01432
Counting sequence:
1, 1, 2, 6, 24, 119, 694, 4582, 33324, 261808, 2190688, 19318688, 178108704, 1705985883, 16891621166, 172188608886, 1801013405436, 19274897768196, 210573149141896, 2343553478425816, 26525044132374656, 304856947930144656, 3553266124166899872, 41952101272633801376, 501228159413699278144, 6054582181256780696704, 73884542290182291304704, 910193895170720544149248, 11312196463176760501700224, 141756115346271817822954691, 1790158821899427408246810846, 22771425534677098061041394646, 291642099099498112188821162588, 3759242107953814033130572455916, 48751015815371292172234643194072, 635852547884023642520478819395592, 8338465173053718017144237028810592, 109913406624791838115057396950319036, 1455919003228078755280002195858923672, 19374979687575816540275835344651133144, 258979765348686847155069655246696267824, 3476328590102910965665689483937046945024, 46851370171582242155071537504570960602624, 633858018177741285037750807248408708401664, 8607098530902491974636809987706092837133824, 117286558208547537293433340721019086325451984, 1603623050878143932722397047915184802200125984, 21996763034860960417259405204172331608463797152, 302664297898124499421697046885532938663308311104, 4176922244743425434851827565214898395775758294208, 57808845869218440075832443346616034420583063507328, 802283220888975310339856786488603816420320224819328, 11163800163529547323754623817431192659251590878268416, 155741808084115897360585014916160126291788254860611968, 2178047449783852638357791655647435547947020212454442752, 30532382238075245259338398193146151040285528444895520512, 428992304950286649659085382315383342788062404084978970112, 6040874727342104396726698678329641023346831718342618510336, 85247065841778966494266703539191483914473291434364353226752, 1205473572352660080103797064048389676169509302028706218563584, 17080691329178796639203288554670322171239249809057073614580224, 242490618234260394252092752186168149866343533745706302824878099, 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12415491425774912921818561551712152901860984373230486000363109734402277040758225591385499620730912929856, 184116925796590523778443139490136323786836501542973241873759790562903603761758069990775456442511819212096, 2732463436354077745057143354171418505402873070359457403918415905809591525436483678854886499535444035558016, 40582544781527006565651633083198385090545971207546357947430601121343380949971200970810483609084087015573376, 603173273162854339822566412441941235050530551864851734059039567852372982050992853961170036242075999045116416
Specification 1
Strategy pack name: row_placements_tracked_fusion_expand_verified_sliding
Tree: http://permpal.com/tree/23958/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[17,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[18,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[11,x,k[0],k[1]]*k[0]-F[11,x,1,k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[17,x,k[0]]
F[15,x,k[0],k[1]] = (F[16,x,k[0],1]*k[0]-F[16,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[16,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[17,x,k[1]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1],1]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1],k[1]*k[2]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[2],k[1]]
F[23,x,k[0],k[1],k[2]] = F[1,x]+F[24,x,k[0],k[1],k[2]]+F[27,x,k[0],k[1],k[2]]+F[31,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[7,x]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[2],k[1]]
F[26,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[22,x,k[0],k[1],k[2]]*k[0]-F[22,x,1,k[1],k[2]])
F[27,x,k[0],k[1],k[2]] = F[17,x,k[0]]*F[28,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[2],k[1]]
F[29,x,k[0],k[1],k[2]] = (F[30,x,k[0],1,k[2]]*k[0]-F[30,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[30,x,k[0],k[1],k[2]] = F[22,x,k[0],k[0]*k[1],k[2]]
F[31,x,k[0],k[1],k[2]] = F[17,x,k[1]]*F[23,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[17,x,k[2]]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = (-F[34,x,k[0],1,k[2]]*k[2]+F[34,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[34,x,k[0],k[1],k[2]] = F[21,x,k[0],k[2],k[1]]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = \frac{F_{4}\! \left(x , y_{0}\right) y_{0}-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}, y_{1}\right) y_{0}-F_{11}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{17}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{16}\! \left(x , y_{0}, 1\right) y_{0}-F_{16}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{17}\! \left(x , y_{0}\right) = y_{0} x
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, y_{1}, 1\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}-F_{22}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{30}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{30}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-F_{34}\! \left(x , y_{0}, 1, y_{2}\right) y_{2}+F_{34}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{1}}{-y_{2}+y_{1}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{2}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_17(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_18(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (k_0*F_11(x, k_0, k_1) - F_11(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_17(x, k_0))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0, 1) + k_1*F_16(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_17(x, k_1)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1, 1))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_1, k_1*k_2))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_2, k_1))
