01243_02143_10243_12043_12403_20143_21043_21403

Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3028, 16684, 94108, 540220, 3143716, 18495860, 109804748, 656833516, 3954548404, 23942531220, 145671568060, 890158736188, 5460685820836, 33616010111524, 207597674882124, 1285745118355308, 7984334747677780, 49703044297320372, 310104296370018652, 1938842703023279260, 12145759083254828932, 76225094627945645380, 479194811433570834028, 3017321218145818486348, 19027643125104547631156, 120161363697987222110676, 759847991382940276253820, 4811041230722463537813372, 30498109301108801897999204, 193553696747847339185522532, 1229702305379398009724107404, 7820698028984556116069392684, 49787089335408547626427303956, 317244275204058398695276771060, 2023290157094936905754735468956, 12914944919376254239110848140892, 82505094763336420264940211677508, 527481965803785867615072164206980, 3374884037261218040881736837253804, 21608324377034313413738409555554828, 138446416564692541614791597044822516, 887623648807912116684596991063963668, 5694443969558856131025040989564917436, 36554304032059998784246373678420545340, 234790463088417283583348946755902596388, 1508925027042198078463658504078759054244, 9702668387240517648688895961997452490444, 62422698688320263379310194402356274391276, 401803449555388755917907579988048240240084, 2587598562120132696874900605113851380743476, 16671896014749303067929801462064552202947548, 107465985251004851523480612041162464741349916, 693024230767981227879403769509968186948990724, 4471064281897534466870926837249073905727669700, 28857090350724834330669971193126807256355669740, 186323487123074297993905945362402995050687700428, 1203512695233644119364411911320171635872095517620, 7776721920732396533374419049213521096585674116692, 50269009822153533908682293811939063725433534073084, 325055277814931541417118205794120132019037087026940, 2102629300943973790455857148265897608537212660233956, 13605436030541881197251809042761705481868893490532324, 88064794577675317514801385964061765616393328994665228, 570201450410254825885833498018182996512694341065402540, 3693062210097924323062772983852833932812591668585335700, 23926192040054242369562042440035343193694818244602704756, 155054968795408794349892846175596349952795066650876696092, 1005123813406523015178400912506375012480620055567816394204, 6517363862161748993584858312574555248698990308475172748484, 42270734248909393664508457880279408472056188584389250052612, 274233204720465439638727817398363580514191938386009629356844, 1779548503698793262984581488049508086784811418606937086108044, 11550649138337646731646388493077089456689160211594055137291636, 74990639369749991982828547154263831155716224613297654261658772, 486977899118924437706289788691037155535504261529666710596057916, 3163082358364917325274784504308337517191339000386774115663763132, 20549838439761147014413462143658850406628512591594756850819801252, 133536713360671569449387645030768288171270407840279702019920147492, 867930779394285959994045473602641649050613293291121810558715862860, 5642343035710614741424794374405606232723460437894199823370645971052, 36687810920577919613510507891919256216606075013169116109186726656340, 238599773052913743825729198227137382525780850755570444582704567556532, 1552037578990814742727710535935722990006380964844282702370523805499484, 10097562432670876246279080571795246584978147321752353830522754388826524, 65706927649499189048901970010811418075084973064988897440755030932929156, 427645910356251027754087979573021440421133497516269108307693797479800388, 2783776346133010329449658789041087980676946826475518919639911361351798636, 18124230306890185373764449858021189795635053948697990609021261221645139276, 118020766409480223913691918816462206678556474127615902167469229533817259828, 768651319079333223529183173072596278619227716833639790244129652865600694996, 5006923084474628039391837155363814418187489268146062724453348241489947241852, 32619824069779657440927456463717628743088803407990283262418421836885137892988, 212549485863749190904400522476805579268737847104379586241610385413557018026596, 1385175793710353984443649612277679617042848998277633174245500424137203786430564

Implicit equation for the generating function in Maple syntax:
F(x)^4+(2*x^2-x-5)*F(x)^3+(6*x^3-13*x^2+7*x+9)*F(x)^2+(-5*x^3+15*x^2-11*x-7)*F(x)+x^3-4*x^2+5*x+2 = 0

Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{4}+\left(2 x^{2}-x -5\right) F \! \left(x \right)^{3}+\left(6 x^{3}-13 x^{2}+7 x +9\right) F \! \left(x \right)^{2}+\left(-5 x^{3}+15 x^{2}-11 x -7\right) F \! \left(x \right)+x^{3}-4 x^{2}+5 x +2 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3028
a(8) = 16684
a(9) = 94108
a(10) = 540220
a(11) = 3143716
a(12) = 18495860
a(13) = 109804748
a(14) = 656833516
a(15) = 3954548404
a(n+16) = -3888*(n-2)*(n-1)*n/(n+15)/(n+14)/(n+16)*a(n)+432*n*(263*n+284)*(n-1)/(n+15)/(n+14)/(n+16)*a(n+1)-72*n*(17081*n^2+48989*n+30852)/(n+15)/(n+14)/(n+16)*a(n+2)+24*(264784*n^3+1436297*n^2+2426893*n+1255902)/(n+15)/(n+14)/(n+16)*a(n+3)-12*(1348919*n^3+10200551*n^2+25136474*n+20250164)/(n+15)/(n+14)/(n+16)*a(n+4)+12*(1225132*n^3+8633313*n^2+13205959*n-5474884)/(n+15)/(n+14)/(n+16)*a(n+5)+6*(4315071*n^3+86386017*n^2+529773610*n+1020351820)/(n+15)/(n+14)/(n+16)*a(n+6)-4*(22222414*n^3+431906652*n^2+2767672229*n+5843547774)/(n+15)/(n+14)/(n+16)*a(n+7)+2*(51986113*n^3+1118463078*n^2+7994045393*n+18974233176)/(n+15)/(n+14)/(n+16)*a(n+8)-(55019999*n^3+1323166683*n^2+10578047320*n+28115446560)/(n+15)/(n+14)/(n+16)*a(n+9)+(15354911*n^3+409446561*n^2+3627823594*n+10683287184)/(n+15)/(n+14)/(n+16)*a(n+10)-3*(776913*n^3+22648409*n^2+219096974*n+703443040)/(n+15)/(n+14)/(n+16)*a(n+11)+3*(55053*n^3+1699075*n^2+17295196*n+57989872)/(n+15)/(n+14)/(n+16)*a(n+12)+(947*n^3+68187*n^2+1247248*n+6772704)/(n+15)/(n+14)/(n+16)*a(n+13)-(949*n^2+25405*n+169548)/(n+16)/(n+15)*a(n+14)+11*(5*n+68)/(n+16)*a(n+15), n >= 16

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3028
a(8) = 16684
a(9) = 94108
a(10) = 540220
a(11) = 3143716
a(12) = 18495860
a(13) = 109804748
a(14) = 656833516
a(15) = 3954548404
