02314_02341_02431_20314_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3290, 18760, 109186, 644188, 3836682, 23005904, 138641666, 838667012, 5088048058, 30938965784, 188473665410, 1149827184108, 7023177409450, 42939995208096, 262751419522690, 1608884741671444, 9857228751613274, 60422226855409512, 370526588712015234, 2272987052284297852, 13947872702619125578, 85611952378126323056, 525606900269662706690, 3227565642140224088612, 19822824146453748981754, 121765155386379368188088, 748065349139475324948866, 4596297459106898975185932, 28243778233944105397603818, 173571463105000255776282176, 1066768497730146034142004610, 6556837190800598193670972212, 40303939860619903494055346074, 247757285820696874061003162376, 1523100315284903744707543684994, 9363783146108828881751510833820, 57569552217336731708422938602378, 353957530830678143862033837751312, 2176329294118732947203644460455682, 13381713593720577941888572917189956, 82283207057578532824872424275230778, 505966627878039962449179777632996952, 3111305577047775618871775601756529538, 19132540971486995680259848762614470188, 117655160678062170632217145767577703466, 723530586777910522451320746736514688736, 4449484624095383867623879981154444364930, 27363321292351771709892278744296426471508, 168280439531220747797866650043533356160474, 1034912640259322541787722824007193800872616, 6364708477755316722554493377109711960830338, 39143323901208246696198680866692048595052220, 240735907623994212661411958140924132189928394, 1480565734412334672519339160135956982510337712, 9105794729138601312338237376190438315985707522, 56002972581778633587574696846799160978272080996, 344434868999669228368669618056416083477654942842, 2118389029722296518335915657029959971726157953016, 13028868232394488710349692029831420993314426551682, 80132711410503161324651535968518832836203521254476, 492850250385960425256083647780092643201529893279338, 3031251438586852885451246297458017074459756959017856, 18643636764605930561750969330935711523328835946697602, 114667636249152240267686944778138558140796804035486068, 705265306789900115226135176663368265665936050645700634, 4337759826483302775966645419192647785526393270835062344, 26679623823031335333919629227761865642089489466592330626, 164094877790299191871449572101445211392596523179025639132, 1009279342633579783056382673183591676481672434526083913738, 6207671135006207874318291438343706303924718049757350745424, 38180965092651553087650994072477919506025535343191113096450, 234836673045601512243887785518807203370663029881768638021508, 1444394051482378560319268811959562326155456803883097265347770, 8883951138305951636473410842398514012480170136046663925695896, 54642086812129596232162816450382631122735179151329967399042946, 336084891914852319035421686169497061971581321511634367727568492, 2067146497778648669689235374326691504059124237015591812841403562, 12714346237002786874597853066757679061992039084022466047226111008, 78201896636645582414732175325764290597916157952028878862143666818, 480995460623666672091670596241299335386281460796607690711543580308, 2958455741238312266169630505179558917553657441058624607428432662106, 18196570858041941667547439383102411577808168007986535705905683824104, 111921720956956195102493848955708659811839391970457676867938001120642, 688397890332470963371446978506186577023910555319813922117304754821884, 4234137754601061763888702705441389343479269175171619428072498258124874, 26042982297952781999577161292738217165291844743316497304364479776489456, 160183104999811387783097182891714397638252200997664295527722931080095746, 985242054144588771222621329477036370340605805294330716557181428963004068, 6059954986738311992489401482787417283885450493144984484395727714350995706, 37273147127002977779981033231913448481625509066608912293939017312074741560, 229257167506708975760968126430921259908435686796594412401714848843515513218, 1410100156886017601063972091174417775057590948753281067200317347318078356620, 8673156173933949319835096288662095598349491366136449217972684196425673789162, 53346327617992854224450309678674408195361907881299029961412025859195727663296
Generating function in Maple syntax:
((-7*x^2+x)*(x^2-6*x+1)^(1/2)-3*x^3-4*x^2+13*x-2)/(20*x^3-26*x^2+16*x-2)
Generating function in latex syntax:
\frac{\left(-7 x^{2}+x \right) \sqrt{x^{2}-6 x +1}-3 x^{3}-4 x^{2}+13 x -2}{20 x^{3}-26 x^{2}+16 x -2}
Generating function in sympy syntax:
(-3*x**3 - 4*x**2 + 13*x + (-7*x**2 + x)*sqrt(x**2 - 6*x + 1) - 2)/(20*x**3 - 26*x**2 + 16*x - 2)
Implicit equation for the generating function in Maple syntax:
(10*x^3-13*x^2+8*x-1)*F(x)^2+(3*x^3+4*x^2-13*x+2)*F(x)-x^3+7*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(10 x^{3}-13 x^{2}+8 x -1\right) F \! \left(x \right)^{2}+\left(3 x^{3}+4 x^{2}-13 x +2\right) F \! \left(x \right)-x^{3}+7 x^{2}+5 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(n+6) = -70*n/(5+n)*a(n)+(82+21*n)/(5+n)*a(5+n)+(650+521*n)/(5+n)*a(n+1)-5*(253+149*n)/(5+n)*a(n+2)+2*(558+265*n)/(5+n)*a(n+3)-2*(233+80*n)/(5+n)*a(n+4), n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a{\left(n + 6 \right)} = - \frac{70 n a{\left(n \right)}}{n + 5} + \frac{\left(21 n + 82\right) a{\left(n + 5 \right)}}{n + 5} - \frac{2 \left(80 n + 233\right) a{\left(n + 4 \right)}}{n + 5} - \frac{5 \left(149 n + 253\right) a{\left(n + 2 \right)}}{n + 5} + \frac{2 \left(265 n + 558\right) a{\left(n + 3 \right)}}{n + 5} + \frac{\left(521 n + 650\right) a{\left(n + 1 \right)}}{n + 5}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24758/
