02413_02431_20413_20431_24013_24031
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3296, 18896, 111080, 665200, 4041016, 24831040, 154014376, 962753936, 6058145376, 38337902272, 243812752064, 1557255290240, 9984374403136, 64232960486400, 414493697727808, 2682072449481856, 17398178970212992, 113115222433569792, 736950033892085888, 4810397337814976256, 31454641165680927104, 206011652592141229056, 1351297047881213874816, 8875974035208003549440, 58377598552324027274752, 384418572026895346682880, 2534293470942927901236224, 16725281693530452697970688, 110490843776701646619763712, 730617697894921123977887744, 4835506961273971119938688000, 32030266255760082816595462144, 212337295554220257094154518528, 1408708778627531949956359004160, 9352522149602313316353878839296, 62134594231516559797083662508032, 413067579509215308250097352650752, 2747757545777556227256146441961472, 18289128625285978142420568227057664, 121801716189853081917517747233660928, 811612694318204566170775356480307200, 5410896429842445173859334388960296960, 36091518037085200051008828588341395456, 240850620666921140450162275475963510784, 1608010103970711443271576733371077165056, 10740397214491293675870897782718058201088, 71768706363421755628480210412056253300736, 479762342653543188315562791850460520906752, 3208388165382526118269940685894110582767616, 21464025388460385615079087341083104228278272, 143645855832738226699614296446529891985293312, 961672376480773156574896309421451597523648512, 6440328725962228530359934679443696229183488000, 43145031729070795782130176875178442924799819776, 289128348508765008553245912409175415171423305728, 1938131229181998784219433062892015051459525148672, 12995829930545786474006900845950842689533986078720, 87166401130565939111533698605384491150523205681152, 584809717311489487747432385005648395351081433694208, 3924611812143388542233344663523964340410701076496384, 26344621087314666910085553913631207729221963548459008, 176887421508683010414349593168074207148671728852402176, 1187978174372179598539807454463445485443464454650200064, 7980376851461058242208331293634299424626764888779784192, 53621481794415038522306344466631286075276140378784268288, 360372684714367497388827522162227573040486340599572594688, 2422478049818231275467278128374110993726622466064012804096, 16287715235802380490722066588790086622953331436132402987008, 109534346862683615912806235290336837697937567887911839334400, 736763194535189006235197583172056020164064522779477328003072, 4956677542699682290804668168518299554591343929632972558303232, 33353110872816555429689722612805616212564000971014631954841600, 224472342931657359219097221669120679338683197041599517785325568, 1511012651975277480768168845329737205173965391436849417369419776, 10173026236648714761230694756040661798969182765544704894564302848, 68502612969954850707413546437852071547948541563840689631500697600, 461357086621488184542713460133870373034530755381100237716579155968, 3107696379140840834847489653860015949988041143737237886973308305408, 20936766049557270956414586953520807256901845649296124596790992306176, 141074531341965917355384062074350454923279793111272477942486054993920, 950723112382500955168639220410943596494768299588715246011004770844672, 6408027751230871944108161973550790494301837743856724636379273093971968, 43197453005148172980272193807318516630283279650687204891292311062839296, 291241930447986352243087799819086364155196504732412033235028064832847872, 1963858940702945275600373798928562687826026983168262791642718807596728320, 13244207597880370346542663555260615086135044796988443028929483687839399936, 89330483253483033847392184839944833768519489042203750901625623711420776448, 602601429882207376543842454119618978865889216249838077004932825571729080320, 4065520905295863197205418481311317089699558731780770508760543288288448872448, 27431947402509365549987848224993970522118992139076486781253451558601506160640, 185118725045304785132906654456931983848883740305338740789930199266040228085760, 1249384855175585766052886889707468144055792656311826327490169157873179937472512, 8433216273486843724829076060107173730932724096723051626730527439200172361383936, 56929887325299704632116105251917767901203779239214539003676543789166435915268096
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24111/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[0,x]*F[11,x]*F[14,x]*F[7,x]
F[14,x] = 1/F[0,x]/F[11,x]/F[20,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[11,x]*F[17,x]*F[58,x]
F[17,x] = 1/F[11,x]/F[58,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[9,x]+F[20,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[21,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]^2*F[11,x]
F[27,x] = F[28,x]
F[28,x] = F[11,x]*F[29,x]
F[29,x] = 1/F[11,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]+F[57,x]
F[32,x] = -F[9,x]+F[33,x]
F[33,x] = F[34,x,1]