a{\left(n + 16 \right)} = - \frac{3888 n \left(n - 2\right) \left(n - 1\right) a{\left(n \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{432 n \left(n - 1\right) \left(263 n + 284\right) a{\left(n + 1 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{72 n \left(17081 n^{2} + 48989 n + 30852\right) a{\left(n + 2 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{11 \left(5 n + 68\right) a{\left(n + 15 \right)}}{n + 16} - \frac{\left(949 n^{2} + 25405 n + 169548\right) a{\left(n + 14 \right)}}{\left(n + 15\right) \left(n + 16\right)} + \frac{\left(947 n^{3} + 68187 n^{2} + 1247248 n + 6772704\right) a{\left(n + 13 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{3 \left(55053 n^{3} + 1699075 n^{2} + 17295196 n + 57989872\right) a{\left(n + 12 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{24 \left(264784 n^{3} + 1436297 n^{2} + 2426893 n + 1255902\right) a{\left(n + 3 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{3 \left(776913 n^{3} + 22648409 n^{2} + 219096974 n + 703443040\right) a{\left(n + 11 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{12 \left(1225132 n^{3} + 8633313 n^{2} + 13205959 n - 5474884\right) a{\left(n + 5 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{12 \left(1348919 n^{3} + 10200551 n^{2} + 25136474 n + 20250164\right) a{\left(n + 4 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{6 \left(4315071 n^{3} + 86386017 n^{2} + 529773610 n + 1020351820\right) a{\left(n + 6 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{\left(15354911 n^{3} + 409446561 n^{2} + 3627823594 n + 10683287184\right) a{\left(n + 10 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{4 \left(22222414 n^{3} + 431906652 n^{2} + 2767672229 n + 5843547774\right) a{\left(n + 7 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{2 \left(51986113 n^{3} + 1118463078 n^{2} + 7994045393 n + 18974233176\right) a{\left(n + 8 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{\left(55019999 n^{3} + 1323166683 n^{2} + 10578047320 n + 28115446560\right) a{\left(n + 9 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)}, \quad n \geq 16

Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24858/
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[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[10,x]+F[126,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[82,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[7,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = 1/F[16,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[23,x]*F[68,x]
F[23,x] = 1/F[16,x]/F[79,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[116,x]+F[26,x]
F[26,x] = 1/F[16,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[108,x]+F[29,x]
F[29,x] = F[30,x]+F[98,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[95,x]
F[34,x] = F[35,x]+F[92,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[5,x]
F[37,x] = F[38,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[36,x]*F[5,x]
F[41,x] = F[42,x]
F[42,x] = F[16,x]*F[43,x]*F[79,x]
F[43,x] = -F[55,x]+F[44,x]
F[44,x] = -F[50,x]+F[45,x]
F[45,x] = 1/F[16,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[0,x]+F[48,x]
F[48,x] = 1/F[16,x]*F[49,x]
F[49,x] = F[2,x]
F[50,x] = -F[55,x]+F[51,x]
F[51,x] = 1/F[16,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[54,x]+F[47,x]
F[54,x] = (1+F[54,x])*x+F[54,x]^2
F[55,x] = F[56,x]
F[56,x] = F[16,x]*F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[48,x]*F[59,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[16,x]*F[5,x]*F[59,x]
F[62,x] = F[5,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[16,x]*F[59,x]*F[65,x]*F[76,x]
F[65,x] = F[5,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[16,x]*F[5,x]*F[65,x]*F[68,x]
F[68,x] = F[1,x]+F[69,x]
F[69,x] = F[16,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[1,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[16,x]*F[71,x]
F[74,x] = F[75,x]
F[75,x] = F[16,x]*F[68,x]*F[70,x]*F[71,x]
F[76,x] = F[71,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[16,x]*F[68,x]*F[71,x]*F[76,x]
F[79,x] = 1/F[16,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = -F[5,x]+F[82,x]
F[82,x] = -F[89,x]+F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[16,x]*F[85,x]
F[85,x] = F[47,x]
F[86,x] = -F[89,x]+F[87,x]
F[87,x] = 1/F[16,x]*F[88,x]
F[88,x] = F[53,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[2,x]*F[71,x]
F[91,x] = F[16,x]*F[74,x]
F[92,x] = F[93,x]
F[93,x] = F[16,x]*F[79,x]*F[94,x]
F[94,x] = F[21,x]+F[4,x]
F[95,x] = F[96,x]
F[96,x] = F[16,x]*F[79,x]*F[97,x]
F[97,x] = F[13,x]+F[43,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[2,x]*F[36,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[103,x]*F[16,x]
F[102,x] = F[54,x]+F[6,x]
F[103,x] = 1/F[16,x]*F[104,x]
F[104,x] = F[105,x]
F[105,x] = -F[98,x]+F[106,x]
F[106,x] = 1/F[16,x]*F[107,x]
F[107,x] = F[7,x]
F[108,x] = F[109,x]+F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[2,x]*F[5,x]
F[111,x] = F[112,x]
F[112,x] = F[102,x]*F[113,x]*F[16,x]
F[113,x] = 1/F[16,x]*F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[2,x]+F[53,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[108,x]*F[36,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[16,x]*F[79,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[0,x]*F[43,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[16,x]*F[4,x]
F[124,x] = 1/F[16,x]*F[125,x]
F[125,x] = F[13,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[111,x]+F[6,x]
F[128,x] = F[129,x]
F[129,x] = F[16,x]*F[21,x]*F[82,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_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{126}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{82}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{68}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{79}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{98}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \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_{95}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{92}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{43}\! \left(x \right) F_{79}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{54}\! \left(x \right) x +F_{54} \left(x \right)^{2}+x
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{58}\! \left(x \right) = F_{48}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{5}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right) F_{65}\! \left(x \right) F_{76}\! \left(x \right)
F_{65}\! \left(x \right) = F_{5}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{16}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{16}\! \left(x \right) F_{68}\! \left(x \right) F_{70}\! \left(x \right) F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{16}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right) F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{47}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{53}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{2}\! \left(x \right) F_{71}\! \left(x \right)