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[23,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[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[30,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = 1/F[23,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[2,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]*F[24,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[22,x]+F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = (1+F[22,x])*x+F[22,x]^2
F[23,x] = x
F[24,x] = F[25,x,1]
F[25,x,k[0]] = F[26,x,k[0]]+F[5,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[25,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = k[0]*F[29,x]
F[29,x] = F[23,x]*F[24,x]
F[30,x] = F[31,x]+F[41,x]
F[31,x] = F[32,x]+F[36,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]*F[34,x]
F[34,x] = 1/F[23,x]*F[35,x]
F[35,x] = F[21,x]
F[36,x] = F[37,x]
F[37,x] = F[23,x]*F[34,x]*F[38,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = (F[40,x,k[0]]*k[0]-F[40,x,1])/(-1+k[0])
F[40,x,k[0]] = x*(1+F[40,x,k[0]])*k[0]+F[40,x,k[0]]^2
F[41,x] = F[42,x]
F[42,x] = F[23,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[23,x]*F[45,x]*F[59,x]
F[45,x] = 1/F[23,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[21,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[23,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[22,x]*F[34,x]
F[52,x] = F[53,x]
F[53,x] = F[23,x]*F[24,x]*F[54,x]*F[56,x]
F[54,x] = 1/F[23,x]/F[56,x]*F[55,x]
F[55,x] = F[47,x]
F[56,x] = F[1,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[23,x]*F[56,x]
F[59,x] = F[60,x,1]
F[60,x,k[0]] = (F[61,x,k[0]]*k[0]-F[61,x,1])/(-1+k[0])
F[61,x,k[0]] = F[24,k[0]*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_{23}\! \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_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{30}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{22}\! \left(x \right) x +F_{22} \left(x \right)^{2}+x
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = y F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{41}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{21}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = x F_{40}\! \left(x , y\right) y +y x +F_{40}\! \left(x , y\right)^{2}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{23}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right) F_{45}\! \left(x \right) F_{59}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{21}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{23}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{34}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{54}\! \left(x \right) F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{23}\! \left(x \right) F_{56}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{1}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{23}\! \left(x \right) F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{60}\! \left(x , y\right) = -\frac{-y F_{61}\! \left(x , y\right)+F_{61}\! \left(x , 1\right)}{-1+y}
F_{61}\! \left(x , y\right) = F_{24}\! \left(y 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_23(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_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_30(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x)/F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_2(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x)*F_24(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x) - F_22(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), (x - 3)*(F_22(x) + 1) + (F_22(x) + 1)**2 + F_22(x) + 2)
Eq(F_23(x), x)
Eq(F_24(x), F_25(x, 1))
Eq(F_25(x, k_0), F_26(x, k_0) + F_5(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_25(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), k_0*F_29(x))
Eq(F_29(x), F_23(x)*F_24(x))
Eq(F_30(x), F_31(x) + F_41(x))
Eq(F_31(x), F_32(x) + F_36(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x)*F_34(x))
Eq(F_34(x), F_35(x)/F_23(x))
Eq(F_35(x), F_21(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_23(x)*F_34(x)*F_38(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), (-k_0*F_40(x, k_0) + F_40(x, 1))/(1 - k_0))
Eq(F_40(x, k_0), (k_0*x - 3)*(F_40(x, k_0) + 1) + (F_40(x, k_0) + 1)**2 + F_40(x, k_0) + 2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_23(x)*F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_23(x)*F_45(x)*F_59(x))
Eq(F_45(x), F_46(x)/F_23(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_21(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_23(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_22(x)*F_34(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_23(x)*F_24(x)*F_54(x)*F_56(x))
Eq(F_54(x), F_55(x)/(F_23(x)*F_56(x)))
Eq(F_55(x), F_47(x))
Eq(F_56(x), F_1(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_23(x)*F_56(x))
Eq(F_59(x), F_60(x, 1))
Eq(F_60(x, k_0), (-k_0*F_61(x, k_0) + F_61(x, 1))/(1 - k_0))
Eq(F_61(x, k_0), F_24(k_0*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:
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[[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24882/
