
F_{67}\! \left(x \right) = F_{16}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \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_{71}\! \left(x \right) = F_{16}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{21}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{16}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{16}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{17}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{16}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{18}\! \left(x \right)+F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{16}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right)
F_{89}\! \left(x \right) = F_{131}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{130}\! \left(x \right)+F_{22}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{16}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{125}\! \left(x \right)}
F_{96}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{16}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{110}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{37}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)+F_{22}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{16}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{16}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{8}\! \left(x \right)
F_{109}\! \left(x \right) = F_{26}\! \left(x \right) F_{65}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{126}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)+F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{16}\! \left(x \right) F_{95}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{16}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{125}\! \left(x \right)}
F_{118}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{56}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{125}\! \left(x \right) = F_{10}\! \left(x \right)+F_{46}\! \left(x \right)
F_{126}\! \left(x \right) = F_{10}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{46}\! \left(x \right)+F_{65}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{130}\! \left(x \right) = F_{117}\! \left(x \right) F_{16}\! \left(x \right)
F_{131}\! \left(x \right) = F_{125}\! \left(x \right)+F_{65}\! \left(x \right)
F_{132}\! \left(x \right) = F_{16}\! \left(x \right) F_{55}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_31(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_26(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_16(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_16(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_16(x)*F_24(x))
Eq(F_24(x), F_14(x) + F_21(x))
Eq(F_25(x), F_16(x)*F_17(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_16(x)*F_29(x))
Eq(F_29(x), F_26(x) + F_30(x))
Eq(F_30(x), F_27(x))
Eq(F_31(x), F_132(x) + F_22(x) + F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_49(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_47(x))
Eq(F_36(x), F_37(x)*F_46(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_13(x) + F_41(x))
Eq(F_41(x), F_18(x) + F_42(x))
Eq(F_42(x), F_22(x) + F_43(x) + F_45(x))
Eq(F_43(x), F_16(x)*F_44(x))
Eq(F_44(x), F_14(x) + F_42(x))
Eq(F_45(x), F_16(x)*F_41(x))
Eq(F_46(x), F_1(x) + F_10(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_10(x)*F_13(x)*F_16(x)*F_38(x))
Eq(F_49(x), F_50(x) + F_99(x))
Eq(F_50(x), F_22(x) + F_51(x) + F_52(x))
Eq(F_51(x), F_16(x)*F_49(x))
Eq(F_52(x), F_16(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_8(x))
Eq(F_55(x), F_31(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_16(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_89(x))
Eq(F_59(x), F_26(x)*F_60(x))
Eq(F_60(x), F_22(x) + F_61(x) + F_87(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_16(x)*F_63(x))
Eq(F_63(x), F_35(x) + F_64(x))
Eq(F_64(x), F_37(x)*F_65(x))
Eq(F_65(x), F_10(x) + F_66(x))
Eq(F_66(x), F_22(x) + F_67(x) + F_77(x))
Eq(F_67(x), F_16(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_14(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_16(x)*F_69(x))
Eq(F_72(x), F_21(x) + F_73(x))
Eq(F_73(x), 2*F_22(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_16(x)*F_75(x))
Eq(F_75(x), F_70(x) + F_73(x))
Eq(F_76(x), F_16(x)*F_72(x))
Eq(F_77(x), F_16(x)*F_78(x))
Eq(F_78(x), F_17(x) + F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_16(x)*F_82(x))
Eq(F_82(x), F_18(x) + F_80(x))
Eq(F_83(x), 2*F_22(x) + F_84(x) + F_86(x))
Eq(F_84(x), F_16(x)*F_85(x))
Eq(F_85(x), F_21(x) + F_83(x))
Eq(F_86(x), F_16(x)*F_79(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_16(x)*F_60(x))
Eq(F_89(x), F_131(x)*F_90(x))
Eq(F_90(x), F_130(x) + F_22(x) + F_91(x))
Eq(F_91(x), F_16(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_95(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_20(x)*F_37(x))
Eq(F_95(x), F_96(x)/F_125(x))
Eq(F_96(x), -F_128(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_16(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_16(x))
Eq(F_101(x), F_102(x) + F_110(x))
Eq(F_102(x), F_103(x)*F_37(x))
Eq(F_103(x), F_104(x) + F_106(x) + F_22(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_103(x)*F_16(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_16(x))
Eq(F_108(x), F_109(x) + F_8(x))
Eq(F_109(x), F_26(x)*F_65(x))
Eq(F_110(x), F_111(x)*F_126(x))
Eq(F_111(x), F_112(x) + F_113(x) + F_22(x))
Eq(F_112(x), F_16(x)*F_95(x))
Eq(F_113(x), F_114(x)*F_16(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_13(x)*F_26(x))
Eq(F_117(x), F_118(x)/F_125(x))
Eq(F_118(x), F_119(x) - F_121(x))
Eq(F_119(x), F_120(x)/F_16(x))
Eq(F_120(x), F_56(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_13(x)*F_26(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_16(x)*F_35(x))
Eq(F_125(x), F_10(x) + F_46(x))
Eq(F_126(x), F_10(x) + F_127(x))
Eq(F_127(x), F_46(x) + F_65(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_20(x)*F_37(x)*F_6(x))
Eq(F_130(x), F_117(x)*F_16(x))
Eq(F_131(x), F_125(x) + F_65(x))
Eq(F_132(x), F_16(x)*F_55(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [4, 2], [4, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [4, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 2], [4, 2], [4, 2]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[5, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[5, 3], [5, 3], [5, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [4, 0], [4, 0], [5, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 3], [0, 3], [5, 3], [5, 3]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}], [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 3], [1, 3], [2, 1], [4, 0], [5, 3]], 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"comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [1], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": 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{"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_row_and_col_placements_expand_verified
Tree: http://permpal.com/tree/24044/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[33,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[8,x]
F[13,x] = F[14,x]+F[19,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[14,x]
F[18,x] = F[14,x]
F[19,x] = F[20,x]
F[20,x] = F[17,x]*F[21,x]*F[8,x]
F[21,x] = F[22,x]+F[26,x]
F[22,x] = F[11,x]*F[23,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[8,x]
F[26,x] = F[10,x]*F[27,x]
F[27,x] = F[11,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]+F[32,x]
F[29,x] = 0
F[30,x] = F[31,x]*F[8,x]
F[31,x] = F[24,x]+F[28,x]
F[32,x] = F[27,x]*F[8,x]
F[33,x] = F[34,x]+F[51,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[8,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[34,x]
F[38,x] = F[39,x]*F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]*F[8,x]
F[41,x] = F[23,x]+F[27,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]*F[8,x]
F[45,x] = F[23,x]+F[46,x]
F[46,x] = F[11,x]+F[47,x]
F[47,x] = F[29,x]+F[48,x]+F[50,x]
F[48,x] = F[49,x]*F[8,x]
F[49,x] = F[24,x]+F[47,x]
F[50,x] = F[46,x]*F[8,x]
F[51,x] = F[144,x]+F[29,x]+F[52,x]
F[52,x] = F[53,x]*F[8,x]
F[53,x] = F[54,x]+F[82,x]
F[54,x] = F[55,x]+F[6,x]
F[55,x] = F[29,x]+F[56,x]+F[58,x]
F[56,x] = F[57,x]
F[57,x] = F[54,x]*F[8,x]
F[58,x] = F[59,x]
F[59,x] = F[17,x]*F[60,x]*F[8,x]
F[60,x] = F[39,x]+F[61,x]
F[61,x] = F[29,x]+F[62,x]+F[72,x]
F[62,x] = F[63,x]*F[8,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[24,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[64,x]*F[8,x]
F[67,x] = F[28,x]+F[68,x]
F[68,x] = 2*F[29,x]+F[69,x]+F[71,x]
F[69,x] = F[70,x]*F[8,x]
F[70,x] = F[65,x]+F[68,x]
F[71,x] = F[67,x]*F[8,x]
F[72,x] = F[73,x]*F[8,x]
F[73,x] = F[27,x]+F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]*F[8,x]