F[34,x,k[0]] = F[35,x,k[0]]+F[43,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[36,x,k[0]]*k[0]-F[36,x,1])
F[36,x,k[0]] = F[1,x]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[42,x,k[0]]
F[39,x,k[0]] = F[36,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[39,x,k[0]]^2*F[42,x,k[0]]
F[42,x,k[0]] = k[0]*x
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[11,x]*F[45,x,k[0]]
F[45,x,k[0]] = 1/(-1+k[0])*(F[46,x,k[0]]*k[0]-F[46,x,1])
F[46,x,k[0]] = F[34,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x]+F[53,x,k[0]]
F[48,x] = -F[9,x]+F[49,x]
F[49,x] = -F[31,x]+F[50,x]
F[50,x] = 1/F[11,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[22,x]+F[9,x]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[42,x,k[0]]*F[48,x]*F[55,x,k[0]]
F[56,x,k[0]] = F[42,x,k[0]]*F[55,x,k[0]]
F[56,x,k[0]] = F[37,x,k[0]]
F[57,x] = F[53,x,1]
F[58,x] = F[1,x]+F[59,x]+F[60,x]
F[59,x] = F[11,x]*F[58,x]
F[60,x] = F[11,x]*F[14,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{20}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{58}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right) F_{58}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{57}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x , 1\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{39}\! \left(x , y\right)^{2} F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = y x
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{48}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{48}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{57}\! \left(x \right) = F_{53}\! \left(x , 1\right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_0(x)*F_11(x)*F_14(x)*F_7(x))
Eq(F_14(x), F_15(x)/(F_0(x)*F_11(x)*F_20(x)))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_11(x)*F_17(x)*F_58(x))
Eq(F_17(x), F_18(x)/(F_11(x)*F_58(x)))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) - F_9(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_21(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_21(x)**2)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_11(x)*F_29(x))
Eq(F_29(x), F_30(x)/F_11(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x) + F_57(x))
Eq(F_32(x), F_33(x) - F_9(x))
Eq(F_33(x), F_34(x, 1))
Eq(F_34(x, k_0), F_35(x, k_0) + F_43(x, k_0))
Eq(F_35(x, k_0), (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_1(x) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_42(x, k_0))
Eq(F_39(x, k_0), F_36(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_39(x, k_0)**2*F_42(x, k_0))
Eq(F_42(x, k_0), k_0*x)
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_11(x)*F_45(x, k_0))
Eq(F_45(x, k_0), (k_0*F_46(x, k_0) - F_46(x, 1))/(k_0 - 1))
Eq(F_46(x, k_0), F_34(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x) + F_53(x, k_0))
Eq(F_48(x), F_49(x) - F_9(x))
Eq(F_49(x), -F_31(x) + F_50(x))
Eq(F_50(x), F_51(x)/F_11(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_22(x) + F_9(x))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_42(x, k_0)*F_48(x)*F_55(x, k_0))
Eq(F_56(x, k_0), F_42(x, k_0)*F_55(x, k_0))
Eq(F_56(x, k_0), F_37(x, k_0))
Eq(F_57(x), F_53(x, 1))
Eq(F_58(x), F_1(x) + F_59(x) + F_60(x))
Eq(F_59(x), F_11(x)*F_58(x))
Eq(F_60(x), F_11(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "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, 4, 1, 3], "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]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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0]]}, {"patt": [1, 3, 0, 2], "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, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 2], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "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": [[1, 1]]}]]}], "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": [1, 3, 0, 2], "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]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "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": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "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]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "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_placements_tracked_fusion
Tree: http://permpal.com/tree/24112/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[0,x]*F[11,x]*F[14,x]*F[7,x]
F[14,x] = 1/F[0,x]/F[11,x]/F[20,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[11,x]*F[17,x]*F[62,x]
F[17,x] = 1/F[11,x]/F[62,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[9,x]+F[20,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[21,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]^2*F[11,x]
F[27,x] = F[28,x]
F[28,x] = F[11,x]*F[29,x]
F[29,x] = 1/F[11,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]+F[61,x]
F[32,x] = -F[9,x]+F[33,x]
F[33,x] = F[34,x,1]