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[23,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[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[27,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = 1/F[23,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[2,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]*F[24,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[22,x]+F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = (1+F[22,x])*x+F[22,x]^2
F[23,x] = x
F[24,x] = F[25,x]+F[5,x]
F[25,x] = F[26,x]
F[26,x] = F[24,x]^2*F[23,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[21,x]*F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[23,x]*F[31,x]
F[31,x] = F[32,x]+F[60,x]
F[32,x] = F[33,x]*F[35,x]
F[33,x] = 1/F[23,x]*F[34,x]
F[34,x] = F[21,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = 1/F[23,x]/F[42,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[42,x]*F[49,x]
F[42,x] = F[43,x]+F[47,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[21,x]
F[46,x] = F[21,x]*F[24,x]
F[47,x] = F[48,x]
F[48,x] = F[23,x]*F[24,x]*F[42,x]
F[49,x] = F[35,x]+F[5,x]
F[50,x] = F[51,x]
F[51,x] = F[23,x]*F[52,x]
F[52,x] = F[53,x]+F[58,x]
F[53,x] = F[54,x]
F[54,x] = F[24,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[23,x]*F[39,x]
F[58,x] = F[59,x]
F[59,x] = F[24,x]*F[39,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[37,x]*F[42,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_{23}\! \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_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{27}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{22}\! \left(x \right) x +F_{22} \left(x \right)^{2}+x
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{60}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{23}\! \left(x \right) F_{42}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{21}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{23}\! \left(x \right) F_{39}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{24}\! \left(x \right) F_{39}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right) F_{42}\! \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_23(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_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_27(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x)/F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_2(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x)*F_24(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x) - F_22(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), (x - 3)*(F_22(x) + 1) + (F_22(x) + 1)**2 + F_22(x) + 2)
Eq(F_23(x), x)
Eq(F_24(x), F_25(x) + F_5(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_24(x)**2)
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_21(x)*F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_23(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_60(x))
Eq(F_32(x), F_33(x)*F_35(x))
Eq(F_33(x), F_34(x)/F_23(x))
Eq(F_34(x), F_21(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x)/(F_23(x)*F_42(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_42(x)*F_49(x))
Eq(F_42(x), F_43(x) + F_47(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_21(x))
Eq(F_46(x), F_21(x)*F_24(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_23(x)*F_24(x)*F_42(x))
Eq(F_49(x), F_35(x) + F_5(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_23(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_58(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_24(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_23(x)*F_39(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_24(x)*F_39(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_37(x)*F_42(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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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:
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[1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 4], [1, 0], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 4], [1, 1], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 4], [1, 4], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 4], [1, 4], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], "pos": [[4, 5]]}, {"patt": [0], "pos": [[4, 6]]}, {"patt": [0, 1], "pos": [[0, 4], [1, 6]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 6]]}, {"patt": [0, 1], "pos": [[3, 5], [3, 5]]}, {"patt": [1, 0], "pos": [[3, 5], [3, 5]]}, {"patt": [0, 1, 2], "pos": [[0, 6], [1, 6], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [0, 2, 1], "pos": [[0, 6], [1, 6], [1, 6]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 6], [1, 1], [1, 6]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 6], [1, 2], [1, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}], "requirements": [[{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24978/
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[23,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[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[27,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = 1/F[23,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[2,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]*F[24,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[22,x]+F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = (1+F[22,x])*x+F[22,x]^2
F[23,x] = x
F[24,x] = F[25,x]+F[5,x]
F[25,x] = F[26,x]