F[77,x] = F[11,x]+F[75,x]
F[78,x] = 2*F[29,x]+F[79,x]+F[81,x]
F[79,x] = F[8,x]*F[80,x]
F[80,x] = F[28,x]+F[78,x]
F[81,x] = F[74,x]*F[8,x]
F[82,x] = F[51,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[8,x]*F[85,x]
F[85,x] = F[140,x]+F[86,x]
F[86,x] = F[87,x]+F[96,x]
F[87,x] = F[23,x]*F[88,x]
F[88,x] = F[105,x]+F[29,x]+F[89,x]
F[89,x] = F[8,x]*F[90,x]
F[90,x] = F[13,x]+F[91,x]
F[91,x] = 1/F[104,x]*F[92,x]
F[92,x] = -F[95,x]+F[93,x]
F[93,x] = 1/F[8,x]*F[94,x]
F[94,x] = F[83,x]
F[95,x] = F[96,x]+F[99,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[43,x]*F[6,x]
F[98,x] = F[39,x]*F[88,x]
F[99,x] = F[100,x]+F[102,x]
F[100,x] = F[101,x]
F[101,x] = F[11,x]*F[43,x]*F[6,x]
F[102,x] = F[103,x]*F[39,x]
F[103,x] = -F[88,x]+F[91,x]
F[104,x] = F[1,x]+F[39,x]
F[105,x] = F[106,x]*F[8,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[43,x]+F[88,x]
F[108,x] = F[109,x]+F[114,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[42,x]*F[8,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[10,x]*F[24,x]
F[113,x] = F[23,x]*F[31,x]
F[114,x] = -F[88,x]+F[115,x]
F[115,x] = -F[137,x]+F[116,x]
F[116,x] = -F[136,x]+F[117,x]
F[117,x] = 1/F[8,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[8,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[10,x]*F[104,x]*F[88,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]+F[98,x]
F[125,x] = F[14,x]*F[34,x]
F[126,x] = F[127,x]+F[135,x]
F[127,x] = F[128,x]*F[14,x]
F[128,x] = F[129,x]+F[132,x]+F[29,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]*F[42,x]*F[8,x]
F[131,x] = F[39,x]+F[61,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]*F[8,x]
F[134,x] = F[128,x]+F[34,x]
F[135,x] = F[61,x]*F[88,x]
F[136,x] = F[115,x]*F[39,x]
F[137,x] = F[136,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[23,x]*F[34,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[23,x]*F[39,x]*F[88,x]
F[142,x] = F[135,x]+F[143,x]
F[143,x] = F[43,x]*F[55,x]
F[144,x] = F[145,x]*F[8,x]
F[145,x] = F[146,x]+F[33,x]
F[146,x] = F[119,x]+F[128,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{33}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{51}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{8}\! \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_{34}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{8}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{8}\! \left(x \right)
F_{45}\! \left(x \right) = F_{23}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{29}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{8}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right) F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{144}\! \left(x \right)+F_{29}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{82}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{55}\! \left(x \right) = F_{29}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{54}\! \left(x \right) F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{17}\! \left(x \right) F_{60}\! \left(x \right) F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{39}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{29}\! \left(x \right)+F_{62}\! \left(x \right)+F_{72}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{24}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{64}\! \left(x \right) F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{28}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{8}\! \left(x \right)
F_{70}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{8}\! \left(x \right)
F_{73}\! \left(x \right) = F_{27}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right) F_{8}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{8}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{28}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{82}\! \left(x \right) = F_{51}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{8}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{140}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{96}\! \left(x \right)
F_{87}\! \left(x \right) = F_{23}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{105}\! \left(x \right)+F_{29}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{8}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{13}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{104}\! \left(x \right)}
F_{92}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{83}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{43}\! \left(x \right) F_{6}\! \left(x \right)
F_{98}\! \left(x \right) = F_{39}\! \left(x \right) F_{88}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right) F_{6}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{39}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{104}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{8}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{43}\! \left(x \right)+F_{88}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{114}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{10}\! \left(x \right) F_{24}\! \left(x \right)
F_{113}\! \left(x \right) = F_{23}\! \left(x \right) F_{31}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = -F_{136}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{8}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{10}\! \left(x \right) F_{104}\! \left(x \right) F_{88}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{98}\! \left(x \right)
F_{125}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{135}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{14}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{132}\! \left(x \right)+F_{29}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{39}\! \left(x \right)+F_{61}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{8}\! \left(x \right)
F_{134}\! \left(x \right) = F_{128}\! \left(x \right)+F_{34}\! \left(x \right)
F_{135}\! \left(x \right) = F_{61}\! \left(x \right) F_{88}\! \left(x \right)
F_{136}\! \left(x \right) = F_{115}\! \left(x \right) F_{39}\! \left(x \right)
F_{137}\! \left(x \right) = F_{136}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right) F_{34}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{23}\! \left(x \right) F_{39}\! \left(x \right) F_{88}\! \left(x \right)
F_{142}\! \left(x \right) = F_{135}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{43}\! \left(x \right) F_{55}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{8}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{33}\! \left(x \right)
F_{146}\! \left(x \right) = F_{119}\! \left(x \right)+F_{128}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_33(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_19(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_14(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_17(x)*F_21(x)*F_8(x))
Eq(F_21(x), F_22(x) + F_26(x))
Eq(F_22(x), F_11(x)*F_23(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_8(x))
Eq(F_26(x), F_10(x)*F_27(x))
Eq(F_27(x), F_11(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x) + F_32(x))
Eq(F_29(x), 0)
Eq(F_30(x), F_31(x)*F_8(x))
Eq(F_31(x), F_24(x) + F_28(x))
Eq(F_32(x), F_27(x)*F_8(x))
Eq(F_33(x), F_34(x) + F_51(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_8(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_34(x))
Eq(F_38(x), F_39(x)*F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x)*F_8(x))
Eq(F_41(x), F_23(x) + F_27(x))
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x)*F_8(x))
Eq(F_45(x), F_23(x) + F_46(x))
Eq(F_46(x), F_11(x) + F_47(x))
Eq(F_47(x), F_29(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_49(x)*F_8(x))
Eq(F_49(x), F_24(x) + F_47(x))
Eq(F_50(x), F_46(x)*F_8(x))
Eq(F_51(x), F_144(x) + F_29(x) + F_52(x))
Eq(F_52(x), F_53(x)*F_8(x))
Eq(F_53(x), F_54(x) + F_82(x))
Eq(F_54(x), F_55(x) + F_6(x))
Eq(F_55(x), F_29(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_54(x)*F_8(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_17(x)*F_60(x)*F_8(x))
Eq(F_60(x), F_39(x) + F_61(x))
Eq(F_61(x), F_29(x) + F_62(x) + F_72(x))
Eq(F_62(x), F_63(x)*F_8(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_24(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_64(x)*F_8(x))
Eq(F_67(x), F_28(x) + F_68(x))
Eq(F_68(x), 2*F_29(x) + F_69(x) + F_71(x))
Eq(F_69(x), F_70(x)*F_8(x))
Eq(F_70(x), F_65(x) + F_68(x))
Eq(F_71(x), F_67(x)*F_8(x))
Eq(F_72(x), F_73(x)*F_8(x))
Eq(F_73(x), F_27(x) + F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_77(x)*F_8(x))
Eq(F_77(x), F_11(x) + F_75(x))
Eq(F_78(x), 2*F_29(x) + F_79(x) + F_81(x))
Eq(F_79(x), F_8(x)*F_80(x))
Eq(F_80(x), F_28(x) + F_78(x))
Eq(F_81(x), F_74(x)*F_8(x))
Eq(F_82(x), F_51(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_8(x)*F_85(x))
