01324_01342_03124_03142_03412_10324_10342
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3134, 17550, 100995, 593988, 3556136, 21606928, 132926679, 826501640, 5186275822, 32804628268, 208958657484, 1339306202448, 8631727381702, 55906514466088, 363712824266129, 2375748977204680, 15574962356287142, 102446532061371980, 675908436455821944, 4471878619585674620, 29662472462609555354, 197221502108467484932, 1314178468088926785543, 8774839661043116429048, 58701246260482569653394, 393390022750522418350742, 2640688411627644450560701, 17753474594906225712506040, 119531029779609459914336126, 805881922997218035767774972, 5440279642155966555092683322, 36770419024044846883148234552, 248813846484437447706723294148, 1685475704078454017576891535864, 11429253868288182637377879426196, 77577897396603547238514849199892, 527062194308186685302219412119678, 3584016311409039126048391884466772, 24391821522558837015788925813696213, 166137541690974985879444469125598184, 1132465297628234795898097147607572270, 7725043388786812107901087437395234204, 52732957565151779216493561818893603500, 360209908773880934216174969730424384408, 2462121314331784556635609398188217688216, 16839615993066194933762158038118990092928, 115242644251907611372715359316164738463220, 789119025556122329848259999282317689821280, 5406430580209638904005260724518903267989936, 37060275561194870180812364602049013003104584, 254172245597951616177481945067680715464583008, 1744058726209696853499867657447312370351587668, 11972918666475148914140265274353412969244232082, 82231413632794612587080222913644602112095785124, 565024774303324520954271561715228862733946515039, 3884031932136433687215111011787105254958636192784, 26710224392995040138735827195576278286934499163670, 183757849749397000485135696934046514649430921525676, 1264684914304364376907022123889198797974701792740732, 8707261092717020281166461171448169804150961919982200, 59970621624947276413875320516467272308666787438656250, 413188743578652088314813943418967076331627632991039264, 2847782198013311453107033830969348973720989409063051999, 19634011115485885631841069760776180247259963105110786216, 135410104397141072973112693355604097698417522945083932018, 934176373370783820009523196174346154851674228479853286628, 6446717048237077727041501604802742859144154934140907888212, 44501697930916032571313442177181641895256825035818144569584, 307283518804353277250610775957890601243100645365980577811116, 2122380671112266017706639670394405537607153320851539086683528, 14663085793753358706572237216200998913306483562304137691103034, 101331023417853658430496238538429866524285209333073042073682368, 700440813692092318178231828058249641096841183785271728716478476, 4842945017592305292786958178847481991521466514916406240649038836, 33492991621767841840071911753653339940852967567113982627408476638, 231687169213792783874081247107545070185945549950583704107880596656, 1603064872766909119340748687403759632520689280521859237089588206212, 11094272020077119194748297292077618775341621143843840005712532403208, 76796731458304663126639426587039472535682484491069268520482357038676, 531717039585875593445695515757741543571214784096188995082509749895040, 3682223267660707502885938276016297170790017875713860510464617019350208, 25505228373798727292039885609865643578435049262243268167083035790150816, 176699698517389339983626770589719004987159774999840973102828164776054748, 1224412907307004831370348027823678874407896929521088687056137962685513324, 8486010428465382258775930661051799847188593693230838570528422293687448974, 58824864004808304871109941325838200486329940290566169099939432320001383436, 407847880821516895627254992433027548492595363211496256372894442280685422973, 2828223025379989609497417773650006896652768013327779369545451572008258769416, 19615779765903361659400565206219302755599006959041782112598119175954614875950, 136073121596420455849963235284113203651759790529711165986399087552164906404380, 944087802342589371403973489924846878600071673691309401070674398570234133185724, 6551249844427562279352152261805938949554820810611526737459810615332821390091768, 45468035697914429942132112833238500184155566164701804118562434914685927054262792, 315614566369929925660761155866580971690240465099512114213316826013060592979209568
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24522/
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[36,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*(1+F[7,x,k[0]])*k[0]-2*F[7,x,k[0]])*(-1+x*(1+F[7,x,k[0]])*k[0])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[36,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]] = x^2*F[16,x,k[0]]^2*k[0]^2-2*x*F[16,x,k[0]]^2*k[0]+x*F[16,x,k[0]]*k[0]+2*F[16,x,k[0]]-1
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[31,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]+F[22,x,k[0]]
F[24,x,k[0]] = F[0,x]*F[23,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]+F[27,x,k[0]]
F[26,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[26,x,k[0]] = F[6,x,k[0]]
F[28,x,k[0]] = F[27,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[20,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[8,x,k[0]]
F[30,x,k[0]] = F[2,x]*F[23,x,k[0]]
F[31,x,k[0]] = (F[32,x,k[0]]*k[0]-F[32,x,1])/(-1+k[0])
F[32,x,k[0]] = F[33,x,k[0]]+F[34,x,k[0]]
F[33,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[31,x,k[0]]*F[36,x]
F[36,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_{36}\! \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}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 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_{36}\! \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}-2 y x F_{16}\! \left(x , y\right)^{2}+x F_{16}\! \left(x , y\right) y +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_{31}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-y F_{32}\! \left(x , y\right)+F_{32}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{36}\! \left(x \right)
