02341_03241_04231_12340_13240_14230_21340
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3140, 17501, 99591, 575344, 3362532, 19835154, 117905606, 705420571, 4244074958, 25658374379, 155788750261, 949506585826, 5806878680779, 35622536908044, 219139063338236, 1351513061977690, 8354737809775790, 51757799199644352, 321275183041895871, 1997897439814942793, 12445348564266913116, 77647599374076776414, 485166157326275374468, 3035661551383821015768, 19018636678898380012556, 119298453407598925602560, 749184654862349418382670, 4709919121068895101286826, 29640313119106735679726851, 186712429569572588580827129, 1177234539709386072394379399, 7429027733166983200788954448, 46920387088227520923128720256, 296575027817305570119687774514, 1876009151384720075491770205077, 11875388066974487481318049986508, 75224493224519114068809095817965, 476822094078880906523507791559230, 3024314756798860412452910077016162, 19193747193682003310353684158467071, 121883261191925677096350528466255756, 774408073576638575554321446372152666, 4922976689683346041186938150961641541, 31311864339590544173617374550953961709, 199253041023555727470260046777545006497, 1268551158360313332821900940939983015132, 8079985008454586553125856138954785312807, 51487951211446585071694345609354187118171, 328236197618889640495888426116898663878074, 2093373909717380709912159924272790110463491, 13356128909569731792144541590607231120796772, 85247597401062574803086943874009819695363004, 544309626628955721249597936824344431109974572, 3476698566668491671758686917421293884857557425, 22214692058418724278891856666283479762218526554, 141991092984321431054837540587901896106484852969, 907872747058954192587853955456592015289771207862, 5806676862663196709571434132744592536031401308587, 37150533912616996428401577256754660653691735330303, 237756983674138084551950778698710800707249985930326, 1522048864325690195367580601165044425526696730309149, 9746471708214380492787478547411171375626166288949948, 62428996466678684690213392256419629490605069433243714, 399983519380671467190274334422419758924183668414545596, 2563371262646001698502796022942450428043426916948208431, 16432043513783960463949427573559914699200717163444823919, 105360881016687321201090297527817036712248469686106063732, 675728408128715291098409589826915673547695826891226710134, 4334781890349113035630687673468628904876521989237200673626, 27813909482724508375719438188970878555252688162604495281128, 178506509921802606512864441636741058567019616051496771348716, 1145884724955513515441531016096809673190837924110476750139695, 7357331967987297349419542345852976017206504138374360656425079, 47248726761674213030965620883841747399307508238080687428409711, 303492572895293771466520733224144359432353494492728053189368547, 1949809422793346229092900860860552770885024951679474988761520083, 12529115534199978986248994394328569728635111509297631351935627283, 80525030025739421904632287645407340369740095506381259730486349535, 517632761289222061969725819137171422219336940965349433487709887648, 3328060420720310355415925660744723201883781751540701465280043484821, 21401169409681997496897349152364551690663570982032721910215512092372, 137644539958466900992366315072982863948592639910518717930693251582659, 885429594567242822339806705894152447851901019133467979805715073178500, 5696670138172073107777802359872185234592516627305950898292086579256502, 36657140816434171163929951736809981471104551314550956361293102222392257, 235920190183860150983964838273089342754672301975945614087989082187704295, 1518585379410333759503715606810510695878189997573121995303390132827832499, 9776412596885792359097569238517036193027514651533168032228581044686444093, 62948399883895588656168956399951851211625678984833153188856130062914987587, 405371709483642051074996330093062321239786825386949182958932015379854877866, 2610865429131775442782061272072453362907924306512330047853375937204303673635, 16818088285924036372381679691018708428723516973311320866051166924875165473826, 108349939193793036403918041475609786687793661284846186884159566943567127761627, 698135092528300915238199853509932734175854561416951943426095298558436286885071
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24757/
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[27,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[27,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[14,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[10,x,k[0]]^2*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]+F[28,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[2,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = F[15,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[27,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[26,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[26,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[27,x] = x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[25,x,k[0]]*F[7,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[34,x,k[0]]*k[0]-F[34,x,1])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[27,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = F[27,x]*F[37,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[5,x]
F[42,x,k[0]] = F[2,x]*F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[44,x,k[0]] = F[43,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[27,x]*F[44,x,k[0]]
F[45,x,k[0]] = F[21,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[27,x]*F[48,x,k[0]]
F[48,x,k[0]] = 1/(-1+k[0])*(F[49,x,k[0]]*k[0]-F[49,x,1])
F[50,x,k[0]] = F[27,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[14,x,k[0]]
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_{27}\! \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_{27}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{10}\! \left(x , y\right)^{2} F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-F_{34}\! \left(x , y\right) y +F_{34}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{-y F_{49}\! \left(x , y\right)+F_{49}\! \left(x , 1\right)}{-1+y}
F_{50}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{14}\! \left(x , y\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_27(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_27(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_14(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_10(x, k_0)**2*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0) + F_28(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_2(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_13(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), F_15(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_10(x, k_0)*F_16(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_27(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_26(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_27(x), x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_27(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_25(x, k_0)*F_7(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_27(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), F_27(x)*F_37(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_5(x))
