02314_02341_03214_03241_30214_30241
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3294, 18852, 110488, 658864, 3981542, 24317396, 149821368, 929862640, 5807548756, 36469986280, 230121741128, 1458217284848, 9275398511782, 59200170401540, 379011431412624, 2433320939252992, 15662430144781372, 101050824665781208, 653372674648650920, 4233029186015271472, 27475619675758678716, 178645962247782010440, 1163423318434757003888, 7588144613868745067232, 49561623645187372405384, 324138185976483246558224, 2122538801316500669793168, 13915244566114481816809184, 91328734645571129677464582, 600038883631298127349930852, 3946233294247117804895929824, 25977385810212358535983975136, 171157940492615000940309476556, 1128674417262335543945960787384, 7448911192418066567141060662440, 49198639684587606078332586133296, 325187911528628082648019064522196, 2150911416314002070461809460840536, 14236533452741978024814029580563888, 94290337109580118757957191878577376, 624884451307760436637644297823429048, 4143725164875933993090066457465252592, 27493537098929080403546216225415746352, 182519426967462656864441900344754846112, 1212320077882355377727696864387479945820, 8056504386645863464671122807837929460456, 53565979466905152029725482386570819275616, 356317251770291735944757162835173340071552, 2371279791146069911358513509615918612298840, 15787742507075282195927981792330615397000048, 105157933078991021614995812203427108890454288, 700716974122151916090806108090955300381426912, 4671065423005435929070998198415705188684410040, 31149880918351860615118477500811913723153091344, 207806267599982823165692102013606650691946168416, 1386812150361442006611788909512861254321152128704, 9258242427571728453290665166538051247153404038416, 61828223128809682823284607114122905392200123620896, 413035983308131478090552726669130007339675738635808, 2760118406938241252313352903360741621370558681012160, 18450248482354649404116567778500306868862894870122950, 123369430594667592932138182630783328341276609502026020, 825163582409720027873506092805280499771979413950137088, 5520725680616666471538385980078308401975746046534518176, 36946433666747538456593092049964581469675357329460058988, 247323779402442456989397209933168822188966259304124767864, 1656048708043056313158143730575715382539618012115865527976, 11091524120978760070414365099903473195478163292130021625136, 74304884941655076312443582392303625870921226226533056360804, 497907602348429984102555186198979275341620244079056102891704, 3337203916247830767870652124793672668173388144222986609329712, 22372616075255974330095182608099357915988640740728291167479520, 150019727126800044171210002141756496575294559524413331788551896, 1006178830955952720828918651974257048312373363038993576431015984, 6749862065935643221584654546137685222700215324358644804715995376, 45290314158623592961766602588735326162630667540199287199345015328, 303951544752440219731027119352428954703039768674566420803337353076, 2040280651719816942393223776429499809409625771448464395793286445688, 13698090165451511016278057474917563215918826476653374197802945797856, 91984101316489232697847607069461389132452881894762049346792073128448, 617797731659778802948737816220869291927950746874764992468692388612744, 4150102779783351332693855793040238889402909769670057632633908403944528, 27883588850230374082966468394150095636977851480136696727300417291445168, 187376055039101280241106099983965167802972377247410923142930275788751264, 1259370444750279513378417794349193181493312225037930637371580696906408136, 8465747697752962335144582726463438899624224105289438314310939785083785456, 56917792356555336714263349005140164020420113909972290820769665502754820896, 382736785263859290022065361821625437191223732217950150367257333253926864448, 2574070103127538022796676266707109969420078119216106542091414392032860237168, 17314388720101402506798086362177944727393494587519442650576316374384034496736, 116482114331989147777373583430541285902059870406822341246180013201764957896672, 783745962963457788473598470403585396783537465076686518500367411644422940353600, 5274169930455229478849416702203459086583342267367022309665314715764369650782108, 35497226915184869263257364123859985383028194940503555298086496794727599982693160
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25219/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[17,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]*F[9,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[13,x,k[0]]^2*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[69,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[26,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[23,x,k[0]]
F[22,x,k[0]] = (F[10,x,k[0]]*k[0]-F[10,x,1])/(-1+k[0])
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[29,x]*F[4,x]
F[28,x,k[0]] = (F[13,x,k[0]]*k[0]-F[13,x,1])/(-1+k[0])
F[30,x,k[0]] = F[29,x]+F[67,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x]+F[66,x,k[0]]
F[33,x] = F[34,x]+F[48,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[35,x]+F[39,x]
F[39,x] = F[1,x]+F[36,x]
F[40,x] = F[41,x]+F[42,x]+F[44,x]
F[41,x] = 0