Eq(F_85(x), F_140(x) + F_86(x))
Eq(F_86(x), F_87(x) + F_96(x))
Eq(F_87(x), F_23(x)*F_88(x))
Eq(F_88(x), F_105(x) + F_29(x) + F_89(x))
Eq(F_89(x), F_8(x)*F_90(x))
Eq(F_90(x), F_13(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_104(x))
Eq(F_92(x), F_93(x) - F_95(x))
Eq(F_93(x), F_94(x)/F_8(x))
Eq(F_94(x), F_83(x))
Eq(F_95(x), F_96(x) + F_99(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_43(x)*F_6(x))
Eq(F_98(x), F_39(x)*F_88(x))
Eq(F_99(x), F_100(x) + F_102(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_11(x)*F_43(x)*F_6(x))
Eq(F_102(x), F_103(x)*F_39(x))
Eq(F_103(x), -F_88(x) + F_91(x))
Eq(F_104(x), F_1(x) + F_39(x))
Eq(F_105(x), F_106(x)*F_8(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_43(x) + F_88(x))
Eq(F_108(x), F_109(x) + F_114(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_42(x)*F_8(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_10(x)*F_24(x))
Eq(F_113(x), F_23(x)*F_31(x))
Eq(F_114(x), F_115(x) - F_88(x))
Eq(F_115(x), F_116(x) - F_137(x))
Eq(F_116(x), F_117(x) - F_136(x))
Eq(F_117(x), F_118(x)/F_8(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_8(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_10(x)*F_104(x)*F_88(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x) + F_98(x))
Eq(F_125(x), F_14(x)*F_34(x))
Eq(F_126(x), F_127(x) + F_135(x))
Eq(F_127(x), F_128(x)*F_14(x))
Eq(F_128(x), F_129(x) + F_132(x) + F_29(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)*F_42(x)*F_8(x))
Eq(F_131(x), F_39(x) + F_61(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x)*F_8(x))
Eq(F_134(x), F_128(x) + F_34(x))
Eq(F_135(x), F_61(x)*F_88(x))
Eq(F_136(x), F_115(x)*F_39(x))
Eq(F_137(x), F_136(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_23(x)*F_34(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_23(x)*F_39(x)*F_88(x))
Eq(F_142(x), F_135(x) + F_143(x))
Eq(F_143(x), F_43(x)*F_55(x))
Eq(F_144(x), F_145(x)*F_8(x))
Eq(F_145(x), F_146(x) + F_33(x))
Eq(F_146(x), F_119(x) + F_128(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_row_and_col_placements_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 4], [2, 1], [2, 4]]}, {"patt": [2, 0, 1], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 4], [2, 0], [2, 4]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 4], [2, 0], [2, 4], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 5], [3, 5], [3, 5]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[3, 5], [3, 1], [3, 5]]}, {"patt": [2, 0, 1], "pos": [[3, 5], [3, 5], [3, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [3, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 5], [3, 0], [3, 5]]}, {"patt": [3, 1, 2, 0], "pos": [[3, 5], [3, 0], [3, 5], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[3, 5]]}], [{"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 4], [1, 2], [3, 0], [3, 1], [3, 5]], [[2, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 3], [1, 0], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 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[[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], 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"own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: insertion_row_and_col_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24045/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[32,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[8,x]
F[13,x] = F[14,x]+F[19,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[14,x]
F[18,x] = F[14,x]
F[19,x] = F[20,x]+F[21,x]+F[22,x]
F[20,x] = 0
F[21,x] = F[13,x]*F[8,x]
F[22,x] = F[23,x]
F[23,x] = F[17,x]*F[24,x]*F[8,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[31,x]
F[26,x] = F[27,x]*F[8,x]
F[27,x] = F[25,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[1,x]+F[28,x]
F[31,x] = F[24,x]*F[8,x]
F[32,x] = F[33,x]+F[50,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[8,x]
F[35,x] = F[30,x]+F[36,x]
F[36,x] = F[37,x]+F[45,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[8,x]
F[39,x] = F[30,x]+F[40,x]
F[40,x] = F[11,x]+F[41,x]
F[41,x] = F[20,x]+F[42,x]+F[44,x]
F[42,x] = F[43,x]*F[8,x]
F[43,x] = F[28,x]+F[41,x]
F[44,x] = F[40,x]*F[8,x]
F[45,x] = F[20,x]+F[46,x]+F[49,x]
F[46,x] = F[47,x]
F[47,x] = F[27,x]*F[48,x]*F[8,x]
F[48,x] = F[1,x]+F[37,x]
F[49,x] = F[36,x]*F[8,x]
F[50,x] = F[141,x]+F[20,x]+F[51,x]
F[51,x] = F[52,x]*F[8,x]
F[52,x] = F[53,x]+F[84,x]
F[53,x] = F[54,x]+F[6,x]
F[54,x] = F[20,x]+F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[53,x]*F[8,x]
F[57,x] = F[58,x]
F[58,x] = F[17,x]*F[59,x]*F[8,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]*F[8,x]
F[62,x] = F[24,x]+F[30,x]
F[63,x] = F[20,x]+F[64,x]+F[74,x]
F[64,x] = F[65,x]*F[8,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[28,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[66,x]*F[8,x]
F[69,x] = F[25,x]+F[70,x]
F[70,x] = 2*F[20,x]+F[71,x]+F[73,x]
F[71,x] = F[72,x]*F[8,x]
F[72,x] = F[67,x]+F[70,x]
F[73,x] = F[69,x]*F[8,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[24,x]+F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[78,x]
F[78,x] = F[79,x]*F[8,x]
F[79,x] = F[11,x]+F[77,x]
F[80,x] = 2*F[20,x]+F[81,x]+F[83,x]
F[81,x] = F[8,x]*F[82,x]
F[82,x] = F[25,x]+F[80,x]
F[83,x] = F[76,x]*F[8,x]
F[84,x] = F[50,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[8,x]*F[87,x]
F[87,x] = F[137,x]+F[88,x]
F[88,x] = F[89,x]+F[98,x]
F[89,x] = F[30,x]*F[90,x]
F[90,x] = F[107,x]+F[20,x]+F[91,x]
F[91,x] = F[8,x]*F[92,x]
F[92,x] = F[13,x]+F[93,x]
F[93,x] = 1/F[106,x]*F[94,x]
F[94,x] = -F[97,x]+F[95,x]
F[95,x] = 1/F[8,x]*F[96,x]
F[96,x] = F[85,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[37,x]*F[6,x]
F[100,x] = F[60,x]*F[90,x]
F[101,x] = F[102,x]+F[104,x]
F[102,x] = F[103,x]
F[103,x] = F[11,x]*F[37,x]*F[6,x]
F[104,x] = F[105,x]*F[60,x]
F[105,x] = -F[90,x]+F[93,x]
F[106,x] = F[1,x]+F[60,x]
F[107,x] = F[108,x]*F[8,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[37,x]+F[90,x]
F[110,x] = F[111,x]+F[45,x]
F[111,x] = -F[90,x]+F[112,x]
F[112,x] = -F[134,x]+F[113,x]
F[113,x] = -F[133,x]+F[114,x]
F[114,x] = 1/F[8,x]*F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[8,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[10,x]*F[106,x]*F[90,x]
F[120,x] = F[121,x]+F[123,x]
F[121,x] = F[100,x]+F[122,x]
F[122,x] = F[14,x]*F[33,x]
F[123,x] = F[124,x]+F[132,x]
F[124,x] = F[125,x]*F[14,x]
F[125,x] = F[126,x]+F[129,x]+F[20,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[48,x]*F[8,x]
F[128,x] = F[60,x]+F[63,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]*F[8,x]
F[131,x] = F[125,x]+F[33,x]
F[132,x] = F[63,x]*F[90,x]
F[133,x] = F[112,x]*F[60,x]
F[134,x] = F[133,x]+F[135,x]
F[135,x] = F[136,x]
F[136,x] = F[14,x]*F[30,x]*F[33,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[30,x]*F[60,x]*F[90,x]
F[139,x] = F[132,x]+F[140,x]
F[140,x] = F[37,x]*F[54,x]
F[141,x] = F[142,x]*F[8,x]
F[142,x] = F[143,x]+F[32,x]
F[143,x] = F[116,x]+F[125,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{32}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right) F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{50}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{30}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{27}\! \left(x \right) F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{49}\! \left(x \right) = F_{36}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{141}\! \left(x \right)+F_{20}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{8}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{84}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{6}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{17}\! \left(x \right) F_{59}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{8}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right)+F_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right) F_{8}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{28}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{66}\! \left(x \right) F_{8}\! \left(x \right)
F_{69}\! \left(x \right) = F_{25}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right) F_{8}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{25}\! \left(x \right)+F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{84}\! \left(x \right) = F_{50}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{8}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{137}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{98}\! \left(x \right)
F_{89}\! \left(x \right) = F_{30}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{107}\! \left(x \right)+F_{20}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{8}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{13}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{106}\! \left(x \right)}