F_{91}\! \left(x \right) = F_{16}\! \left(x \right) F_{74}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{103}\! \left(x \right) F_{16}\! \left(x \right)
F_{102}\! \left(x \right) = F_{54}\! \left(x \right)+F_{6}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{7}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{102}\! \left(x \right) F_{113}\! \left(x \right) F_{16}\! \left(x \right)
F_{113}\! \left(x \right) = \frac{F_{114}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right) F_{36}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{13}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{111}\! \left(x \right)+F_{6}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{82}\! \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_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_126(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_82(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)/F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_23(x)*F_68(x))
Eq(F_23(x), F_24(x)/(F_16(x)*F_79(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_116(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_108(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_98(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_95(x))
Eq(F_34(x), F_35(x) + F_92(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_5(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_36(x)*F_5(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_16(x)*F_43(x)*F_79(x))
Eq(F_43(x), F_44(x) - F_55(x))
Eq(F_44(x), F_45(x) - F_50(x))
Eq(F_45(x), F_46(x)/F_16(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), -F_0(x) + F_48(x))
Eq(F_48(x), F_49(x)/F_16(x))
Eq(F_49(x), F_2(x))
Eq(F_50(x), F_51(x) - F_55(x))
Eq(F_51(x), F_52(x)/F_16(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_47(x) - F_54(x))
Eq(F_54(x), (x - 3)*(F_54(x) + 1) + (F_54(x) + 1)**2 + F_54(x) + 2)
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_16(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_48(x)*F_59(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_16(x)*F_5(x)*F_59(x))
Eq(F_62(x), F_5(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_16(x)*F_59(x)*F_65(x)*F_76(x))
Eq(F_65(x), F_5(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_16(x)*F_5(x)*F_65(x)*F_68(x))
Eq(F_68(x), F_1(x) + F_69(x))
Eq(F_69(x), F_16(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_1(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_16(x)*F_71(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_16(x)*F_68(x)*F_70(x)*F_71(x))
Eq(F_76(x), F_71(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_16(x)*F_68(x)*F_71(x)*F_76(x))
Eq(F_79(x), F_80(x)/F_16(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), -F_5(x) + F_82(x))
Eq(F_82(x), F_83(x) - F_89(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_16(x))
Eq(F_85(x), F_47(x))
Eq(F_86(x), F_87(x) - F_89(x))
Eq(F_87(x), F_88(x)/F_16(x))
Eq(F_88(x), F_53(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_2(x)*F_71(x))
Eq(F_91(x), F_16(x)*F_74(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_16(x)*F_79(x)*F_94(x))
Eq(F_94(x), F_21(x) + F_4(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_16(x)*F_79(x)*F_97(x))
Eq(F_97(x), F_13(x) + F_43(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_2(x)*F_36(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_103(x)*F_16(x))
Eq(F_102(x), F_54(x) + F_6(x))
Eq(F_103(x), F_104(x)/F_16(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_98(x))
Eq(F_106(x), F_107(x)/F_16(x))
Eq(F_107(x), F_7(x))
Eq(F_108(x), F_109(x) + F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_2(x)*F_5(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_102(x)*F_113(x)*F_16(x))
Eq(F_113(x), F_114(x)/F_16(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_2(x) + F_53(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_108(x)*F_36(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_16(x)*F_79(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_0(x)*F_43(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_16(x)*F_4(x))
Eq(F_124(x), F_125(x)/F_16(x))
Eq(F_125(x), F_13(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_111(x) + F_6(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_16(x)*F_21(x)*F_82(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 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"assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25129/
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[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[10,x]+F[126,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[83,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[7,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = 1/F[16,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[23,x]*F[69,x]
F[23,x] = 1/F[16,x]/F[80,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[116,x]+F[26,x]
F[26,x] = 1/F[16,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[109,x]+F[29,x]
F[29,x] = F[30,x]+F[99,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[96,x]
F[34,x] = F[35,x]+F[93,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[5,x]
F[37,x] = F[38,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[36,x]*F[5,x]
F[41,x] = F[42,x]
F[42,x] = F[16,x]*F[43,x]*F[80,x]
F[43,x] = -F[56,x]+F[44,x]
F[44,x] = -F[53,x]+F[45,x]
F[45,x] = 1/F[16,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = (1+F[48,x])*x+F[48,x]^2
F[49,x] = -F[2,x]+F[50,x]
F[50,x] = -F[5,x]+F[51,x]
F[51,x] = 1/F[16,x]*F[52,x]
F[52,x] = F[2,x]
F[53,x] = -F[56,x]+F[54,x]
F[54,x] = 1/F[16,x]*F[55,x]
F[55,x] = F[49,x]
F[56,x] = F[57,x]
F[57,x] = F[16,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[51,x]*F[60,x]
F[60,x] = F[5,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[16,x]*F[5,x]*F[60,x]
F[63,x] = F[5,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]*F[60,x]*F[66,x]*F[77,x]
F[66,x] = F[5,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[16,x]*F[5,x]*F[66,x]*F[69,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[16,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[1,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[16,x]*F[72,x]