F[34,x,k[0]] = F[35,x,k[0]]+F[49,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[36,x,k[0]]*k[0]-F[36,x,1])
F[36,x,k[0]] = F[1,x]+F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[45,x,k[0]]
F[39,x,k[0]] = F[40,x,1,k[0]]
F[40,x,k[0],k[1]] = F[41,x,k[0]*k[1],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0]]+F[46,x,k[0],k[1]]
F[42,x,k[0]] = F[1,x]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]^2*F[45,x,k[0]]
F[45,x,k[0]] = k[0]*x
F[46,x,k[0],k[1]] = F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = F[42,x,k[0]]*F[45,x,k[1]]*F[48,x,k[0],k[1]]
F[48,x,k[0],k[1]] = (-F[40,x,1,k[1]]*k[1]+F[40,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[11,x]*F[51,x,k[0]]
F[51,x,k[0]] = 1/(-1+k[0])*(F[52,x,k[0]]*k[0]-F[52,x,1])
F[52,x,k[0]] = F[34,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x]+F[59,x,k[0]]
F[54,x] = -F[9,x]+F[55,x]
F[55,x] = -F[31,x]+F[56,x]
F[56,x] = 1/F[11,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = -F[22,x]+F[9,x]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[39,x,k[0]]*F[45,x,k[0]]*F[54,x]
F[61,x] = F[59,x,1]
F[62,x] = F[1,x]+F[63,x]+F[64,x]
F[63,x] = F[11,x]*F[62,x]
F[64,x] = F[11,x]*F[14,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{20}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{62}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right) F_{62}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{61}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x , 1\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , 1, y\right)
F_{40}\! \left(x , y , z\right) = F_{41}\! \left(x , y z , z\right)
F_{41}\! \left(x , y , z\right) = F_{42}\! \left(x , y\right)+F_{46}\! \left(x , y , z\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{42}\! \left(x , y\right)^{2} F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = y x
F_{46}\! \left(x , y , z\right) = F_{47}\! \left(x , y , z\right)
F_{47}\! \left(x , y , z\right) = F_{42}\! \left(x , y\right) F_{45}\! \left(x , z\right) F_{48}\! \left(x , y , z\right)
F_{48}\! \left(x , y , z\right) = -\frac{z F_{40}\! \left(x , 1, z\right)-y F_{40}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{54}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{45}\! \left(x , y\right) F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x , 1\right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{62}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_0(x)*F_11(x)*F_14(x)*F_7(x))
Eq(F_14(x), F_15(x)/(F_0(x)*F_11(x)*F_20(x)))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_11(x)*F_17(x)*F_62(x))
Eq(F_17(x), F_18(x)/(F_11(x)*F_62(x)))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) - F_9(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_21(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_21(x)**2)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_11(x)*F_29(x))
Eq(F_29(x), F_30(x)/F_11(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x) + F_61(x))
Eq(F_32(x), F_33(x) - F_9(x))
Eq(F_33(x), F_34(x, 1))
Eq(F_34(x, k_0), F_35(x, k_0) + F_49(x, k_0))
Eq(F_35(x, k_0), (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_1(x) + F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_45(x, k_0))
Eq(F_39(x, k_0), F_40(x, 1, k_0))
Eq(F_40(x, k_0, k_1), F_41(x, k_0*k_1, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0) + F_46(x, k_0, k_1))
Eq(F_42(x, k_0), F_1(x) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0)**2*F_45(x, k_0))
Eq(F_45(x, k_0), k_0*x)
Eq(F_46(x, k_0, k_1), F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), F_42(x, k_0)*F_45(x, k_1)*F_48(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), (-k_0*F_40(x, k_0/k_1, k_1) + k_1*F_40(x, 1, k_1))/(-k_0 + k_1))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_11(x)*F_51(x, k_0))
Eq(F_51(x, k_0), (k_0*F_52(x, k_0) - F_52(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_34(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x) + F_59(x, k_0))
Eq(F_54(x), F_55(x) - F_9(x))
Eq(F_55(x), -F_31(x) + F_56(x))
Eq(F_56(x), F_57(x)/F_11(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), -F_22(x) + F_9(x))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_39(x, k_0)*F_45(x, k_0)*F_54(x))
Eq(F_61(x), F_59(x, 1))
Eq(F_62(x), F_1(x) + F_63(x) + F_64(x))
Eq(F_63(x), F_11(x)*F_62(x))
Eq(F_64(x), F_11(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "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, 4, 1, 3], "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]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 0, 2], "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [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, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [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"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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