F_{94}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{85}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{100}\! \left(x \right) = F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{60}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{8}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{37}\! \left(x \right)+F_{90}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{45}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{8}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{10}\! \left(x \right) F_{106}\! \left(x \right) F_{90}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{123}\! \left(x \right)
F_{121}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{132}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{14}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{129}\! \left(x \right)+F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{128}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{125}\! \left(x \right)+F_{33}\! \left(x \right)
F_{132}\! \left(x \right) = F_{63}\! \left(x \right) F_{90}\! \left(x \right)
F_{133}\! \left(x \right) = F_{112}\! \left(x \right) F_{60}\! \left(x \right)
F_{134}\! \left(x \right) = F_{133}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{14}\! \left(x \right) F_{30}\! \left(x \right) F_{33}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{30}\! \left(x \right) F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{139}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{37}\! \left(x \right) F_{54}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{8}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{32}\! \left(x \right)
F_{143}\! \left(x \right) = F_{116}\! \left(x \right)+F_{125}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_32(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_19(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_14(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_22(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_13(x)*F_8(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_17(x)*F_24(x)*F_8(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_31(x))
Eq(F_26(x), F_27(x)*F_8(x))
Eq(F_27(x), F_25(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_1(x) + F_28(x))
Eq(F_31(x), F_24(x)*F_8(x))
Eq(F_32(x), F_33(x) + F_50(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_8(x))
Eq(F_35(x), F_30(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_45(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_8(x))
Eq(F_39(x), F_30(x) + F_40(x))
Eq(F_40(x), F_11(x) + F_41(x))
Eq(F_41(x), F_20(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_43(x)*F_8(x))
Eq(F_43(x), F_28(x) + F_41(x))
Eq(F_44(x), F_40(x)*F_8(x))
Eq(F_45(x), F_20(x) + F_46(x) + F_49(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_27(x)*F_48(x)*F_8(x))
Eq(F_48(x), F_1(x) + F_37(x))
Eq(F_49(x), F_36(x)*F_8(x))
Eq(F_50(x), F_141(x) + F_20(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_8(x))
Eq(F_52(x), F_53(x) + F_84(x))
Eq(F_53(x), F_54(x) + F_6(x))
Eq(F_54(x), F_20(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_53(x)*F_8(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_17(x)*F_59(x)*F_8(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x)*F_8(x))
Eq(F_62(x), F_24(x) + F_30(x))
Eq(F_63(x), F_20(x) + F_64(x) + F_74(x))
Eq(F_64(x), F_65(x)*F_8(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_28(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_66(x)*F_8(x))
Eq(F_69(x), F_25(x) + F_70(x))
Eq(F_70(x), 2*F_20(x) + F_71(x) + F_73(x))
Eq(F_71(x), F_72(x)*F_8(x))
Eq(F_72(x), F_67(x) + F_70(x))
Eq(F_73(x), F_69(x)*F_8(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_24(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_79(x)*F_8(x))
Eq(F_79(x), F_11(x) + F_77(x))
Eq(F_80(x), 2*F_20(x) + F_81(x) + F_83(x))
Eq(F_81(x), F_8(x)*F_82(x))
Eq(F_82(x), F_25(x) + F_80(x))
Eq(F_83(x), F_76(x)*F_8(x))
Eq(F_84(x), F_50(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_8(x)*F_87(x))
Eq(F_87(x), F_137(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_98(x))
Eq(F_89(x), F_30(x)*F_90(x))
Eq(F_90(x), F_107(x) + F_20(x) + F_91(x))
Eq(F_91(x), F_8(x)*F_92(x))
Eq(F_92(x), F_13(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_106(x))
Eq(F_94(x), F_95(x) - F_97(x))
Eq(F_95(x), F_96(x)/F_8(x))
Eq(F_96(x), F_85(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_37(x)*F_6(x))
Eq(F_100(x), F_60(x)*F_90(x))
Eq(F_101(x), F_102(x) + F_104(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_11(x)*F_37(x)*F_6(x))
Eq(F_104(x), F_105(x)*F_60(x))
Eq(F_105(x), -F_90(x) + F_93(x))
Eq(F_106(x), F_1(x) + F_60(x))
Eq(F_107(x), F_108(x)*F_8(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_37(x) + F_90(x))
Eq(F_110(x), F_111(x) + F_45(x))
Eq(F_111(x), F_112(x) - F_90(x))
Eq(F_112(x), F_113(x) - F_134(x))
Eq(F_113(x), F_114(x) - F_133(x))
Eq(F_114(x), F_115(x)/F_8(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_8(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_10(x)*F_106(x)*F_90(x))
Eq(F_120(x), F_121(x) + F_123(x))
Eq(F_121(x), F_100(x) + F_122(x))
Eq(F_122(x), F_14(x)*F_33(x))
Eq(F_123(x), F_124(x) + F_132(x))
Eq(F_124(x), F_125(x)*F_14(x))
Eq(F_125(x), F_126(x) + F_129(x) + F_20(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_48(x)*F_8(x))
Eq(F_128(x), F_60(x) + F_63(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x)*F_8(x))
Eq(F_131(x), F_125(x) + F_33(x))
Eq(F_132(x), F_63(x)*F_90(x))
Eq(F_133(x), F_112(x)*F_60(x))
Eq(F_134(x), F_133(x) + F_135(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_14(x)*F_30(x)*F_33(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_30(x)*F_60(x)*F_90(x))
Eq(F_139(x), F_132(x) + F_140(x))
Eq(F_140(x), F_37(x)*F_54(x))
Eq(F_141(x), F_142(x)*F_8(x))
Eq(F_142(x), F_143(x) + F_32(x))
Eq(F_143(x), F_116(x) + F_125(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 4], [2, 1], [2, 4]]}, {"patt": [2, 0, 1], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 4], [2, 0], [2, 4]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 4], [2, 0], [2, 4], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 1]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 5], [3, 5], [3, 5]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[3, 5], [3, 1], [3, 5]]}, {"patt": [2, 0, 1], "pos": [[3, 5], [3, 5], [3, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [3, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 5], [3, 0], [3, 5]]}, {"patt": [3, 1, 2, 0], "pos": [[3, 5], [3, 0], [3, 5], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[3, 5]]}], [{"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 4], [1, 2], [3, 0], [3, 1], [3, 5]], [[2, 3]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 3], [1, 0], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 3], [1, 0], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: insertion_row_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24046/
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[11,x]*F[4,x]
F[4,x] = F[33,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[11,x]*F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]*F[9,x]
F[11,x] = x
F[12,x] = F[13,x]+F[18,x]
F[13,x] = F[14,x]
F[14,x] = F[11,x]*F[15,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[1,x]+F[13,x]
F[17,x] = F[13,x]
F[18,x] = F[19,x]+F[20,x]+F[21,x]
F[19,x] = 0
F[20,x] = F[11,x]*F[12,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[16,x]*F[23,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[9,x]
F[26,x] = F[19,x]+F[27,x]+F[32,x]
F[27,x] = F[11,x]*F[28,x]
F[28,x] = F[26,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[1,x]+F[29,x]
F[32,x] = F[11,x]*F[23,x]
F[33,x] = F[34,x]+F[50,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[1,x]+F[34,x]
F[38,x] = F[39,x]*F[47,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[41,x]
F[41,x] = F[42,x]+F[9,x]
F[42,x] = F[29,x]+F[43,x]
F[43,x] = F[19,x]+F[44,x]+F[46,x]
F[44,x] = F[11,x]*F[45,x]
F[45,x] = F[24,x]+F[43,x]
F[46,x] = F[11,x]*F[42,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[47,x]*F[9,x]
F[50,x] = F[133,x]+F[19,x]+F[51,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[53,x]+F[63,x]
F[53,x] = F[13,x]+F[54,x]
F[54,x] = F[19,x]+F[55,x]+F[56,x]
F[55,x] = F[11,x]*F[53,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[16,x]*F[58,x]
F[58,x] = F[29,x]+F[59,x]
F[59,x] = F[19,x]+F[60,x]+F[62,x]
F[60,x] = F[11,x]*F[61,x]
F[61,x] = F[24,x]+F[59,x]
F[62,x] = F[11,x]*F[58,x]
F[63,x] = F[64,x]+F[99,x]