F[75,x] = F[76,x]
F[76,x] = F[16,x]*F[69,x]*F[71,x]*F[72,x]
F[77,x] = F[72,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[16,x]*F[69,x]*F[72,x]*F[77,x]
F[80,x] = 1/F[16,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = -F[5,x]+F[83,x]
F[83,x] = -F[90,x]+F[84,x]
F[84,x] = -F[87,x]+F[85,x]
F[85,x] = 1/F[16,x]*F[86,x]
F[86,x] = F[47,x]
F[87,x] = -F[90,x]+F[88,x]
F[88,x] = 1/F[16,x]*F[89,x]
F[89,x] = F[49,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[2,x]*F[72,x]
F[92,x] = F[16,x]*F[75,x]
F[93,x] = F[94,x]
F[94,x] = F[16,x]*F[80,x]*F[95,x]
F[95,x] = F[13,x]+F[43,x]
F[96,x] = F[97,x]
F[97,x] = F[16,x]*F[80,x]*F[98,x]
F[98,x] = F[21,x]+F[4,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[2,x]*F[36,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[104,x]*F[16,x]
F[103,x] = F[48,x]+F[6,x]
F[104,x] = 1/F[16,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[99,x]+F[107,x]
F[107,x] = 1/F[16,x]*F[108,x]
F[108,x] = F[7,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[0,x]*F[5,x]
F[111,x] = F[112,x]+F[6,x]
F[112,x] = F[113,x]
F[113,x] = F[103,x]*F[114,x]*F[16,x]
F[114,x] = 1/F[16,x]*F[115,x]
F[115,x] = F[50,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[109,x]*F[36,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[16,x]*F[80,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[0,x]*F[43,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[16,x]*F[4,x]
F[124,x] = 1/F[16,x]*F[125,x]
F[125,x] = F[13,x]
F[126,x] = F[111,x]+F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[16,x]*F[21,x]*F[83,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_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{126}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{83}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{69}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{80}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{99}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \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_{96}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{93}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{43}\! \left(x \right) F_{80}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{48}\! \left(x \right) x +F_{48} \left(x \right)^{2}+x
F_{49}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{49}\! \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_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{51}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{5}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{5}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right) F_{66}\! \left(x \right) F_{77}\! \left(x \right)
F_{66}\! \left(x \right) = F_{5}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{66}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{16}\! \left(x \right) F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{71}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{72}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{47}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{49}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{2}\! \left(x \right) F_{72}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{75}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{104}\! \left(x \right) F_{16}\! \left(x \right)
F_{103}\! \left(x \right) = F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{7}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{6}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{16}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{115}\! \left(x \right) = F_{50}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{109}\! \left(x \right) F_{36}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{16}\! \left(x \right) F_{80}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{13}\! \left(x \right)
F_{126}\! \left(x \right) = F_{111}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{83}\! \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_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_126(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_83(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)/F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_23(x)*F_69(x))
Eq(F_23(x), F_24(x)/(F_16(x)*F_80(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_116(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_109(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_99(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_96(x))
Eq(F_34(x), F_35(x) + F_93(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_5(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_36(x)*F_5(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_16(x)*F_43(x)*F_80(x))
Eq(F_43(x), F_44(x) - F_56(x))
Eq(F_44(x), F_45(x) - F_53(x))
Eq(F_45(x), F_46(x)/F_16(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), (x - 3)*(F_48(x) + 1) + (F_48(x) + 1)**2 + F_48(x) + 2)
Eq(F_49(x), -F_2(x) + F_50(x))
Eq(F_50(x), -F_5(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_16(x))
Eq(F_52(x), F_2(x))
Eq(F_53(x), F_54(x) - F_56(x))
Eq(F_54(x), F_55(x)/F_16(x))
Eq(F_55(x), F_49(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_63(x))
Eq(F_59(x), F_51(x)*F_60(x))
Eq(F_60(x), F_5(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_16(x)*F_5(x)*F_60(x))
Eq(F_63(x), F_5(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x)*F_60(x)*F_66(x)*F_77(x))
Eq(F_66(x), F_5(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_16(x)*F_5(x)*F_66(x)*F_69(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_16(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_1(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_16(x)*F_72(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_16(x)*F_69(x)*F_71(x)*F_72(x))
Eq(F_77(x), F_72(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_16(x)*F_69(x)*F_72(x)*F_77(x))
Eq(F_80(x), F_81(x)/F_16(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), -F_5(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_90(x))
Eq(F_84(x), F_85(x) - F_87(x))
Eq(F_85(x), F_86(x)/F_16(x))
Eq(F_86(x), F_47(x))
Eq(F_87(x), F_88(x) - F_90(x))
Eq(F_88(x), F_89(x)/F_16(x))
Eq(F_89(x), F_49(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_2(x)*F_72(x))
Eq(F_92(x), F_16(x)*F_75(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_16(x)*F_80(x)*F_95(x))