F[26,x] = F[24,x]^2*F[23,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[21,x]*F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[23,x]*F[31,x]
F[31,x] = F[32,x]+F[60,x]
F[32,x] = F[33,x]*F[35,x]
F[33,x] = 1/F[23,x]*F[34,x]
F[34,x] = F[21,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = 1/F[23,x]/F[42,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[42,x]*F[49,x]
F[42,x] = F[43,x]+F[47,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[21,x]
F[46,x] = F[21,x]*F[24,x]
F[47,x] = F[48,x]
F[48,x] = F[23,x]*F[24,x]*F[42,x]
F[49,x] = F[35,x]+F[5,x]
F[50,x] = F[51,x]
F[51,x] = F[23,x]*F[52,x]
F[52,x] = F[53,x]+F[58,x]
F[53,x] = F[54,x]
F[54,x] = F[24,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[23,x]*F[39,x]
F[58,x] = F[59,x]
F[59,x] = F[24,x]*F[39,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[37,x]*F[42,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_{23}\! \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_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{27}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = x F_{22}\! \left(x \right)+F_{22} \left(x \right)^{2}+x
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{60}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{23}\! \left(x \right) F_{42}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{21}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{23}\! \left(x \right) F_{39}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{24}\! \left(x \right) F_{39}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right) F_{42}\! \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_23(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_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_27(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x)/F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_2(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x)*F_24(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x) - F_22(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), (x - 3)*(F_22(x) + 1) + (F_22(x) + 1)**2 + F_22(x) + 2)
Eq(F_23(x), x)
Eq(F_24(x), F_25(x) + F_5(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_24(x)**2)
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_21(x)*F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_23(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_60(x))
Eq(F_32(x), F_33(x)*F_35(x))
Eq(F_33(x), F_34(x)/F_23(x))
Eq(F_34(x), F_21(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x)/(F_23(x)*F_42(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_42(x)*F_49(x))
Eq(F_42(x), F_43(x) + F_47(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_21(x))
Eq(F_46(x), F_21(x)*F_24(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_23(x)*F_24(x)*F_42(x))
Eq(F_49(x), F_35(x) + F_5(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_23(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_58(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_24(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_23(x)*F_39(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_24(x)*F_39(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_37(x)*F_42(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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, "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, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], 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[1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 4], [1, 0], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 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3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], "pos": [[4, 5]]}, {"patt": [0], "pos": [[4, 6]]}, {"patt": [0, 1], "pos": [[0, 4], [1, 6]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 6]]}, {"patt": [0, 1], "pos": [[3, 5], [3, 5]]}, {"patt": [1, 0], "pos": [[3, 5], [3, 5]]}, {"patt": [0, 1, 2], "pos": [[0, 6], [1, 6], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [0, 2, 1], "pos": [[0, 6], [1, 6], [1, 6]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 6], [1, 6], [1, 6]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 6], [1, 1], [1, 6]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 6], [1, 6], [1, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 6], [1, 2], [1, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 6], [1, 6], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [1, 6]]}], "requirements": [[{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25071/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[136,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[39,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[4,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[26,x]+F[19,x]
F[19,x] = 1/F[4,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[2,x]+F[22,x]
F[22,x] = -F[25,x]+F[23,x]
F[23,x] = 1/F[4,x]*F[24,x]
F[24,x] = F[2,x]
F[25,x] = 2+F[25,x]^2+(-2+x)*F[25,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = F[23,x]*F[28,x]
F[28,x] = (1+F[28,x])*x+F[28,x]^2
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[38,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[37,x]*F[4,x]
F[34,x] = F[25,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]^2*F[4,x]
F[37,x] = F[16,x]+F[32,x]
F[38,x] = F[28,x]*F[37,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[34,x]*F[43,x]
F[43,x] = 1/F[4,x]*F[44,x]
F[44,x] = F[10,x]