F[64,x] = F[19,x]+F[65,x]+F[78,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[53,x]+F[67,x]
F[67,x] = F[64,x]+F[68,x]
F[68,x] = 2*F[19,x]+F[69,x]+F[70,x]
F[69,x] = F[11,x]*F[67,x]
F[70,x] = F[71,x]
F[71,x] = F[11,x]*F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[68,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[29,x]*F[39,x]
F[76,x] = F[77,x]
F[77,x] = F[29,x]^2*F[16,x]*F[39,x]
F[78,x] = F[11,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[39,x]+F[64,x]
F[81,x] = F[82,x]+F[88,x]
F[82,x] = F[19,x]+F[83,x]+F[86,x]
F[83,x] = F[84,x]
F[84,x] = F[11,x]*F[61,x]*F[85,x]
F[85,x] = F[1,x]+F[39,x]
F[86,x] = F[11,x]*F[87,x]
F[87,x] = F[39,x]+F[82,x]
F[88,x] = 2*F[19,x]+F[89,x]+F[97,x]
F[89,x] = F[90,x]
F[90,x] = F[11,x]*F[91,x]
F[91,x] = F[92,x]+F[94,x]
F[92,x] = F[93,x]
F[93,x] = F[13,x]*F[24,x]*F[9,x]
F[94,x] = F[88,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[24,x]^2*F[13,x]*F[39,x]
F[97,x] = F[11,x]*F[98,x]
F[98,x] = F[64,x]+F[88,x]
F[99,x] = F[100,x]+F[128,x]+F[129,x]+F[19,x]
F[100,x] = F[101,x]*F[11,x]
F[101,x] = F[102,x]+F[115,x]
F[102,x] = F[103,x]+F[54,x]
F[103,x] = 2*F[19,x]+F[104,x]+F[105,x]
F[104,x] = F[102,x]*F[11,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[11,x]*F[16,x]
F[107,x] = F[108,x]+F[111,x]
F[108,x] = F[109,x]
F[109,x] = F[11,x]*F[110,x]
F[110,x] = F[108,x]+F[29,x]
F[111,x] = 2*F[19,x]+F[112,x]+F[114,x]
F[112,x] = F[11,x]*F[113,x]
F[113,x] = F[111,x]+F[59,x]
F[114,x] = F[107,x]*F[11,x]
F[115,x] = F[116,x]+F[99,x]
F[116,x] = F[117,x]
F[117,x] = 3*F[19,x]+F[118,x]+F[120,x]
F[118,x] = F[11,x]*F[119,x]
F[119,x] = F[117,x]+F[68,x]
F[120,x] = F[121,x]
F[121,x] = F[11,x]*F[122,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[117,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[29,x]^2*F[39,x]
F[126,x] = F[127,x]
F[127,x] = F[29,x]^3*F[16,x]*F[39,x]
F[128,x] = F[11,x]*F[63,x]
F[129,x] = -F[130,x]-2*F[19,x]+F[68,x]
F[130,x] = F[11,x]*F[131,x]
F[131,x] = F[102,x]+F[132,x]
F[132,x] = F[117,x]+F[68,x]
F[133,x] = F[11,x]*F[134,x]
F[134,x] = F[135,x]+F[80,x]
F[135,x] = F[136,x]+F[82,x]
F[136,x] = F[137,x]+F[176,x]+F[178,x]+F[19,x]
F[137,x] = F[11,x]*F[138,x]
F[138,x] = F[139,x]+F[152,x]
F[139,x] = F[140,x]+F[18,x]
F[140,x] = 2*F[19,x]+F[141,x]+F[142,x]
F[141,x] = F[11,x]*F[139,x]
F[142,x] = F[143,x]
F[143,x] = F[11,x]*F[144,x]*F[16,x]
F[144,x] = F[145,x]+F[148,x]
F[145,x] = F[146,x]
F[146,x] = F[11,x]*F[147,x]
F[147,x] = F[145,x]+F[24,x]
F[148,x] = 2*F[19,x]+F[149,x]+F[151,x]
F[149,x] = F[11,x]*F[150,x]
F[150,x] = F[148,x]+F[26,x]
F[151,x] = F[11,x]*F[144,x]
F[152,x] = F[136,x]+F[153,x]
F[153,x] = F[154,x]
F[154,x] = 3*F[19,x]+F[155,x]+F[168,x]
F[155,x] = F[11,x]*F[156,x]
F[156,x] = F[154,x]+F[157,x]
F[157,x] = 2*F[19,x]+F[158,x]+F[160,x]
F[158,x] = F[11,x]*F[159,x]
F[159,x] = F[157,x]+F[64,x]
F[160,x] = F[161,x]
F[161,x] = F[11,x]*F[162,x]
F[162,x] = F[163,x]+F[166,x]
F[163,x] = F[157,x]+F[164,x]
F[164,x] = F[165,x]
F[165,x] = F[24,x]*F[39,x]
F[166,x] = F[167,x]
F[167,x] = F[24,x]^2*F[16,x]*F[39,x]
F[168,x] = F[169,x]
F[169,x] = F[11,x]*F[170,x]
F[170,x] = F[171,x]+F[174,x]
F[171,x] = F[154,x]+F[172,x]
F[172,x] = F[173,x]
F[173,x] = F[24,x]^2*F[39,x]
F[174,x] = F[175,x]
F[175,x] = F[24,x]^3*F[16,x]*F[39,x]
F[176,x] = F[11,x]*F[177,x]
F[177,x] = F[136,x]+F[64,x]
F[178,x] = -F[179,x]-2*F[19,x]+F[157,x]
F[179,x] = F[11,x]*F[180,x]
F[180,x] = F[139,x]+F[181,x]
F[181,x] = F[154,x]+F[157,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_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{33}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{50}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \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_{34}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{47}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{29}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{24}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{42}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{47}\! \left(x \right) F_{9}\! \left(x \right)
F_{50}\! \left(x \right) = F_{133}\! \left(x \right)+F_{19}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{63}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right)+F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{29}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{99}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right)+F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{53}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{29}\! \left(x \right) F_{39}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{29} \left(x \right)^{2} F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{82}\! \left(x \right) = F_{19}\! \left(x \right)+F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{39}\! \left(x \right)+F_{82}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{89}\! \left(x \right)+F_{97}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{11}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right) F_{9}\! \left(x \right)
F_{94}\! \left(x \right) = F_{88}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{97}\! \left(x \right) = F_{11}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{64}\! \left(x \right)+F_{88}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{128}\! \left(x \right)+F_{129}\! \left(x \right)+F_{19}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{11}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{115}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{54}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right) F_{11}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{111}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{11}\! \left(x \right) F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{29}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{112}\! \left(x \right)+F_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right) F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{111}\! \left(x \right)+F_{59}\! \left(x \right)
F_{114}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{99}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{118}\! \left(x \right)+F_{120}\! \left(x \right)
F_{118}\! \left(x \right) = F_{11}\! \left(x \right) F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{117}\! \left(x \right)+F_{68}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{11}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{117}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{29} \left(x \right)^{2} F_{39}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{29} \left(x \right)^{3} F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{128}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{130}\! \left(x \right)-2 F_{19}\! \left(x \right)+F_{68}\! \left(x \right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{102}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{117}\! \left(x \right)+F_{68}\! \left(x \right)
F_{133}\! \left(x \right) = F_{11}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{80}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{82}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{176}\! \left(x \right)+F_{178}\! \left(x \right)+F_{19}\! \left(x \right)
F_{137}\! \left(x \right) = F_{11}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{152}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{18}\! \left(x \right)
F_{140}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{11}\! \left(x \right) F_{139}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{11}\! \left(x \right) F_{144}\! \left(x \right) F_{16}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{148}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)+F_{24}\! \left(x \right)
F_{148}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{149}\! \left(x \right)+F_{151}\! \left(x \right)
F_{149}\! \left(x \right) = F_{11}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{26}\! \left(x \right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{144}\! \left(x \right)
F_{152}\! \left(x \right) = F_{136}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = 3 F_{19}\! \left(x \right)+F_{155}\! \left(x \right)+F_{168}\! \left(x \right)
F_{155}\! \left(x \right) = F_{11}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{154}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{158}\! \left(x \right)+F_{160}\! \left(x \right)
F_{158}\! \left(x \right) = F_{11}\! \left(x \right) F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{157}\! \left(x \right)+F_{64}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{11}\! \left(x \right) F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{166}\! \left(x \right)
