02341_03241_12340_13240_23140
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3507, 20951, 129199, 815721, 5244547, 34208870, 225772609, 1504679134, 10111155468, 68427577436, 465939345086, 3189831287111, 21942057259756, 151577539318948, 1051120079594337, 7314254737830529, 51056505943481725, 357418334744473924, 2508672502312129405, 17650696246245659336, 124465897113433892968, 879505324113447733409, 6226768117831942171959, 44163771523932062399685, 313760051748605270847414, 2232599855222122385113468, 15909770340277520660702051, 113532056712076803056268826, 811222172693681016784023983, 5803579252347075530216320634, 41567847803269473055086930924, 298055903158105261744568176897, 2139398260755895385131457277919, 15371502138443407131076034054359, 110547895291944394649508649211384, 795745910482105857533900887758293, 5732839474294894949774884715662886, 41335148220054105676564673474068820, 298268672721460176206572765568685213, 2153869213751500571158097192884792829, 15564695875536807766441855640518292571, 112553376950046634378732240564558474586, 814443126154659176280032407462078373491, 5897063980313741723678269710584950813720, 42724102385715878403208209548255592755186, 309714757280004396066853010675993669309877, 2246431041108254903682411850334731844543035, 16302621993912725940743655917182287400909743, 118371304492461167653730634037108468710497540, 859907847603406920795954038594800494530271259, 6249801456781410789348825052591470248266451654, 45444579148312487343413237546840703208750325160, 330592203173266092026692102319245084257942522807, 2405975669112455269154505672008756625731665221119, 17517484082016370098093710382722304655330504780985, 127593392381808690858008737257526293371957899165092, 929725944964871614281984192015225768582388875097043, 6777143126331271948069100614660231434995618919837815, 49419481318869196291642503361486765081701287282597839, 360499476978598502759559844542037300034478774913100313, 2630639631269626530973210439843430583857738998646783883, 19202770095579666670970641967706384757866496989167433186, 140219348966252410657093278990738020824258740370975579069, 1024211082534204910492610946696739714808393282589368137358, 7483496326545884447132720285429513183288090949715731902612, 54695228546920804299960938997608679397338172334367181997875, 399871598394240971389677732397878485138151572257330176495855, 2924249749019074331708024034540330584222965120460687724726671, 21390840411217780642747493538856222388600629928279805226589324, 156515570053992638502420225936484427336550777691676903098833091, 1145514298660274741425830280014668382882373950809168820951574722, 8385979984584122945032220527112962560672159392493480049822096260, 61406543533877572388536718606685347415618401188095106115294606395, 449759450680987349031455584682827476172253460664626633779920375649, 3294944847199883831609148184412650684612460216380479835934756475459, 24144359849396425975582870851757309660407767415276727517672330935484, 176962202241799288178325300717133570635921333280870817299382929244211, 1297299566990515889516604175757151104148450214271423918800388335385070, 9512457314945107725562244781323996463995944693676364812026038486106664, 69764692810324538858685411000197336977902794099999302040149498153265651, 511760866226345429204337573919076138575829912778812260488530481254380927, 3754783116383675319769717735741757816211222957587387465782754335230204401, 27554154003589470199307943293239595758985447920679013422402731680594524136, 202242235916530109796742117077746414491845057289200566681775075925431666359, 1484695386709181989205356922592384046318327307849687086531131218279653253672, 10901388505237280226319030601168296731107663685400258450386962383708034104230, 80057776338350734221925622482466724690838443390713573678518467295769221609545, 588031811657943176326104846235992196751249301671995566838133703140867325479651, 4319884248456788353716127142109167680615190272201548908939685091555758697052115, 31740651527095443011934839701547344426548959381911706009201804296729395266279382, 233254751376035124445536520969442025403891339879521350375001806267328116648922561, 1714409792366360011393344574201690524767043851028862332028776343591691315251047878, 12602794161757560023495884086045307967426185058125188269375752359995174728953077092, 92658601745971898171467911381784135736436178919309029458289445397222416308166105201
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24429/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[52,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[44,x,k[0]]+F[45,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[14,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[13,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[10,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]*F[5,x]
F[22,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[22,x,k[0]]+F[30,x,k[0]]+F[38,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]*F[5,x]
F[26,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[28,x,k[0]]+F[29,x]
F[29,x] = 2+F[29,x]^2+(-2+x)*F[29,x]
F[30,x,k[0]] = F[31,x,k[0]]*F[5,x]
F[31,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[33,x,k[0]] = F[32,x,k[0]]*F[5,x]
F[24,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[24,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[15,x,k[0]]*F[29,x]*F[35,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[5,x]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[41,x]+F[42,x,k[0]]
F[41,x] = F[24,x,1]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[15,x,k[0]]*F[29,x]*F[40,x,k[0]]
F[44,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[45,x,k[0]] = F[15,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[47,x,k[0]]+F[48,x]
F[48,x] = F[1,x]+F[49,x]+F[51,x]
F[49,x] = F[5,x]*F[50,x]
F[50,x] = F[10,x,1]
F[51,x] = F[5,x]*F[6,x]
F[52,x] = F[5,x]*F[50,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{31}\! \left(x , y\right) = -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{39}\! \left(x , y\right) = -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{45}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{51}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_52(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_44(x, k_0) + F_45(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_14(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_12(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_10(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_15(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x)*F_5(x))