F[45,x] = F[133,x]*F[46,x]
F[46,x] = 1/F[120,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[129,x]+F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]+F[73,x]
F[52,x] = F[53,x]*F[65,x]
F[53,x] = F[28,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[4,x]+F[54,x]
F[59,x] = F[60,x]
F[60,x] = F[34,x]*F[4,x]*F[46,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[25,x]*F[4,x]
F[63,x] = F[64,x]
F[64,x] = F[34,x]*F[4,x]*F[56,x]
F[65,x] = 1/F[25,x]*F[66,x]
F[66,x] = -F[67,x]+F[8,x]
F[67,x] = -F[72,x]+F[68,x]
F[68,x] = 1/F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[71,x]+F[6,x]
F[71,x] = (x^2+4*x-1)*F[71,x]^2+(4*x^2-5*x+2)*F[71,x]+4*x^2-x
F[72,x] = F[28,x]*F[65,x]
F[73,x] = -F[128,x]+F[74,x]
F[74,x] = F[126,x]+F[75,x]
F[75,x] = F[28,x]*F[76,x]
F[76,x] = 1/F[25,x]*F[77,x]
F[77,x] = -F[108,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[25,x]*F[4,x]*F[80,x]
F[80,x] = 1/F[25,x]*F[81,x]
F[81,x] = -F[95,x]+F[82,x]
F[82,x] = 1/F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[87,x]+F[85,x]
F[85,x] = 1/F[4,x]*F[86,x]
F[86,x] = F[11,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = 1/F[4,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[23,x]+F[92,x]
F[92,x] = -F[93,x]+F[8,x]
F[93,x] = F[94,x]
F[94,x] = F[25,x]*F[4,x]*F[43,x]
F[95,x] = F[58,x]*F[96,x]
F[96,x] = 1/F[25,x]/F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[34,x]*F[4,x]
F[100,x] = F[101,x]+F[98,x]
F[101,x] = F[102,x]+F[106,x]
F[102,x] = F[103,x]+F[34,x]
F[103,x] = F[104,x]+F[22,x]
F[104,x] = F[105,x]
F[105,x] = F[103,x]*F[34,x]*F[4,x]
F[106,x] = F[107,x]
F[107,x] = F[37,x]*F[4,x]
F[108,x] = -F[116,x]+F[109,x]
F[109,x] = -F[74,x]+F[110,x]
F[110,x] = 1/F[4,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = -F[113,x]+F[11,x]
F[113,x] = -F[71,x]+F[114,x]
F[114,x] = -F[115,x]+F[65,x]
F[115,x] = -2+x^2+8*x+F[115,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[115,x]
F[116,x] = -F[118,x]+F[117,x]
F[117,x] = -F[78,x]+F[85,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[58,x]
F[120,x] = F[121,x]+F[65,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]^2*F[71,x]
F[123,x] = F[1,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[123,x]^2*F[4,x]
F[126,x] = F[127,x]
F[127,x] = F[120,x]*F[54,x]
F[128,x] = F[54,x]*F[65,x]
F[129,x] = F[130,x]*F[34,x]
F[130,x] = 1/F[4,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = F[113,x]+F[71,x]
F[133,x] = F[134,x]+F[8,x]
F[134,x] = F[135,x]
F[135,x] = F[133,x]*F[34,x]*F[4,x]
F[136,x] = F[137,x]
F[137,x] = F[4,x]*F[43,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{136}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{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_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{2}\! \left(x \right)
F_{25}\! \left(x \right) = F_{25}\! \left(x \right) x +F_{25} \left(x \right)^{2}-2 F_{25}\! \left(x \right)+2
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{28}\! \left(x \right) x +F_{28} \left(x \right)^{2}+x
F_{29}\! \left(x \right) = F_{30}\! \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_{38}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{25}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{38}\! \left(x \right) = F_{28}\! \left(x \right) F_{37}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{34}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)
F_{45}\! \left(x \right) = F_{133}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{120}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{73}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{53}\! \left(x \right) = F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right)+F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{66}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{71}\! \left(x \right)+F_{6}\! \left(x \right)
F_{71}\! \left(x \right) = x^{2} F_{71} \left(x \right)^{2}+4 x^{2} F_{71}\! \left(x \right)+4 x F_{71} \left(x \right)^{2}+4 x^{2}-5 x F_{71}\! \left(x \right)-F_{71} \left(x \right)^{2}-x +2 F_{71}\! \left(x \right)
F_{72}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{126}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{28}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{77}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{81}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{83}\! \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_{4}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{11}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{8}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{95}\! \left(x \right) = F_{58}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{34}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{22}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{113}\! \left(x \right)+F_{11}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{71}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{65}\! \left(x \right)
F_{115}\! \left(x \right) = x^{2} F_{115} \left(x \right)^{2}+2 x^{2} F_{115}\! \left(x \right)+4 x F_{115} \left(x \right)^{2}+x^{2}-13 x F_{115}\! \left(x \right)-F_{115} \left(x \right)^{2}+8 x +4 F_{115}\! \left(x \right)-2
F_{116}\! \left(x \right) = -F_{118}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{58}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{65}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123} \left(x \right)^{2} F_{71}\! \left(x \right)