Eq(F_95(x), F_13(x) + F_43(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_16(x)*F_80(x)*F_98(x))
Eq(F_98(x), F_21(x) + F_4(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_2(x)*F_36(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_104(x)*F_16(x))
Eq(F_103(x), F_48(x) + F_6(x))
Eq(F_104(x), F_105(x)/F_16(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_99(x))
Eq(F_107(x), F_108(x)/F_16(x))
Eq(F_108(x), F_7(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_0(x)*F_5(x))
Eq(F_111(x), F_112(x) + F_6(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_103(x)*F_114(x)*F_16(x))
Eq(F_114(x), F_115(x)/F_16(x))
Eq(F_115(x), F_50(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_109(x)*F_36(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_16(x)*F_80(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_0(x)*F_43(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_16(x)*F_4(x))
Eq(F_124(x), F_125(x)/F_16(x))
Eq(F_125(x), F_13(x))
Eq(F_126(x), F_111(x) + F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_16(x)*F_21(x)*F_83(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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"BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25416/
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[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[10,x]+F[126,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[83,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[7,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = 1/F[16,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[23,x]*F[69,x]
F[23,x] = 1/F[16,x]/F[80,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[116,x]+F[26,x]
F[26,x] = 1/F[16,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[109,x]+F[29,x]
F[29,x] = F[30,x]+F[99,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[96,x]
F[34,x] = F[35,x]+F[93,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[5,x]
F[37,x] = F[38,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[36,x]*F[5,x]
F[41,x] = F[42,x]
F[42,x] = F[16,x]*F[43,x]*F[80,x]
F[43,x] = -F[56,x]+F[44,x]
F[44,x] = -F[53,x]+F[45,x]
F[45,x] = 1/F[16,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = (1+F[48,x])*x+F[48,x]^2
F[49,x] = -F[2,x]+F[50,x]
F[50,x] = -F[5,x]+F[51,x]
F[51,x] = 1/F[16,x]*F[52,x]
F[52,x] = F[2,x]
F[53,x] = -F[56,x]+F[54,x]
F[54,x] = 1/F[16,x]*F[55,x]
F[55,x] = F[49,x]
F[56,x] = F[57,x]
F[57,x] = F[16,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[51,x]*F[60,x]
F[60,x] = F[5,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[16,x]*F[5,x]*F[60,x]
F[63,x] = F[5,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]*F[60,x]*F[66,x]*F[77,x]
F[66,x] = F[5,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[16,x]*F[5,x]*F[66,x]*F[69,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[16,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[1,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[16,x]*F[72,x]
F[75,x] = F[76,x]
F[76,x] = F[16,x]*F[69,x]*F[71,x]*F[72,x]
F[77,x] = F[72,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[16,x]*F[69,x]*F[72,x]*F[77,x]
F[80,x] = 1/F[16,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = -F[5,x]+F[83,x]
F[83,x] = -F[90,x]+F[84,x]
F[84,x] = -F[87,x]+F[85,x]
F[85,x] = 1/F[16,x]*F[86,x]
F[86,x] = F[47,x]
F[87,x] = -F[90,x]+F[88,x]
F[88,x] = 1/F[16,x]*F[89,x]
F[89,x] = F[49,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[2,x]*F[72,x]
F[92,x] = F[16,x]*F[75,x]
F[93,x] = F[94,x]
F[94,x] = F[16,x]*F[80,x]*F[95,x]
F[95,x] = F[13,x]+F[43,x]
F[96,x] = F[97,x]
F[97,x] = F[16,x]*F[80,x]*F[98,x]
F[98,x] = F[21,x]+F[4,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[2,x]*F[36,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[104,x]*F[16,x]
F[103,x] = F[48,x]+F[6,x]
F[104,x] = 1/F[16,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[99,x]+F[107,x]
F[107,x] = 1/F[16,x]*F[108,x]
F[108,x] = F[7,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[0,x]*F[5,x]
F[111,x] = F[112,x]+F[6,x]
F[112,x] = F[113,x]
F[113,x] = F[103,x]*F[114,x]*F[16,x]
F[114,x] = 1/F[16,x]*F[115,x]
F[115,x] = F[50,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[109,x]*F[36,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[16,x]*F[80,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[0,x]*F[43,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[16,x]*F[4,x]
F[124,x] = 1/F[16,x]*F[125,x]
F[125,x] = F[13,x]
F[126,x] = F[111,x]+F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[16,x]*F[21,x]*F[83,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_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{126}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{83}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{69}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{80}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{99}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \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_{96}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{93}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{43}\! \left(x \right) F_{80}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{48}\! \left(x \right) x +F_{48} \left(x \right)^{2}+x
F_{49}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{49}\! \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_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{51}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{5}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{5}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right) F_{66}\! \left(x \right) F_{77}\! \left(x \right)
F_{66}\! \left(x \right) = F_{5}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{66}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{16}\! \left(x \right) F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{71}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{72}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{47}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{49}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{2}\! \left(x \right) F_{72}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{75}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{104}\! \left(x \right) F_{16}\! \left(x \right)