Eq(F_42(x, k_0), F_2(x)*F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_44(x, k_0), F_43(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_27(x)*F_44(x, k_0))
Eq(F_45(x, k_0), F_21(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_27(x)*F_48(x, k_0))
Eq(F_48(x, k_0), (k_0*F_49(x, k_0) - F_49(x, 1))/(k_0 - 1))
Eq(F_50(x, k_0), F_27(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_14(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, 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0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [4, 2], [4, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 3], [2, 2], [4, 2], [4, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 3], [2, 2], [4, 3], [4, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 3], [4, 2], [4, 2], [4, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 2], [2, 3], [4, 2], [4, 3], [4, 2]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[2, 2], [2, 2], [2, 2], [4, 2], [4, 2]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[2, 2], [2, 2], [2, 2], [4, 3], [4, 2]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[2, 2], [2, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[2, 2], [2, 2], [4, 2], [4, 3], [4, 2]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[4, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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": [1, 2, 0], "pos": [[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]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "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": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "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": "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25507/
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[27,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[27,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[14,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[10,x,k[0]]^2*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]+F[28,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[2,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = F[15,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[27,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[26,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[26,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[27,x] = x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[25,x,k[0]]*F[7,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[34,x,k[0]]*k[0]-F[34,x,1])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[27,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = F[27,x]*F[37,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[5,x]
F[42,x,k[0]] = F[2,x]*F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[44,x,k[0]] = F[43,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[27,x]*F[44,x,k[0]]
F[45,x,k[0]] = F[21,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[27,x]*F[48,x,k[0]]
F[48,x,k[0]] = 1/(-1+k[0])*(F[49,x,k[0]]*k[0]-F[49,x,1])
F[50,x,k[0]] = F[27,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[14,x,k[0]]
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_{27}\! \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_{27}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{10}\! \left(x , y\right)^{2} F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-F_{34}\! \left(x , y\right) y +F_{34}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{-y F_{49}\! \left(x , y\right)+F_{49}\! \left(x , 1\right)}{-1+y}
F_{50}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{14}\! \left(x , y\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_27(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_27(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_14(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_10(x, k_0)**2*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0) + F_28(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_2(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_13(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), F_15(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_10(x, k_0)*F_16(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_27(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_26(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_27(x), x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_27(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_25(x, k_0)*F_7(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_27(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), F_27(x)*F_37(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_5(x))
Eq(F_42(x, k_0), F_2(x)*F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_44(x, k_0), F_43(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_27(x)*F_44(x, k_0))
Eq(F_45(x, k_0), F_21(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_27(x)*F_48(x, k_0))
Eq(F_48(x, k_0), (k_0*F_49(x, k_0) - F_49(x, 1))/(k_0 - 1))
Eq(F_50(x, k_0), F_27(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_14(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [3, 2], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 2], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 2], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [3, 2], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [5, 3], [5, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 0], "pos": [[5, 3], [5, 3], [5, 2]]}, {"patt": [1, 2, 0], "pos": [[5, 3], [5, 3], [5, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 2], [3, 3], [3, 2], [3, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 2], [3, 3], [3, 2], [3, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[3, 2], [3, 2], [3, 2], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 3], [5, 2], [5, 2], [5, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 3], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 2], [3, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 2], [3, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 2], [3, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 2], [3, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 3], [3, 2], [5, 2], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 3], [3, 2], [5, 3], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 3], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 2], [3, 3], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[3, 2], [3, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[3, 2], [3, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[3, 2], [3, 2], [3, 2], [5, 3], [5, 2]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[3, 2], [3, 2], [5, 2], [5, 3], [5, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[2, 0], [2, 2], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[3, 2], [3, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[3, 2], [3, 3], [3, 2], [5, 2], [5, 2]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[3, 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