F_{123}\! \left(x \right) = F_{1}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{123} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{120}\! \left(x \right) F_{54}\! \left(x \right)
F_{128}\! \left(x \right) = F_{54}\! \left(x \right) F_{65}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{34}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{113}\! \left(x \right)+F_{71}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{8}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_136(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(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_4(x))
Eq(F_13(x), F_14(x) + F_39(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_26(x))
Eq(F_19(x), F_20(x)/F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_2(x) + F_22(x))
Eq(F_22(x), F_23(x) - F_25(x))
Eq(F_23(x), F_24(x)/F_4(x))
Eq(F_24(x), F_2(x))
Eq(F_25(x), (x - 2)*F_25(x) + F_25(x)**2 + 2)
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_23(x)*F_28(x))
Eq(F_28(x), (x - 3)*(F_28(x) + 1) + (F_28(x) + 1)**2 + F_28(x) + 2)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_38(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_37(x)*F_4(x))
Eq(F_34(x), F_25(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)**2*F_4(x))
Eq(F_37(x), F_16(x) + F_32(x))
Eq(F_38(x), F_28(x)*F_37(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_34(x)*F_43(x))
Eq(F_43(x), F_44(x)/F_4(x))
Eq(F_44(x), F_10(x))
Eq(F_45(x), F_133(x)*F_46(x))
Eq(F_46(x), F_47(x)/F_120(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), -F_129(x) + F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) + F_73(x))
Eq(F_52(x), F_53(x)*F_65(x))
Eq(F_53(x), F_28(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_4(x) + F_54(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_34(x)*F_4(x)*F_46(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_25(x)*F_4(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_34(x)*F_4(x)*F_56(x))
Eq(F_65(x), F_66(x)/F_25(x))
Eq(F_66(x), -F_67(x) + F_8(x))
Eq(F_67(x), F_68(x) - F_72(x))
Eq(F_68(x), F_69(x)/F_4(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_6(x) - F_71(x))
Eq(F_71(x), x**2 + 8*x + (F_71(x) + 1)**2*(x**2 + 4*x - 1) + (F_71(x) + 1)*(2*x**2 - 13*x + 3) + F_71(x) - 2)
Eq(F_72(x), F_28(x)*F_65(x))
Eq(F_73(x), -F_128(x) + F_74(x))
Eq(F_74(x), F_126(x) + F_75(x))
Eq(F_75(x), F_28(x)*F_76(x))
Eq(F_76(x), F_77(x)/F_25(x))
Eq(F_77(x), -F_108(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_25(x)*F_4(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_25(x))
Eq(F_81(x), F_82(x) - F_95(x))
Eq(F_82(x), F_83(x)/F_4(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) - F_87(x))
Eq(F_85(x), F_86(x)/F_4(x))
Eq(F_86(x), F_11(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_4(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_23(x) + F_92(x))
Eq(F_92(x), F_8(x) - F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_25(x)*F_4(x)*F_43(x))
Eq(F_95(x), F_58(x)*F_96(x))
Eq(F_96(x), F_97(x)/(F_25(x)*F_4(x)))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_34(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_98(x))
Eq(F_101(x), F_102(x) + F_106(x))
Eq(F_102(x), F_103(x) + F_34(x))
Eq(F_103(x), F_104(x) + F_22(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_103(x)*F_34(x)*F_4(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_37(x)*F_4(x))
Eq(F_108(x), F_109(x) - F_116(x))
Eq(F_109(x), F_110(x) - F_74(x))
Eq(F_110(x), F_111(x)/F_4(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_11(x) - F_113(x))
Eq(F_113(x), F_114(x) - F_71(x))
Eq(F_114(x), -F_115(x) + F_65(x))
Eq(F_115(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_115(x)**2 + (2*x**2 - 13*x + 4)*F_115(x) - 2)
Eq(F_116(x), F_117(x) - F_118(x))
Eq(F_117(x), -F_78(x) + F_85(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_58(x))
Eq(F_120(x), F_121(x) + F_65(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)**2*F_71(x))
Eq(F_123(x), F_1(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_123(x)**2*F_4(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_120(x)*F_54(x))
Eq(F_128(x), F_54(x)*F_65(x))
Eq(F_129(x), F_130(x)*F_34(x))
Eq(F_130(x), F_131(x)/F_4(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_113(x) + F_71(x))
Eq(F_133(x), F_134(x) + F_8(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_133(x)*F_34(x)*F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_4(x)*F_43(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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "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": 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"RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0, 1], "pos": [[0, 5], [0, 5]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 4], [2, 4]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 5]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 3], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25162/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[136,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[39,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[4,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[26,x]+F[19,x]
F[19,x] = 1/F[4,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[2,x]+F[22,x]
F[22,x] = -F[25,x]+F[23,x]
F[23,x] = 1/F[4,x]*F[24,x]
F[24,x] = F[2,x]