F_{103}\! \left(x \right) = F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{7}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{6}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{16}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{115}\! \left(x \right) = F_{50}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{109}\! \left(x \right) F_{36}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{16}\! \left(x \right) F_{80}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{13}\! \left(x \right)
F_{126}\! \left(x \right) = F_{111}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{83}\! \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_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_126(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_83(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)/F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_23(x)*F_69(x))
Eq(F_23(x), F_24(x)/(F_16(x)*F_80(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_116(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_109(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_99(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_96(x))
Eq(F_34(x), F_35(x) + F_93(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_5(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_36(x)*F_5(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_16(x)*F_43(x)*F_80(x))
Eq(F_43(x), F_44(x) - F_56(x))
Eq(F_44(x), F_45(x) - F_53(x))
Eq(F_45(x), F_46(x)/F_16(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), (x - 3)*(F_48(x) + 1) + (F_48(x) + 1)**2 + F_48(x) + 2)
Eq(F_49(x), -F_2(x) + F_50(x))
Eq(F_50(x), -F_5(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_16(x))
Eq(F_52(x), F_2(x))
Eq(F_53(x), F_54(x) - F_56(x))
Eq(F_54(x), F_55(x)/F_16(x))
Eq(F_55(x), F_49(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_63(x))
Eq(F_59(x), F_51(x)*F_60(x))
Eq(F_60(x), F_5(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_16(x)*F_5(x)*F_60(x))
Eq(F_63(x), F_5(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x)*F_60(x)*F_66(x)*F_77(x))
Eq(F_66(x), F_5(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_16(x)*F_5(x)*F_66(x)*F_69(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_16(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_1(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_16(x)*F_72(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_16(x)*F_69(x)*F_71(x)*F_72(x))
Eq(F_77(x), F_72(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_16(x)*F_69(x)*F_72(x)*F_77(x))
Eq(F_80(x), F_81(x)/F_16(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), -F_5(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_90(x))
Eq(F_84(x), F_85(x) - F_87(x))
Eq(F_85(x), F_86(x)/F_16(x))
Eq(F_86(x), F_47(x))
Eq(F_87(x), F_88(x) - F_90(x))
Eq(F_88(x), F_89(x)/F_16(x))
Eq(F_89(x), F_49(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_2(x)*F_72(x))
Eq(F_92(x), F_16(x)*F_75(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_16(x)*F_80(x)*F_95(x))
Eq(F_95(x), F_13(x) + F_43(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_16(x)*F_80(x)*F_98(x))
Eq(F_98(x), F_21(x) + F_4(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_2(x)*F_36(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_104(x)*F_16(x))
Eq(F_103(x), F_48(x) + F_6(x))
Eq(F_104(x), F_105(x)/F_16(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_99(x))
Eq(F_107(x), F_108(x)/F_16(x))
Eq(F_108(x), F_7(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_0(x)*F_5(x))
Eq(F_111(x), F_112(x) + F_6(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_103(x)*F_114(x)*F_16(x))
Eq(F_114(x), F_115(x)/F_16(x))
Eq(F_115(x), F_50(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_109(x)*F_36(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_16(x)*F_80(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_0(x)*F_43(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_16(x)*F_4(x))
Eq(F_124(x), F_125(x)/F_16(x))
Eq(F_125(x), F_13(x))
Eq(F_126(x), F_111(x) + F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_16(x)*F_21(x)*F_83(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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"BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": false}}]}

Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25557/
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[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[10,x]+F[106,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[48,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[7,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = 1/F[16,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[23,x]*F[70,x]
F[23,x] = 1/F[16,x]/F[45,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[96,x]+F[26,x]
F[26,x] = 1/F[16,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[89,x]+F[29,x]
F[29,x] = F[30,x]+F[79,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[76,x]
F[34,x] = F[35,x]+F[72,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]+F[5,x]
F[38,x] = F[39,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[37,x]*F[5,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[44,x]*F[48,x]
F[44,x] = F[45,x]
F[45,x] = 1/F[16,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[5,x]+F[48,x]
F[48,x] = -F[61,x]+F[49,x]
F[49,x] = -F[58,x]+F[50,x]
F[50,x] = 1/F[16,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = (1+F[53,x])*x+F[53,x]^2
F[54,x] = -F[2,x]+F[55,x]
F[55,x] = -F[5,x]+F[56,x]
F[56,x] = 1/F[16,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[16,x]*F[60,x]
F[60,x] = F[54,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[2,x]*F[63,x]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]*F[63,x]
F[66,x] = F[16,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[16,x]*F[63,x]*F[69,x]*F[70,x]
F[69,x] = F[63,x]+F[67,x]
F[70,x] = F[1,x]+F[71,x]
F[71,x] = F[16,x]*F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[16,x]*F[45,x]*F[74,x]
F[74,x] = F[13,x]+F[75,x]
F[75,x] = F[48,x]
F[76,x] = F[77,x]
F[77,x] = F[16,x]*F[45,x]*F[78,x]
F[78,x] = F[21,x]+F[4,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[2,x]*F[36,x]
F[81,x] = F[82,x]
F[82,x] = F[16,x]*F[83,x]*F[84,x]
F[83,x] = F[53,x]+F[6,x]
F[84,x] = 1/F[16,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = -F[79,x]+F[87,x]
F[87,x] = 1/F[16,x]*F[88,x]
F[88,x] = F[7,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[0,x]*F[5,x]
F[91,x] = F[6,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[16,x]*F[83,x]*F[94,x]
F[94,x] = 1/F[16,x]*F[95,x]