Eq(F_22(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_22(x, k_0) + F_30(x, k_0) + F_38(x, k_0))
Eq(F_23(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)*F_5(x))
Eq(F_26(x, k_0), F_15(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_28(x, k_0) + F_29(x))
Eq(F_29(x), (x - 2)*F_29(x) + F_29(x)**2 + 2)
Eq(F_30(x, k_0), F_31(x, k_0)*F_5(x))
Eq(F_31(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_32(x, k_0)*F_5(x))
Eq(F_24(x, k_0), F_1(x) + F_33(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_24(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_15(x, k_0)*F_29(x)*F_35(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_5(x))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x) + F_42(x, k_0))
Eq(F_41(x), F_24(x, 1))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_15(x, k_0)*F_29(x)*F_40(x, k_0))
Eq(F_44(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_45(x, k_0), F_15(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_47(x, k_0) + F_48(x))
Eq(F_48(x), F_1(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_5(x)*F_50(x))
Eq(F_50(x), F_10(x, 1))
Eq(F_51(x), F_5(x)*F_6(x))
Eq(F_52(x), F_5(x)*F_50(x))
Pack JSON:
{"name": "row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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_placement", "strategy_class": "RowAndColumnPlacementFactory", "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:
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[[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 0], [2, 1], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 3]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 2], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 1], [2, 2], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25680/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[52,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[44,x,k[0]]+F[45,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[14,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[13,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[10,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]*F[5,x]
F[22,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[22,x,k[0]]+F[30,x,k[0]]+F[38,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]*F[5,x]
F[26,x,k[0]] = F[15,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[28,x,k[0]]+F[29,x]
F[29,x] = 2+F[29,x]^2+(-2+x)*F[29,x]
F[30,x,k[0]] = F[31,x,k[0]]*F[5,x]
F[31,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[33,x,k[0]] = F[32,x,k[0]]*F[5,x]
F[24,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[24,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[15,x,k[0]]*F[29,x]*F[35,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[5,x]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[41,x]+F[42,x,k[0]]
F[41,x] = F[24,x,1]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[15,x,k[0]]*F[29,x]*F[40,x,k[0]]
F[44,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[45,x,k[0]] = F[15,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[47,x,k[0]]+F[48,x]
F[48,x] = F[1,x]+F[49,x]+F[51,x]
F[49,x] = F[5,x]*F[50,x]
F[50,x] = F[10,x,1]
F[51,x] = F[5,x]*F[6,x]
F[52,x] = F[5,x]*F[50,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{31}\! \left(x , y\right) = -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{39}\! \left(x , y\right) = -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{45}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{51}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{50}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_52(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_44(x, k_0) + F_45(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_14(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_12(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_10(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_15(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x)*F_5(x))
Eq(F_22(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_22(x, k_0) + F_30(x, k_0) + F_38(x, k_0))
Eq(F_23(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)*F_5(x))
Eq(F_26(x, k_0), F_15(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_28(x, k_0) + F_29(x))
Eq(F_29(x), (x - 2)*F_29(x) + F_29(x)**2 + 2)
Eq(F_30(x, k_0), F_31(x, k_0)*F_5(x))
Eq(F_31(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_32(x, k_0)*F_5(x))
Eq(F_24(x, k_0), F_1(x) + F_33(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_24(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_15(x, k_0)*F_29(x)*F_35(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_5(x))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x) + F_42(x, k_0))
Eq(F_41(x), F_24(x, 1))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_15(x, k_0)*F_29(x)*F_40(x, k_0))
Eq(F_44(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_45(x, k_0), F_15(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_47(x, k_0) + F_48(x))
Eq(F_48(x), F_1(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_5(x)*F_50(x))
Eq(F_50(x), F_10(x, 1))
Eq(F_51(x), F_5(x)*F_6(x))
Eq(F_52(x), F_5(x)*F_50(x))
Pack JSON:
{"name": "row_and_col_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_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 1], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": 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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 3], [0, 3], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 3], [0, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 0], [0, 3], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 3], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 0], [0, 3], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 1], [0, 3], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 1], [0, 3], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 1], [0, 3], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 1], [0, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], 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