F[25,x] = 2+F[25,x]^2+(-2+x)*F[25,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = F[23,x]*F[28,x]
F[28,x] = (1+F[28,x])*x+F[28,x]^2
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[38,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[37,x]*F[4,x]
F[34,x] = F[25,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]^2*F[4,x]
F[37,x] = F[16,x]+F[32,x]
F[38,x] = F[28,x]*F[37,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[34,x]*F[43,x]
F[43,x] = 1/F[4,x]*F[44,x]
F[44,x] = F[10,x]
F[45,x] = F[133,x]*F[46,x]
F[46,x] = 1/F[120,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[129,x]+F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]+F[73,x]
F[52,x] = F[53,x]*F[65,x]
F[53,x] = F[28,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[4,x]+F[54,x]
F[59,x] = F[60,x]
F[60,x] = F[34,x]*F[4,x]*F[46,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[25,x]*F[4,x]
F[63,x] = F[64,x]
F[64,x] = F[34,x]*F[4,x]*F[56,x]
F[65,x] = 1/F[25,x]*F[66,x]
F[66,x] = -F[67,x]+F[8,x]
F[67,x] = -F[72,x]+F[68,x]
F[68,x] = 1/F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[71,x]+F[6,x]
F[71,x] = (x^2+4*x-1)*F[71,x]^2+(4*x^2-5*x+2)*F[71,x]+4*x^2-x
F[72,x] = F[28,x]*F[65,x]
F[73,x] = -F[128,x]+F[74,x]
F[74,x] = F[126,x]+F[75,x]
F[75,x] = F[28,x]*F[76,x]
F[76,x] = 1/F[25,x]*F[77,x]
F[77,x] = -F[108,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[25,x]*F[4,x]*F[80,x]
F[80,x] = 1/F[25,x]*F[81,x]
F[81,x] = -F[95,x]+F[82,x]
F[82,x] = 1/F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[87,x]+F[85,x]
F[85,x] = 1/F[4,x]*F[86,x]
F[86,x] = F[11,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = 1/F[4,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[23,x]+F[92,x]
F[92,x] = -F[93,x]+F[8,x]
F[93,x] = F[94,x]
F[94,x] = F[25,x]*F[4,x]*F[43,x]
F[95,x] = F[58,x]*F[96,x]
F[96,x] = 1/F[25,x]/F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[34,x]*F[4,x]
F[100,x] = F[101,x]+F[98,x]
F[101,x] = F[102,x]+F[106,x]
F[102,x] = F[103,x]+F[34,x]
F[103,x] = F[104,x]+F[22,x]
F[104,x] = F[105,x]
F[105,x] = F[103,x]*F[34,x]*F[4,x]
F[106,x] = F[107,x]
F[107,x] = F[37,x]*F[4,x]
F[108,x] = -F[116,x]+F[109,x]
F[109,x] = -F[74,x]+F[110,x]
F[110,x] = 1/F[4,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = -F[113,x]+F[11,x]
F[113,x] = -F[71,x]+F[114,x]
F[114,x] = -F[115,x]+F[65,x]
F[115,x] = -2+x^2+8*x+F[115,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[115,x]
F[116,x] = -F[118,x]+F[117,x]
F[117,x] = -F[78,x]+F[85,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[58,x]
F[120,x] = F[121,x]+F[65,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]^2*F[71,x]
F[123,x] = F[1,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[123,x]^2*F[4,x]
F[126,x] = F[127,x]
F[127,x] = F[120,x]*F[54,x]
F[128,x] = F[54,x]*F[65,x]
F[129,x] = F[130,x]*F[34,x]
F[130,x] = 1/F[4,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = F[113,x]+F[71,x]
F[133,x] = F[134,x]+F[8,x]
F[134,x] = F[135,x]
F[135,x] = F[133,x]*F[34,x]*F[4,x]
F[136,x] = F[137,x]
F[137,x] = F[4,x]*F[43,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{136}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{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_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{2}\! \left(x \right)
F_{25}\! \left(x \right) = F_{25}\! \left(x \right) x +F_{25} \left(x \right)^{2}-2 F_{25}\! \left(x \right)+2
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{28}\! \left(x \right) x +F_{28} \left(x \right)^{2}+x
F_{29}\! \left(x \right) = F_{30}\! \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_{38}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{25}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{38}\! \left(x \right) = F_{28}\! \left(x \right) F_{37}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{34}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)
F_{45}\! \left(x \right) = F_{133}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{120}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{73}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{53}\! \left(x \right) = F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right)+F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{66}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{71}\! \left(x \right)+F_{6}\! \left(x \right)
F_{71}\! \left(x \right) = x^{2} F_{71} \left(x \right)^{2}+4 x^{2} F_{71}\! \left(x \right)+4 x F_{71} \left(x \right)^{2}+4 x^{2}-5 x F_{71}\! \left(x \right)-F_{71} \left(x \right)^{2}-x +2 F_{71}\! \left(x \right)
F_{72}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{126}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{28}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{77}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{81}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{83}\! \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_{4}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{11}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{8}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{95}\! \left(x \right) = F_{58}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{34}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{22}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{113}\! \left(x \right)+F_{11}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{71}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{65}\! \left(x \right)