F[95,x] = F[55,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[36,x]*F[89,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[16,x]*F[45,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[0,x]*F[75,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[16,x]*F[4,x]
F[104,x] = 1/F[16,x]*F[105,x]
F[105,x] = F[13,x]
F[106,x] = F[107,x]+F[91,x]
F[107,x] = F[108,x]
F[108,x] = F[16,x]*F[21,x]*F[48,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_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{106}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{48}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{70}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{45}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{79}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \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_{76}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{72}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{5}\! \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_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right) F_{48}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{53}\! \left(x \right) x +F_{53} \left(x \right)^{2}+x
F_{54}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{16}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right) F_{69}\! \left(x \right) F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \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_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{13}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{48}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{53}\! \left(x \right)+F_{6}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{7}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{91}\! \left(x \right) = F_{6}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{55}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{36}\! \left(x \right) F_{89}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right) F_{75}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{13}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{91}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{48}\! \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_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_106(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_48(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)/F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_23(x)*F_70(x))
Eq(F_23(x), F_24(x)/(F_16(x)*F_45(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_96(x))
Eq(F_26(x), F_27(x)/F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) - F_89(x))
Eq(F_29(x), F_30(x) + F_79(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_76(x))
Eq(F_34(x), F_35(x) + F_72(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) + F_5(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_37(x)*F_5(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_44(x)*F_48(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)/F_16(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) - F_5(x))
Eq(F_48(x), F_49(x) - F_61(x))
Eq(F_49(x), F_50(x) - F_58(x))
Eq(F_50(x), F_51(x)/F_16(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), (x - 3)*(F_53(x) + 1) + (F_53(x) + 1)**2 + F_53(x) + 2)
Eq(F_54(x), -F_2(x) + F_55(x))
Eq(F_55(x), -F_5(x) + F_56(x))
Eq(F_56(x), F_57(x)/F_16(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), F_59(x) - F_61(x))
Eq(F_59(x), F_60(x)/F_16(x))
Eq(F_60(x), F_54(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_2(x)*F_63(x))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x)*F_63(x))
Eq(F_66(x), F_16(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_16(x)*F_63(x)*F_69(x)*F_70(x))
Eq(F_69(x), F_63(x) + F_67(x))
Eq(F_70(x), F_1(x) + F_71(x))
Eq(F_71(x), F_16(x)*F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_16(x)*F_45(x)*F_74(x))
Eq(F_74(x), F_13(x) + F_75(x))
Eq(F_75(x), F_48(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_16(x)*F_45(x)*F_78(x))
Eq(F_78(x), F_21(x) + F_4(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_2(x)*F_36(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_16(x)*F_83(x)*F_84(x))
Eq(F_83(x), F_53(x) + F_6(x))
Eq(F_84(x), F_85(x)/F_16(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), -F_79(x) + F_87(x))
Eq(F_87(x), F_88(x)/F_16(x))
Eq(F_88(x), F_7(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_0(x)*F_5(x))
Eq(F_91(x), F_6(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_16(x)*F_83(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_16(x))
Eq(F_95(x), F_55(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_36(x)*F_89(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_16(x)*F_45(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_0(x)*F_75(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_16(x)*F_4(x))
Eq(F_104(x), F_105(x)/F_16(x))
Eq(F_105(x), F_13(x))
Eq(F_106(x), F_107(x) + F_91(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_16(x)*F_21(x)*F_48(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], 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"strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3]], "symmetry": true}}]}

Specification 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25580/
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[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[16,x]*F[9,x]
F[9,x] = F[10,x]+F[106,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]*F[48,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[7,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = 1/F[16,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[23,x]*F[70,x]
F[23,x] = 1/F[16,x]/F[45,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[96,x]+F[26,x]
F[26,x] = 1/F[16,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[89,x]+F[29,x]
F[29,x] = F[30,x]+F[79,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[33,x]
F[33,x] = F[34,x]+F[76,x]
F[34,x] = F[35,x]+F[72,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]+F[5,x]
F[38,x] = F[39,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[37,x]*F[5,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[44,x]*F[48,x]
F[44,x] = F[45,x]
F[45,x] = 1/F[16,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[5,x]+F[48,x]
F[48,x] = -F[61,x]+F[49,x]
F[49,x] = -F[58,x]+F[50,x]
F[50,x] = 1/F[16,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = (1+F[53,x])*x+F[53,x]^2