F_{163}\! \left(x \right) = F_{157}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{24}\! \left(x \right) F_{39}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{11}\! \left(x \right) F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{174}\! \left(x \right)
F_{171}\! \left(x \right) = F_{154}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{39}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{24} \left(x \right)^{3} F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{176}\! \left(x \right) = F_{11}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{136}\! \left(x \right)+F_{64}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{179}\! \left(x \right)-2 F_{19}\! \left(x \right)+F_{157}\! \left(x \right)
F_{179}\! \left(x \right) = F_{11}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{139}\! \left(x \right)+F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{154}\! \left(x \right)+F_{157}\! \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_11(x)*F_4(x))
Eq(F_4(x), F_33(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_11(x)*F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x)*F_9(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_18(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_11(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_1(x) + F_13(x))
Eq(F_17(x), F_13(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_21(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_11(x)*F_12(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_16(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_9(x))
Eq(F_26(x), F_19(x) + F_27(x) + F_32(x))
Eq(F_27(x), F_11(x)*F_28(x))
Eq(F_28(x), F_26(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_1(x) + F_29(x))
Eq(F_32(x), F_11(x)*F_23(x))
Eq(F_33(x), F_34(x) + F_50(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_1(x) + F_34(x))
Eq(F_38(x), F_39(x)*F_47(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_9(x))
Eq(F_42(x), F_29(x) + F_43(x))
Eq(F_43(x), F_19(x) + F_44(x) + F_46(x))
Eq(F_44(x), F_11(x)*F_45(x))
Eq(F_45(x), F_24(x) + F_43(x))
Eq(F_46(x), F_11(x)*F_42(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_47(x)*F_9(x))
Eq(F_50(x), F_133(x) + F_19(x) + F_51(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_63(x))
Eq(F_53(x), F_13(x) + F_54(x))
Eq(F_54(x), F_19(x) + F_55(x) + F_56(x))
Eq(F_55(x), F_11(x)*F_53(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_16(x)*F_58(x))
Eq(F_58(x), F_29(x) + F_59(x))
Eq(F_59(x), F_19(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_11(x)*F_61(x))
Eq(F_61(x), F_24(x) + F_59(x))
Eq(F_62(x), F_11(x)*F_58(x))
Eq(F_63(x), F_64(x) + F_99(x))
Eq(F_64(x), F_19(x) + F_65(x) + F_78(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_53(x) + F_67(x))
Eq(F_67(x), F_64(x) + F_68(x))
Eq(F_68(x), 2*F_19(x) + F_69(x) + F_70(x))
Eq(F_69(x), F_11(x)*F_67(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_11(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_68(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_29(x)*F_39(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_16(x)*F_29(x)**2*F_39(x))
Eq(F_78(x), F_11(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_39(x) + F_64(x))
Eq(F_81(x), F_82(x) + F_88(x))
Eq(F_82(x), F_19(x) + F_83(x) + F_86(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_11(x)*F_61(x)*F_85(x))
Eq(F_85(x), F_1(x) + F_39(x))
Eq(F_86(x), F_11(x)*F_87(x))
Eq(F_87(x), F_39(x) + F_82(x))
Eq(F_88(x), 2*F_19(x) + F_89(x) + F_97(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_11(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_94(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_13(x)*F_24(x)*F_9(x))
Eq(F_94(x), F_88(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_13(x)*F_24(x)**2*F_39(x))
Eq(F_97(x), F_11(x)*F_98(x))
Eq(F_98(x), F_64(x) + F_88(x))
Eq(F_99(x), F_100(x) + F_128(x) + F_129(x) + F_19(x))
Eq(F_100(x), F_101(x)*F_11(x))
Eq(F_101(x), F_102(x) + F_115(x))
Eq(F_102(x), F_103(x) + F_54(x))
Eq(F_103(x), F_104(x) + F_105(x) + 2*F_19(x))
Eq(F_104(x), F_102(x)*F_11(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_11(x)*F_16(x))
Eq(F_107(x), F_108(x) + F_111(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_11(x)*F_110(x))
Eq(F_110(x), F_108(x) + F_29(x))
Eq(F_111(x), F_112(x) + F_114(x) + 2*F_19(x))
Eq(F_112(x), F_11(x)*F_113(x))
Eq(F_113(x), F_111(x) + F_59(x))
Eq(F_114(x), F_107(x)*F_11(x))
Eq(F_115(x), F_116(x) + F_99(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x) + F_120(x) + 3*F_19(x))
Eq(F_118(x), F_11(x)*F_119(x))
Eq(F_119(x), F_117(x) + F_68(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_11(x)*F_122(x))
Eq(F_122(x), F_123(x) + F_126(x))
Eq(F_123(x), F_117(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_29(x)**2*F_39(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_16(x)*F_29(x)**3*F_39(x))
Eq(F_128(x), F_11(x)*F_63(x))
Eq(F_129(x), -F_130(x) - 2*F_19(x) + F_68(x))
Eq(F_130(x), F_11(x)*F_131(x))
Eq(F_131(x), F_102(x) + F_132(x))
Eq(F_132(x), F_117(x) + F_68(x))
Eq(F_133(x), F_11(x)*F_134(x))
Eq(F_134(x), F_135(x) + F_80(x))
Eq(F_135(x), F_136(x) + F_82(x))
Eq(F_136(x), F_137(x) + F_176(x) + F_178(x) + F_19(x))
Eq(F_137(x), F_11(x)*F_138(x))
Eq(F_138(x), F_139(x) + F_152(x))
Eq(F_139(x), F_140(x) + F_18(x))
Eq(F_140(x), F_141(x) + F_142(x) + 2*F_19(x))
Eq(F_141(x), F_11(x)*F_139(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_11(x)*F_144(x)*F_16(x))
Eq(F_144(x), F_145(x) + F_148(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_11(x)*F_147(x))
Eq(F_147(x), F_145(x) + F_24(x))
Eq(F_148(x), F_149(x) + F_151(x) + 2*F_19(x))
Eq(F_149(x), F_11(x)*F_150(x))
Eq(F_150(x), F_148(x) + F_26(x))
Eq(F_151(x), F_11(x)*F_144(x))
Eq(F_152(x), F_136(x) + F_153(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x) + F_168(x) + 3*F_19(x))
Eq(F_155(x), F_11(x)*F_156(x))
Eq(F_156(x), F_154(x) + F_157(x))
Eq(F_157(x), F_158(x) + F_160(x) + 2*F_19(x))
Eq(F_158(x), F_11(x)*F_159(x))
Eq(F_159(x), F_157(x) + F_64(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_11(x)*F_162(x))
Eq(F_162(x), F_163(x) + F_166(x))
Eq(F_163(x), F_157(x) + F_164(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_24(x)*F_39(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_16(x)*F_24(x)**2*F_39(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_11(x)*F_170(x))
Eq(F_170(x), F_171(x) + F_174(x))
Eq(F_171(x), F_154(x) + F_172(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_24(x)**2*F_39(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_16(x)*F_24(x)**3*F_39(x))
Eq(F_176(x), F_11(x)*F_177(x))
Eq(F_177(x), F_136(x) + F_64(x))
Eq(F_178(x), F_157(x) - F_179(x) - 2*F_19(x))
Eq(F_179(x), F_11(x)*F_180(x))
Eq(F_180(x), F_139(x) + F_181(x))
Eq(F_181(x), F_154(x) + F_157(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_row_placements_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[4, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 3, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], 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{"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [4, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 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0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 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"pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": 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{"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": 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"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": 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{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: insertion_point_row_placements_expand_verified
Tree: http://permpal.com/tree/24047/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[32,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]*F[27,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[8,x]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[8,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[8,x]
F[21,x] = F[1,x]+F[19,x]
F[22,x] = F[23,x]+F[24,x]+F[26,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[16,x]+F[22,x]
F[26,x] = F[18,x]*F[8,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[8,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[1,x]+F[27,x]
F[31,x] = F[27,x]
F[32,x] = F[33,x]+F[47,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[8,x]
F[35,x] = F[15,x]+F[36,x]
F[36,x] = F[12,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]*F[39,x]*F[8,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[16,x]*F[21,x]