Eq(F_23(x, k_0, k_1, k_2), F_1(x) + F_24(x, k_0, k_1, k_2) + F_27(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_7(x))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_2, k_1))
Eq(F_26(x, k_0, k_1, k_2), (k_0*F_22(x, k_0, k_1, k_2) - F_22(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_27(x, k_0, k_1, k_2), F_17(x, k_0)*F_28(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_2, k_1))
Eq(F_29(x, k_0, k_1, k_2), (-k_0*F_30(x, k_0, 1, k_2) + k_1*F_30(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1, k_2), F_22(x, k_0, k_0*k_1, k_2))
Eq(F_31(x, k_0, k_1, k_2), F_17(x, k_1)*F_23(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_17(x, k_2)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), (-k_1*F_34(x, k_0, k_1/k_2, k_2) + k_2*F_34(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_34(x, k_0, k_1, k_2), F_21(x, k_0, k_2, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}], "iterative": false, "name": "row_placements_tracked_fusion_expand_verified_sliding", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [4, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [3, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [3, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"av_12": 1, "av_123": 0, "class_module": "tilings.strategies.sliding", "strategy_class": "SlidingStrategy", "symmetry_type": 2}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_expand_verified_sliding
Tree: http://permpal.com/tree/23959/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[18,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[19,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[18,x,k[0]]
F[16,x,k[0],k[1]] = (F[17,x,k[0],1]*k[0]-F[17,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0],k[1]] = F[18,x,k[1]]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1],1]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[1]*k[2]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[2],k[1]]
F[24,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1],k[2]]+F[28,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]*F[8,x]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[2],k[1]]
F[27,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[23,x,k[0],k[1],k[2]]*k[0]-F[23,x,1,k[1],k[2]])
F[28,x,k[0],k[1],k[2]] = F[18,x,k[0]]*F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = F[30,x,k[0],k[2],k[1]]
F[30,x,k[0],k[1],k[2]] = (F[31,x,k[0],1,k[2]]*k[0]-F[31,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[31,x,k[0],k[1],k[2]] = F[23,x,k[0],k[0]*k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[18,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[18,x,k[2]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (-F[35,x,k[0],1,k[2]]*k[2]+F[35,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[35,x,k[0],k[1],k[2]] = F[22,x,k[0],k[2],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{17}\! \left(x , y_{0}, 1\right)-y_{1} F_{17}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{18}\! \left(x , y_{0}\right) = y_{0} x
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{1}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}, 1\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{30}\! \left(x , y_{0}, y_{2}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{31}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{31}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{2}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} F_{35}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)}{-y_{2}+y_{1}}
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{2}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_18(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_19(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_18(x, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0, 1) + k_1*F_17(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0, k_1), F_18(x, k_1)*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1, 1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_1*k_2))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_2, k_1))
Eq(F_24(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1, k_2) + F_28(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2)*F_8(x))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_2, k_1))
Eq(F_27(x, k_0, k_1, k_2), (k_0*F_23(x, k_0, k_1, k_2) - F_23(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_28(x, k_0, k_1, k_2), F_18(x, k_0)*F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_30(x, k_0, k_2, k_1))
Eq(F_30(x, k_0, k_1, k_2), (-k_0*F_31(x, k_0, 1, k_2) + k_1*F_31(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1, k_2), F_23(x, k_0, k_0*k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_18(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_18(x, k_2)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_1*F_35(x, k_0, k_1/k_2, k_2) + k_2*F_35(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_35(x, k_0, k_1, k_2), F_22(x, k_0, k_2, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.sliding", "strategy_class": "SlidingFactory", "use_symmetries": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob_expand_verified_sliding", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": 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