01324_01342_10324_10342_13024_13042_13402

Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3124, 17332, 98089, 563143, 3268559, 19136030, 112829657, 669231966, 3989717077, 23891012898, 143624756445, 866453782125, 5243660838232, 31825370041268, 193667976727146, 1181404394914433, 7223018882426037, 44253849288123468, 271666563937556861, 1670788395312968149, 10293418335123806754, 63519656156081621623, 392580182736756361331, 2429881482866648412541, 15060728887777928501862, 93471954165544111398430, 580849448851680172820794, 3613826077301803845056521, 22509640728716379317405690, 140360644113105439711013958, 876146760440518844560226619, 5474489348385267926102283931, 34239492541380221388244053193, 214343708408405019599724683419, 1343004983977265595902214642152, 8421949238675344009114375991074, 52856841186615552796346205060496, 331993539593247670708293931376883, 2086819411037989859659893057279089, 13126669294010377790514071325892437, 82627938408056667830964654555851289, 520464155567374729852418096613149329, 3280466831264900143862206541712198946, 20689561710922495188040649737184247381, 130565405176070601907059160700793643972, 824436045318852232883186601118047310881, 5208697058781960404440031616786065065442, 32925786995979447382003716907485186764389, 208242901608665699659552143689985712419654, 1317721480414033374381820179357432085014325, 8342364492280570748400992659035223545094217, 52839642972439103304832855217190381334305929, 334833677217292530301319928040612515228867701, 2122709628912743104236603134764216441124725361, 13462886247081741329237327315301524531587095750, 85421281113620815118058950171720843822399375676, 542211517189716777127958084002864477553941597035, 3443030099114477825690379061343656158267274539828, 21871431862916914180362443155150755264685181520934, 138986632314053297249027098774627025740685350089144, 883534620597956469336517454341678335449730720014537, 5618551043269135387557537566502257380049257887622098, 35741352796447793526950842320656522571427798434882724, 227436094398578177270331315695499050586604302924459925, 1447723263534574829765777040222200143748410372078903163, 9218189900585266720645409248764144138722344228146198531, 58713233941133213455679152197042697168094883292130943455, 374070164418564314957484328251799879764649851644942594744, 2383929755802756270207128274676504767203512695956140589670, 15196860661611417301271870480629147174312368206132630006888, 96901656776347482693205163062110742715773394061358714540561, 618048256622297572232436717074555791046829158460706184806824, 3942979432103261225852519191712251703999840214661579698413711, 25161398016333964037874051057856547444398477177593753136570168, 160601812905608876195587340474022924564031491084093427715416404, 1025342421436614420306399168528616295221964590737598710624373818, 6547683752529672555283158251096329324003226758303410787549343444, 41821954086509053947914070668266294829816787604248708670744289871, 267187697429081824735826450713148423926441527554045899077162059952, 1707347174610180675225154028866915646205726991694681789847826308896, 10912349904262185476229259579337407410350971637506761759348526764823, 69759550623792296262046096736060500366658754040050627401451061253287, 446042224329372168105391378819330132684868915970392021445980108488807, 2852549612177273822641613534339011616852559223727685362880360541452271, 18246243570431194536375781192437853746953050552223420697230765601285290, 116733340266985193147043193901638080838632703686221893664059480631898555, 746957266343965387700590778244409393964566813933826721609510344295116336, 4780510447280838160094734852368107850899660096640684583579011392463047992, 30600518586023604800172809545954775201703415194303570811576295048221074456, 195910485974252832762055059550215392794618131569478310668197291855437205500, 1254467428086794783131466670578883513929284635771597181124990619038791482299, 8034010395725018888366326362151976765500282714501010513663913254374359221754, 51460643025693874563805084339081478582877508645763419429436162186807041376852, 329675306890752921568006109510319700070347766723918786836944268536907903213566

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24823/
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[39,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x*F[7,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[7,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[7,x,k[0]]+x^2*k[0]^2)*(1+F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[39,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[21,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]
F[16,x,k[0]] = 1+F[16,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[16,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[16,x,k[0]]+k[0]*x*F[16,x,k[0]]^4
F[17,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[19,x,k[0]] = F[18,x,k[0]]*F[20,x,k[0]]
F[19,x,k[0]] = F[6,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[0,x]*F[23,x,k[0]]*F[32,x,k[0]]
F[24,x,k[0]] = F[16,x,k[0]]+F[23,x,k[0]]
F[25,x,k[0]] = F[0,x]*F[24,x,k[0]]
F[26,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[27,x,k[0]] = F[20,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[6,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[20,x,k[0]]*F[29,x,k[0]]
F[30,x,k[0]] = F[8,x,k[0]]
F[31,x,k[0]] = F[2,x]*F[24,x,k[0]]
F[32,x,k[0]] = (F[33,x,k[0]]*k[0]-F[33,x,1])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[34,x,k[0]]^2*F[20,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[32,x,k[0]]*F[34,x,k[0]]*F[39,x]