F_{115}\! \left(x \right) = x^{2} F_{115} \left(x \right)^{2}+2 x^{2} F_{115}\! \left(x \right)+4 x F_{115} \left(x \right)^{2}+x^{2}-13 x F_{115}\! \left(x \right)-F_{115} \left(x \right)^{2}+8 x +4 F_{115}\! \left(x \right)-2
F_{116}\! \left(x \right) = -F_{118}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{58}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{65}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123} \left(x \right)^{2} F_{71}\! \left(x \right)
F_{123}\! \left(x \right) = F_{1}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{123} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{120}\! \left(x \right) F_{54}\! \left(x \right)
F_{128}\! \left(x \right) = F_{54}\! \left(x \right) F_{65}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{34}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{113}\! \left(x \right)+F_{71}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{8}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_136(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(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_4(x))
Eq(F_13(x), F_14(x) + F_39(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_26(x))
Eq(F_19(x), F_20(x)/F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_2(x) + F_22(x))
Eq(F_22(x), F_23(x) - F_25(x))
Eq(F_23(x), F_24(x)/F_4(x))
Eq(F_24(x), F_2(x))
Eq(F_25(x), (x - 2)*F_25(x) + F_25(x)**2 + 2)
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_23(x)*F_28(x))
Eq(F_28(x), (x - 3)*(F_28(x) + 1) + (F_28(x) + 1)**2 + F_28(x) + 2)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_38(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_37(x)*F_4(x))
Eq(F_34(x), F_25(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)**2*F_4(x))
Eq(F_37(x), F_16(x) + F_32(x))
Eq(F_38(x), F_28(x)*F_37(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_34(x)*F_43(x))
Eq(F_43(x), F_44(x)/F_4(x))
Eq(F_44(x), F_10(x))
Eq(F_45(x), F_133(x)*F_46(x))
Eq(F_46(x), F_47(x)/F_120(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), -F_129(x) + F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) + F_73(x))
Eq(F_52(x), F_53(x)*F_65(x))
Eq(F_53(x), F_28(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_4(x) + F_54(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_34(x)*F_4(x)*F_46(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_25(x)*F_4(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_34(x)*F_4(x)*F_56(x))
Eq(F_65(x), F_66(x)/F_25(x))
Eq(F_66(x), -F_67(x) + F_8(x))
Eq(F_67(x), F_68(x) - F_72(x))
Eq(F_68(x), F_69(x)/F_4(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_6(x) - F_71(x))
Eq(F_71(x), x**2 + 8*x + (F_71(x) + 1)**2*(x**2 + 4*x - 1) + (F_71(x) + 1)*(2*x**2 - 13*x + 3) + F_71(x) - 2)
Eq(F_72(x), F_28(x)*F_65(x))
Eq(F_73(x), -F_128(x) + F_74(x))
Eq(F_74(x), F_126(x) + F_75(x))
Eq(F_75(x), F_28(x)*F_76(x))
Eq(F_76(x), F_77(x)/F_25(x))
Eq(F_77(x), -F_108(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_25(x)*F_4(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_25(x))
Eq(F_81(x), F_82(x) - F_95(x))
Eq(F_82(x), F_83(x)/F_4(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) - F_87(x))
Eq(F_85(x), F_86(x)/F_4(x))
Eq(F_86(x), F_11(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_4(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_23(x) + F_92(x))
Eq(F_92(x), F_8(x) - F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_25(x)*F_4(x)*F_43(x))
Eq(F_95(x), F_58(x)*F_96(x))
Eq(F_96(x), F_97(x)/(F_25(x)*F_4(x)))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_34(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_98(x))
Eq(F_101(x), F_102(x) + F_106(x))
Eq(F_102(x), F_103(x) + F_34(x))
Eq(F_103(x), F_104(x) + F_22(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_103(x)*F_34(x)*F_4(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_37(x)*F_4(x))
Eq(F_108(x), F_109(x) - F_116(x))
Eq(F_109(x), F_110(x) - F_74(x))
Eq(F_110(x), F_111(x)/F_4(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_11(x) - F_113(x))
Eq(F_113(x), F_114(x) - F_71(x))
Eq(F_114(x), -F_115(x) + F_65(x))
Eq(F_115(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_115(x)**2 + (2*x**2 - 13*x + 4)*F_115(x) - 2)
Eq(F_116(x), F_117(x) - F_118(x))
Eq(F_117(x), -F_78(x) + F_85(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_58(x))
Eq(F_120(x), F_121(x) + F_65(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)**2*F_71(x))
Eq(F_123(x), F_1(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_123(x)**2*F_4(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_120(x)*F_54(x))
Eq(F_128(x), F_54(x)*F_65(x))
Eq(F_129(x), F_130(x)*F_34(x))
Eq(F_130(x), F_131(x)/F_4(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_113(x) + F_71(x))
Eq(F_133(x), F_134(x) + F_8(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_133(x)*F_34(x)*F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_4(x)*F_43(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, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 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1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "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": 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{"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, 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