F[41,x] = F[15,x]*F[42,x]
F[42,x] = F[16,x]+F[43,x]
F[43,x] = F[23,x]+F[44,x]+F[45,x]
F[44,x] = F[42,x]*F[8,x]
F[45,x] = F[46,x]*F[8,x]
F[46,x] = F[19,x]+F[43,x]
F[47,x] = F[191,x]+F[23,x]+F[48,x]
F[48,x] = F[49,x]*F[8,x]
F[49,x] = F[50,x]+F[61,x]
F[50,x] = F[27,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[30,x]*F[53,x]*F[8,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[16,x]+F[55,x]
F[55,x] = F[23,x]+F[56,x]+F[58,x]
F[56,x] = F[57,x]*F[8,x]
F[57,x] = F[19,x]+F[55,x]
F[58,x] = F[54,x]*F[8,x]
F[59,x] = F[16,x]*F[60,x]
F[60,x] = F[21,x]+F[54,x]
F[61,x] = F[172,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]*F[8,x]
F[64,x] = F[65,x]+F[70,x]
F[65,x] = F[62,x]+F[66,x]
F[66,x] = F[30,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]*F[8,x]
F[69,x] = F[15,x]+F[46,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[62,x]+F[67,x]
F[73,x] = F[27,x]*F[67,x]
F[74,x] = F[116,x]+F[75,x]
F[75,x] = F[76,x]+F[97,x]
F[76,x] = F[23,x]+F[77,x]+F[87,x]
F[77,x] = F[78,x]*F[8,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[16,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[79,x]*F[8,x]
F[82,x] = F[43,x]+F[83,x]
F[83,x] = 2*F[23,x]+F[84,x]+F[86,x]
F[84,x] = F[8,x]*F[85,x]
F[85,x] = F[80,x]+F[83,x]
F[86,x] = F[8,x]*F[82,x]
F[87,x] = F[8,x]*F[88,x]
F[88,x] = F[46,x]+F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[91,x]
F[91,x] = F[8,x]*F[92,x]
F[92,x] = F[19,x]+F[90,x]
F[93,x] = 2*F[23,x]+F[94,x]+F[96,x]
F[94,x] = F[8,x]*F[95,x]
F[95,x] = F[43,x]+F[93,x]
F[96,x] = F[8,x]*F[89,x]
F[97,x] = 1/F[12,x]*F[98,x]
F[98,x] = -F[103,x]+F[99,x]
F[99,x] = -F[114,x]+F[100,x]
F[100,x] = -F[112,x]+F[101,x]
F[101,x] = 1/F[8,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[8,x]
F[105,x] = F[106,x]+F[111,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[27,x]*F[36,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[15,x]*F[47,x]
F[110,x] = F[36,x]*F[62,x]
F[111,x] = F[27,x]*F[36,x]*F[67,x]
F[112,x] = F[113,x]*F[12,x]*F[21,x]*F[27,x]
F[113,x] = F[1,x]+F[67,x]
F[114,x] = F[115,x]+F[47,x]
F[115,x] = F[12,x]*F[62,x]
F[116,x] = 1/F[127,x]*F[117,x]
F[117,x] = -F[122,x]+F[118,x]
F[118,x] = -F[190,x]+F[119,x]
F[119,x] = -F[188,x]+F[120,x]
F[120,x] = 1/F[8,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[8,x]
F[124,x] = F[125,x]+F[137,x]
F[125,x] = F[113,x]*F[126,x]*F[27,x]
F[126,x] = F[127,x]+F[132,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[8,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[1,x]+F[127,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]
F[133,x] = F[130,x]*F[134,x]*F[8,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[15,x]*F[19,x]
F[136,x] = F[21,x]*F[46,x]
F[137,x] = F[138,x]+F[185,x]
F[138,x] = F[139,x]+F[184,x]
F[139,x] = F[140,x]+F[165,x]+F[23,x]
F[140,x] = F[141,x]*F[8,x]
F[141,x] = F[142,x]+F[147,x]
F[142,x] = F[143,x]+F[27,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[30,x]*F[8,x]
F[145,x] = F[146,x]+F[18,x]
F[146,x] = F[14,x]*F[19,x]
F[147,x] = F[148,x]+F[62,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[8,x]
F[150,x] = F[151,x]+F[164,x]
F[151,x] = F[152,x]+F[156,x]
F[152,x] = F[153,x]+F[62,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[27,x]*F[67,x]
F[155,x] = F[16,x]*F[62,x]
F[156,x] = F[148,x]+F[157,x]
F[157,x] = F[158,x]+F[163,x]
F[158,x] = F[159,x]*F[27,x]
F[159,x] = F[160,x]
F[160,x] = F[113,x]*F[161,x]*F[8,x]
F[161,x] = F[135,x]+F[162,x]
F[162,x] = F[21,x]*F[57,x]
F[163,x] = F[148,x]*F[16,x]
F[164,x] = F[60,x]*F[62,x]
F[165,x] = F[166,x]*F[8,x]
F[166,x] = F[167,x]+F[72,x]
F[167,x] = F[168,x]+F[172,x]
F[168,x] = F[169,x]
F[169,x] = F[113,x]*F[170,x]*F[8,x]
F[170,x] = F[171,x]+F[40,x]
F[171,x] = F[15,x]*F[25,x]
F[172,x] = F[173,x]
F[173,x] = F[174,x]*F[8,x]
F[174,x] = F[175,x]+F[183,x]
F[175,x] = F[176,x]+F[179,x]
F[176,x] = F[177,x]+F[62,x]
F[177,x] = F[178,x]+F[73,x]
F[178,x] = F[19,x]*F[62,x]
F[179,x] = F[172,x]+F[180,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[168,x]*F[27,x]
F[182,x] = F[172,x]*F[19,x]
F[183,x] = F[14,x]*F[62,x]
F[184,x] = F[127,x]*F[62,x]
F[185,x] = F[186,x]+F[187,x]
F[186,x] = F[139,x]*F[19,x]
F[187,x] = F[132,x]*F[62,x]
F[188,x] = F[138,x]+F[189,x]
F[189,x] = F[127,x]*F[15,x]*F[27,x]
F[190,x] = F[127,x]*F[15,x]*F[27,x]*F[67,x]
F[191,x] = F[192,x]*F[8,x]
F[192,x] = F[193,x]+F[72,x]
F[193,x] = F[148,x]+F[159,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{32}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \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_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{23}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{8}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right)+F_{43}\! \left(x \right)
F_{47}\! \left(x \right) = F_{191}\! \left(x \right)+F_{23}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{8}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{50}\! \left(x \right) = F_{27}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{30}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{16}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{23}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right) F_{8}\! \left(x \right)
F_{57}\! \left(x \right) = F_{19}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{21}\! \left(x \right)+F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{172}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{8}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{30}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right) F_{8}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{46}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{27}\! \left(x \right) F_{67}\! \left(x \right)
F_{74}\! \left(x \right) = F_{116}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{97}\! \left(x \right)
F_{76}\! \left(x \right) = F_{23}\! \left(x \right)+F_{77}\! \left(x \right)+F_{87}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right) F_{8}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{16}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{79}\! \left(x \right) F_{8}\! \left(x \right)
F_{82}\! \left(x \right) = F_{43}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{8}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{8}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{46}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{8}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{19}\! \left(x \right)+F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{43}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{8}\! \left(x \right) F_{89}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{98}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{8}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{111}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{27}\! \left(x \right) F_{36}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{15}\! \left(x \right) F_{47}\! \left(x \right)
F_{110}\! \left(x \right) = F_{36}\! \left(x \right) F_{62}\! \left(x \right)
F_{111}\! \left(x \right) = F_{27}\! \left(x \right) F_{36}\! \left(x \right) F_{67}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right) F_{21}\! \left(x \right) F_{27}\! \left(x \right)
F_{113}\! \left(x \right) = F_{1}\! \left(x \right)+F_{67}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{47}\! \left(x \right)
F_{115}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{127}\! \left(x \right)}
F_{117}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{190}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{188}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{8}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{137}\! \left(x \right)
F_{125}\! \left(x \right) = F_{113}\! \left(x \right) F_{126}\! \left(x \right) F_{27}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{132}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{8}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{1}\! \left(x \right)+F_{127}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{130}\! \left(x \right) F_{134}\! \left(x \right) F_{8}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{136}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{185}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{184}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{165}\! \left(x \right)+F_{23}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{8}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{147}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{27}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{18}\! \left(x \right)