F[39,x] = 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_{39}\! \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 , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = x^{2} F_{16}\! \left(x , y\right)^{2} y^{2}+y x F_{16}\! \left(x , y\right)^{4}-x F_{16}\! \left(x , y\right)^{3} y -2 x F_{16}\! \left(x , y\right)^{2} y +2 x F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , y\right)^{3}+3 F_{16}\! \left(x , y\right)^{2}-2 F_{16}\! \left(x , y\right)+1
F_{17}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{23}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{34}\! \left(x , y\right)^{2} F_{20}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{34}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = x
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_39(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_7(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_7(x, k_0) + 1) + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_39(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_21(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_17(x, k_0))
Eq(F_16(x, k_0), k_0*x*F_16(x, k_0)**4 + (-k_0*x - 1)*F_16(x, k_0)**3 + (2*k_0*x - 2)*F_16(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_16(x, k_0)**2 + 1)
Eq(F_17(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_20(x, k_0))
Eq(F_19(x, k_0), F_6(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_0(x)*F_23(x, k_0)*F_32(x, k_0))
Eq(F_24(x, k_0), F_16(x, k_0) + F_23(x, k_0))
Eq(F_25(x, k_0), F_0(x)*F_24(x, k_0))
Eq(F_26(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_27(x, k_0), F_20(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_6(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_20(x, k_0)*F_29(x, k_0))
Eq(F_30(x, k_0), F_8(x, k_0))
Eq(F_31(x, k_0), F_2(x)*F_24(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_20(x, k_0)*F_34(x, k_0)**2)
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_32(x, k_0)*F_34(x, k_0)*F_39(x))
Eq(F_39(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, 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"TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"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": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2]], "symmetry": true}}, {"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"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2]], "symmetry": true}}]}

Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25213/
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[39,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (1+F[7,x,k[0]])*(x*F[7,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[7,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[7,x,k[0]]+x^2*k[0]^2)
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[39,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[21,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]
F[16,x,k[0]] = 1+F[16,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[16,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[16,x,k[0]]+k[0]*x*F[16,x,k[0]]^4
F[17,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[19,x,k[0]] = F[18,x,k[0]]*F[20,x,k[0]]
F[19,x,k[0]] = F[6,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[0,x]*F[23,x,k[0]]*F[32,x,k[0]]
F[24,x,k[0]] = F[16,x,k[0]]+F[23,x,k[0]]
F[25,x,k[0]] = F[0,x]*F[24,x,k[0]]
F[26,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[27,x,k[0]] = F[20,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[6,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[20,x,k[0]]*F[29,x,k[0]]
F[30,x,k[0]] = F[8,x,k[0]]
F[31,x,k[0]] = F[2,x]*F[24,x,k[0]]
F[32,x,k[0]] = (F[33,x,k[0]]*k[0]-F[33,x,1])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[34,x,k[0]]^2*F[20,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[32,x,k[0]]*F[34,x,k[0]]*F[39,x]
F[39,x] = 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_{39}\! \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 , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = x^{2} F_{16}\! \left(x , y\right)^{2} y^{2}+y x F_{16}\! \left(x , y\right)^{4}-x F_{16}\! \left(x , y\right)^{3} y -2 x F_{16}\! \left(x , y\right)^{2} y +2 x F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , y\right)^{3}+3 F_{16}\! \left(x , y\right)^{2}-2 F_{16}\! \left(x , y\right)+1
F_{17}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{23}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{33}\! \left(x , y\right)+F_{33}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{34}\! \left(x , y\right)^{2} F_{20}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{34}\! \left(x , y\right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = x
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_39(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_7(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_7(x, k_0) + 1) + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_39(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_21(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_17(x, k_0))
Eq(F_16(x, k_0), k_0*x*F_16(x, k_0)**4 + (-k_0*x - 1)*F_16(x, k_0)**3 + (2*k_0*x - 2)*F_16(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_16(x, k_0)**2 + 1)
Eq(F_17(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_20(x, k_0))
Eq(F_19(x, k_0), F_6(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_0(x)*F_23(x, k_0)*F_32(x, k_0))
Eq(F_24(x, k_0), F_16(x, k_0) + F_23(x, k_0))
Eq(F_25(x, k_0), F_0(x)*F_24(x, k_0))