F[54,x] = -F[2,x]+F[55,x]
F[55,x] = -F[5,x]+F[56,x]
F[56,x] = 1/F[16,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[16,x]*F[60,x]
F[60,x] = F[54,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[2,x]*F[63,x]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]*F[63,x]
F[66,x] = F[16,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[16,x]*F[63,x]*F[69,x]*F[70,x]
F[69,x] = F[63,x]+F[67,x]
F[70,x] = F[1,x]+F[71,x]
F[71,x] = F[16,x]*F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[16,x]*F[45,x]*F[74,x]
F[74,x] = F[13,x]+F[75,x]
F[75,x] = F[48,x]
F[76,x] = F[77,x]
F[77,x] = F[16,x]*F[45,x]*F[78,x]
F[78,x] = F[21,x]+F[4,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[2,x]*F[36,x]
F[81,x] = F[82,x]
F[82,x] = F[16,x]*F[83,x]*F[84,x]
F[83,x] = F[53,x]+F[6,x]
F[84,x] = 1/F[16,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = -F[79,x]+F[87,x]
F[87,x] = 1/F[16,x]*F[88,x]
F[88,x] = F[7,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[0,x]*F[5,x]
F[91,x] = F[6,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[16,x]*F[83,x]*F[94,x]
F[94,x] = 1/F[16,x]*F[95,x]
F[95,x] = F[55,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[36,x]*F[89,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[16,x]*F[45,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[0,x]*F[75,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[16,x]*F[4,x]
F[104,x] = 1/F[16,x]*F[105,x]
F[105,x] = F[13,x]
F[106,x] = F[107,x]+F[91,x]
F[107,x] = F[108,x]
F[108,x] = F[16,x]*F[21,x]*F[48,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_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{106}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{48}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{7}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{70}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{45}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{79}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \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_{76}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{72}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{5}\! \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_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right) F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right) F_{48}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{53}\! \left(x \right) x +F_{53} \left(x \right)^{2}+x
F_{54}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{16}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right) F_{69}\! \left(x \right) F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \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_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{13}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{48}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{53}\! \left(x \right)+F_{6}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{7}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{91}\! \left(x \right) = F_{6}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{55}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{36}\! \left(x \right) F_{89}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right) F_{75}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{13}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{91}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{48}\! \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_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_106(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_16(x)*F_48(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_7(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)/F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_23(x)*F_70(x))
Eq(F_23(x), F_24(x)/(F_16(x)*F_45(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_96(x))
Eq(F_26(x), F_27(x)/F_16(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) - F_89(x))
Eq(F_29(x), F_30(x) + F_79(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_76(x))
Eq(F_34(x), F_35(x) + F_72(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) + F_5(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_37(x)*F_5(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_44(x)*F_48(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)/F_16(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) - F_5(x))
Eq(F_48(x), F_49(x) - F_61(x))
Eq(F_49(x), F_50(x) - F_58(x))
Eq(F_50(x), F_51(x)/F_16(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), (x - 3)*(F_53(x) + 1) + (F_53(x) + 1)**2 + F_53(x) + 2)
Eq(F_54(x), -F_2(x) + F_55(x))
Eq(F_55(x), -F_5(x) + F_56(x))
Eq(F_56(x), F_57(x)/F_16(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), F_59(x) - F_61(x))
Eq(F_59(x), F_60(x)/F_16(x))
Eq(F_60(x), F_54(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_2(x)*F_63(x))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x)*F_63(x))
Eq(F_66(x), F_16(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_16(x)*F_63(x)*F_69(x)*F_70(x))
Eq(F_69(x), F_63(x) + F_67(x))
Eq(F_70(x), F_1(x) + F_71(x))
Eq(F_71(x), F_16(x)*F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_16(x)*F_45(x)*F_74(x))
Eq(F_74(x), F_13(x) + F_75(x))
Eq(F_75(x), F_48(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_16(x)*F_45(x)*F_78(x))
Eq(F_78(x), F_21(x) + F_4(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_2(x)*F_36(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_16(x)*F_83(x)*F_84(x))
Eq(F_83(x), F_53(x) + F_6(x))
Eq(F_84(x), F_85(x)/F_16(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), -F_79(x) + F_87(x))
Eq(F_87(x), F_88(x)/F_16(x))
Eq(F_88(x), F_7(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_0(x)*F_5(x))
Eq(F_91(x), F_6(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_16(x)*F_83(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_16(x))
Eq(F_95(x), F_55(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_36(x)*F_89(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_16(x)*F_45(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_0(x)*F_75(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_16(x)*F_4(x))
Eq(F_104(x), F_105(x)/F_16(x))
Eq(F_105(x), F_13(x))
Eq(F_106(x), F_107(x) + F_91(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_16(x)*F_21(x)*F_48(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], 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