F_{36}\! \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_36(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*(k_0*x - 2)*(F_7(x, k_0) + 1)**2 + (k_0*x + 1)*(F_7(x, k_0) + 1) + 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_36(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*(k_0*x - 2)*F_16(x, k_0)**2 + (k_0*x + 2)*F_16(x, k_0) - 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)*F_31(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0) + F_22(x, k_0))
Eq(F_24(x, k_0), F_0(x)*F_23(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0) + F_27(x, k_0))
Eq(F_26(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_26(x, k_0), F_6(x, k_0))
Eq(F_28(x, k_0), F_27(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_20(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_8(x, k_0))
Eq(F_30(x, k_0), F_2(x)*F_23(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_32(x, k_0) + F_32(x, 1))/(1 - k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_34(x, k_0))
Eq(F_33(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_31(x, k_0)*F_36(x))
Eq(F_36(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": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 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]]}], "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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"pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 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], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2]], "symmetry": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24595/
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[36,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*(1+F[7,x,k[0]])*k[0]-2*F[7,x,k[0]])*(-1+x*(1+F[7,x,k[0]])*k[0])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[36,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]] = x^2*F[16,x,k[0]]^2*k[0]^2-2*x*F[16,x,k[0]]^2*k[0]+x*F[16,x,k[0]]*k[0]+2*F[16,x,k[0]]-1
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[31,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]+F[22,x,k[0]]
F[24,x,k[0]] = F[0,x]*F[23,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]+F[27,x,k[0]]
F[26,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[26,x,k[0]] = F[6,x,k[0]]
F[28,x,k[0]] = F[27,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[20,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[8,x,k[0]]
F[30,x,k[0]] = F[2,x]*F[23,x,k[0]]
F[31,x,k[0]] = (F[32,x,k[0]]*k[0]-F[32,x,1])/(-1+k[0])
F[32,x,k[0]] = F[33,x,k[0]]+F[34,x,k[0]]
F[33,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[31,x,k[0]]*F[36,x]
F[36,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_{36}\! \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}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 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_{36}\! \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}-2 y x F_{16}\! \left(x , y\right)^{2}+x F_{16}\! \left(x , y\right) y +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_{31}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-y F_{32}\! \left(x , y\right)+F_{32}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{36}\! \left(x \right)
F_{36}\! \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_36(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*(k_0*x - 2)*(F_7(x, k_0) + 1)**2 + (k_0*x + 1)*(F_7(x, k_0) + 1) + 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_36(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*(k_0*x - 2)*F_16(x, k_0)**2 + (k_0*x + 2)*F_16(x, k_0) - 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)*F_31(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0) + F_22(x, k_0))
Eq(F_24(x, k_0), F_0(x)*F_23(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0) + F_27(x, k_0))
Eq(F_26(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_26(x, k_0), F_6(x, k_0))
Eq(F_28(x, k_0), F_27(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_20(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_8(x, k_0))
Eq(F_30(x, k_0), F_2(x)*F_23(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_32(x, k_0) + F_32(x, 1))/(1 - k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_34(x, k_0))
Eq(F_33(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_31(x, k_0)*F_36(x))
Eq(F_36(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": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 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]]}], "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, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [2, 2], [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": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [2, 0], [2, 0]]}, {"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": [2, 0, 1, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [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": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[1, 0], [2, 2], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[2, 0], [2, 2], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [2, 2], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 2], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [2, 2], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[2, 0], [2, 2], [2, 2], [2, 0], [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]]}], "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, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [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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