Eq(F_26(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_27(x, k_0), F_20(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_6(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_20(x, k_0)*F_29(x, k_0))
Eq(F_30(x, k_0), F_8(x, k_0))
Eq(F_31(x, k_0), F_2(x)*F_24(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_33(x, k_0) + F_33(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_20(x, k_0)*F_34(x, k_0)**2)
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_32(x, k_0)*F_34(x, k_0)*F_39(x))
Eq(F_39(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 0], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 2], [2, 0], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[1, 0], [2, 2], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[2, 0], [2, 2], [2, 0], [2, 0], [2, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [2, 2], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 2], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [2, 2], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[2, 0], [2, 2], [2, 2], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 0], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 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"strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 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, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": 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{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"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": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2]], "symmetry": true}}, {"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"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2]], "symmetry": true}}]}

Specification 3
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25948/
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[31,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]
F[7,x,k[0]] = F[14,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[18,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]*F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = 1+F[11,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[11,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[11,x,k[0]]+k[0]*x*F[11,x,k[0]]^4
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]*F[14,x,k[0]]*F[15,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[14,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[31,x]
F[20,x,k[0]] = F[21,x,k[0]]+F[25,x,k[0]]
F[21,x,k[0]] = F[11,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[14,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[0,x]*F[12,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = (F[28,x,k[0]]*k[0]-F[28,x,1])/(-1+k[0])
F[28,x,k[0]] = F[15,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]*F[31,x]
F[31,x] = 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_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = x^{2} F_{11}\! \left(x , y\right)^{2} y^{2}+y x F_{11}\! \left(x , y\right)^{4}-x F_{11}\! \left(x , y\right)^{3} y -2 x F_{11}\! \left(x , y\right)^{2} y +2 x F_{11}\! \left(x , y\right) y -F_{11}\! \left(x , y\right)^{3}+3 F_{11}\! \left(x , y\right)^{2}-2 F_{11}\! \left(x , y\right)+1
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{12}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = x
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_31(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0))
Eq(F_7(x, k_0), F_14(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_18(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x)*F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), k_0*x*F_11(x, k_0)**4 + (-k_0*x - 1)*F_11(x, k_0)**3 + (2*k_0*x - 2)*F_11(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_11(x, k_0)**2 + 1)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0)*F_11(x, k_0)*F_14(x, k_0)*F_15(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0)*F_15(x, k_0)**2)
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_31(x))
Eq(F_20(x, k_0), F_21(x, k_0) + F_25(x, k_0))
Eq(F_21(x, k_0), F_11(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_14(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_0(x)*F_12(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), (-k_0*F_28(x, k_0) + F_28(x, 1))/(1 - k_0))
Eq(F_28(x, k_0), F_15(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_15(x, k_0)*F_27(x, k_0)*F_31(x))
Eq(F_31(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"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], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [3, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [3, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [4, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [3, 0], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [3, 0], [4, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [4, 0], [4, 2]]}, {"patt": [2, 0, 1], "pos": [[3, 2], [3, 0], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[3, 2], [3, 0], [4, 2]]}, {"patt": [2, 0, 1], "pos": [[3, 2], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [4, 0], [4, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[4, 2], [4, 0], [4, 2], [4, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[4, 2], [4, 0], [4, 2], [4, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 2], [4, 2], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [4, 2], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [4, 0], [4, 2], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2, 4], 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