F_{146}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{62}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{8}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{164}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{156}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{62}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{27}\! \left(x \right) F_{67}\! \left(x \right)
F_{155}\! \left(x \right) = F_{16}\! \left(x \right) F_{62}\! \left(x \right)
F_{156}\! \left(x \right) = F_{148}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{163}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{27}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{113}\! \left(x \right) F_{161}\! \left(x \right) F_{8}\! \left(x \right)
F_{161}\! \left(x \right) = F_{135}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{21}\! \left(x \right) F_{57}\! \left(x \right)
F_{163}\! \left(x \right) = F_{148}\! \left(x \right) F_{16}\! \left(x \right)
F_{164}\! \left(x \right) = F_{60}\! \left(x \right) F_{62}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{8}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{72}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{172}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{113}\! \left(x \right) F_{170}\! \left(x \right) F_{8}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{40}\! \left(x \right)
F_{171}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{8}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{183}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{179}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{62}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{73}\! \left(x \right)
F_{178}\! \left(x \right) = F_{19}\! \left(x \right) F_{62}\! \left(x \right)
F_{179}\! \left(x \right) = F_{172}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{168}\! \left(x \right) F_{27}\! \left(x \right)
F_{182}\! \left(x \right) = F_{172}\! \left(x \right) F_{19}\! \left(x \right)
F_{183}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{184}\! \left(x \right) = F_{127}\! \left(x \right) F_{62}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{187}\! \left(x \right)
F_{186}\! \left(x \right) = F_{139}\! \left(x \right) F_{19}\! \left(x \right)
F_{187}\! \left(x \right) = F_{132}\! \left(x \right) F_{62}\! \left(x \right)
F_{188}\! \left(x \right) = F_{138}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{127}\! \left(x \right) F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{190}\! \left(x \right) = F_{127}\! \left(x \right) F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{67}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{8}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{72}\! \left(x \right)
F_{193}\! \left(x \right) = F_{148}\! \left(x \right)+F_{159}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_32(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x)*F_27(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_8(x))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_8(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_8(x))
Eq(F_21(x), F_1(x) + F_19(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_26(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_16(x) + F_22(x))
Eq(F_26(x), F_18(x)*F_8(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_8(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_1(x) + F_27(x))
Eq(F_31(x), F_27(x))
Eq(F_32(x), F_33(x) + F_47(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_8(x))
Eq(F_35(x), F_15(x) + F_36(x))
Eq(F_36(x), F_12(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x)*F_39(x)*F_8(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_16(x)*F_21(x))
Eq(F_41(x), F_15(x)*F_42(x))
Eq(F_42(x), F_16(x) + F_43(x))
Eq(F_43(x), F_23(x) + F_44(x) + F_45(x))
Eq(F_44(x), F_42(x)*F_8(x))
Eq(F_45(x), F_46(x)*F_8(x))
Eq(F_46(x), F_19(x) + F_43(x))
Eq(F_47(x), F_191(x) + F_23(x) + F_48(x))
Eq(F_48(x), F_49(x)*F_8(x))
Eq(F_49(x), F_50(x) + F_61(x))
Eq(F_50(x), F_27(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_30(x)*F_53(x)*F_8(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_16(x) + F_55(x))
Eq(F_55(x), F_23(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_57(x)*F_8(x))
Eq(F_57(x), F_19(x) + F_55(x))
Eq(F_58(x), F_54(x)*F_8(x))
Eq(F_59(x), F_16(x)*F_60(x))
Eq(F_60(x), F_21(x) + F_54(x))
Eq(F_61(x), F_172(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)*F_8(x))
Eq(F_64(x), F_65(x) + F_70(x))
Eq(F_65(x), F_62(x) + F_66(x))
Eq(F_66(x), F_30(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x)*F_8(x))
Eq(F_69(x), F_15(x) + F_46(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_62(x) + F_67(x))
Eq(F_73(x), F_27(x)*F_67(x))
Eq(F_74(x), F_116(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_97(x))
Eq(F_76(x), F_23(x) + F_77(x) + F_87(x))
Eq(F_77(x), F_78(x)*F_8(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_16(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_79(x)*F_8(x))
Eq(F_82(x), F_43(x) + F_83(x))
Eq(F_83(x), 2*F_23(x) + F_84(x) + F_86(x))
Eq(F_84(x), F_8(x)*F_85(x))
Eq(F_85(x), F_80(x) + F_83(x))
Eq(F_86(x), F_8(x)*F_82(x))
Eq(F_87(x), F_8(x)*F_88(x))
Eq(F_88(x), F_46(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_8(x)*F_92(x))
Eq(F_92(x), F_19(x) + F_90(x))
Eq(F_93(x), 2*F_23(x) + F_94(x) + F_96(x))
Eq(F_94(x), F_8(x)*F_95(x))
Eq(F_95(x), F_43(x) + F_93(x))
Eq(F_96(x), F_8(x)*F_89(x))
Eq(F_97(x), F_98(x)/F_12(x))
Eq(F_98(x), -F_103(x) + F_99(x))
Eq(F_99(x), F_100(x) - F_114(x))
Eq(F_100(x), F_101(x) - F_112(x))
Eq(F_101(x), F_102(x)/F_8(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_8(x))
Eq(F_105(x), F_106(x) + F_111(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_27(x)*F_36(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_15(x)*F_47(x))
Eq(F_110(x), F_36(x)*F_62(x))
Eq(F_111(x), F_27(x)*F_36(x)*F_67(x))
Eq(F_112(x), F_113(x)*F_12(x)*F_21(x)*F_27(x))
Eq(F_113(x), F_1(x) + F_67(x))
Eq(F_114(x), F_115(x) + F_47(x))
Eq(F_115(x), F_12(x)*F_62(x))
Eq(F_116(x), F_117(x)/F_127(x))
Eq(F_117(x), F_118(x) - F_122(x))
Eq(F_118(x), F_119(x) - F_190(x))
Eq(F_119(x), F_120(x) - F_188(x))
Eq(F_120(x), F_121(x)/F_8(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_8(x))
Eq(F_124(x), F_125(x) + F_137(x))
Eq(F_125(x), F_113(x)*F_126(x)*F_27(x))
Eq(F_126(x), F_127(x) + F_132(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_8(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_1(x) + F_127(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_130(x)*F_134(x)*F_8(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_15(x)*F_19(x))
Eq(F_136(x), F_21(x)*F_46(x))
Eq(F_137(x), F_138(x) + F_185(x))
Eq(F_138(x), F_139(x) + F_184(x))
Eq(F_139(x), F_140(x) + F_165(x) + F_23(x))
Eq(F_140(x), F_141(x)*F_8(x))
Eq(F_141(x), F_142(x) + F_147(x))
Eq(F_142(x), F_143(x) + F_27(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_30(x)*F_8(x))
Eq(F_145(x), F_146(x) + F_18(x))
Eq(F_146(x), F_14(x)*F_19(x))
Eq(F_147(x), F_148(x) + F_62(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_8(x))
Eq(F_150(x), F_151(x) + F_164(x))
Eq(F_151(x), F_152(x) + F_156(x))
Eq(F_152(x), F_153(x) + F_62(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_27(x)*F_67(x))
Eq(F_155(x), F_16(x)*F_62(x))
Eq(F_156(x), F_148(x) + F_157(x))
Eq(F_157(x), F_158(x) + F_163(x))
Eq(F_158(x), F_159(x)*F_27(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_113(x)*F_161(x)*F_8(x))
Eq(F_161(x), F_135(x) + F_162(x))
Eq(F_162(x), F_21(x)*F_57(x))
Eq(F_163(x), F_148(x)*F_16(x))
Eq(F_164(x), F_60(x)*F_62(x))
Eq(F_165(x), F_166(x)*F_8(x))
Eq(F_166(x), F_167(x) + F_72(x))
Eq(F_167(x), F_168(x) + F_172(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_113(x)*F_170(x)*F_8(x))
Eq(F_170(x), F_171(x) + F_40(x))
Eq(F_171(x), F_15(x)*F_25(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_174(x)*F_8(x))
Eq(F_174(x), F_175(x) + F_183(x))
Eq(F_175(x), F_176(x) + F_179(x))
Eq(F_176(x), F_177(x) + F_62(x))
Eq(F_177(x), F_178(x) + F_73(x))
Eq(F_178(x), F_19(x)*F_62(x))
Eq(F_179(x), F_172(x) + F_180(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_168(x)*F_27(x))
Eq(F_182(x), F_172(x)*F_19(x))
Eq(F_183(x), F_14(x)*F_62(x))
Eq(F_184(x), F_127(x)*F_62(x))
Eq(F_185(x), F_186(x) + F_187(x))
Eq(F_186(x), F_139(x)*F_19(x))
Eq(F_187(x), F_132(x)*F_62(x))
Eq(F_188(x), F_138(x) + F_189(x))
Eq(F_189(x), F_127(x)*F_15(x)*F_27(x))
Eq(F_190(x), F_127(x)*F_15(x)*F_27(x)*F_67(x))
Eq(F_191(x), F_192(x)*F_8(x))
Eq(F_192(x), F_193(x) + F_72(x))
Eq(F_193(x), F_148(x) + F_159(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_row_placements_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 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