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[34,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[36,x]
F[47,x] = F[40,x]
F[48,x] = -F[53,x]+F[49,x]
F[49,x] = -F[54,x]+F[50,x]
F[50,x] = 1/F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[2,x]+F[53,x]
F[53,x] = -F[39,x]+F[5,x]
F[54,x] = F[55,x,1]
F[56,x,k[0]] = -k[0]*(F[55,x,1]-F[55,x,k[0]])/(-1+k[0])
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[58,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[5,x]+F[59,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[64,x,k[0]]
F[61,x,k[0]] = F[0,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]*F[60,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[55,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[66,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[25,x,k[0]]*F[4,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{13}\! \left(x , y\right)^{2} F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{48}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = 0
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{40}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{5}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{56}\! \left(x , y\right) = -\frac{y \left(F_{55}\! \left(x , 1\right)-F_{55}\! \left(x , y\right)\right)}{-1+y}
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_17(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_16(x, k_0)*F_9(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_13(x, k_0)**2*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_69(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_26(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_23(x, k_0))
Eq(F_22(x, k_0), (-k_0*F_10(x, k_0) + F_10(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_29(x)*F_4(x))
Eq(F_28(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_29(x) + F_67(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x) + F_66(x, k_0))
Eq(F_33(x), F_34(x) + F_48(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_35(x) + F_39(x))
Eq(F_39(x), F_1(x) + F_36(x))
Eq(F_40(x), F_41(x) + F_42(x) + F_44(x))
Eq(F_41(x), 0)
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_34(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_36(x))
Eq(F_47(x), F_40(x))
Eq(F_48(x), F_49(x) - F_53(x))
Eq(F_49(x), F_50(x) - F_54(x))
Eq(F_50(x), F_51(x)/F_4(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_2(x) + F_53(x))
Eq(F_53(x), -F_39(x) + F_5(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_56(x, k_0), -F_55(x, 1) + (-k_0*F_55(x, k_0) + F_55(x, 1))/(1 - k_0))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_58(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_5(x) + F_59(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_64(x, k_0))
Eq(F_61(x, k_0), F_0(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_13(x, k_0)*F_16(x, k_0)*F_60(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_55(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_66(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_25(x, k_0)*F_4(x))
Pack JSON:
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Specification JSON:
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[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 2]]}]}}}]}, {"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": "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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25729/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[17,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]*F[9,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[13,x,k[0]]^2*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[69,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[26,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]+F[23,x,k[0]]
F[22,x,k[0]] = (F[10,x,k[0]]*k[0]-F[10,x,1])/(-1+k[0])
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[29,x]*F[4,x]
F[28,x,k[0]] = (F[13,x,k[0]]*k[0]-F[13,x,1])/(-1+k[0])
F[30,x,k[0]] = F[29,x]+F[67,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x]+F[66,x,k[0]]
F[33,x] = F[34,x]+F[48,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[35,x]+F[39,x]
F[39,x] = F[1,x]+F[36,x]
F[40,x] = F[41,x]+F[42,x]+F[44,x]
F[41,x] = 0
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[34,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[36,x]
F[47,x] = F[40,x]
F[48,x] = -F[53,x]+F[49,x]
F[49,x] = -F[54,x]+F[50,x]
F[50,x] = 1/F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[2,x]+F[53,x]
F[53,x] = -F[39,x]+F[5,x]
F[54,x] = F[55,x,1]
F[56,x,k[0]] = -k[0]*(F[55,x,1]-F[55,x,k[0]])/(-1+k[0])
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[58,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[5,x]+F[59,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[64,x,k[0]]
F[61,x,k[0]] = F[0,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]*F[60,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[55,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[66,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[25,x,k[0]]*F[4,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{13}\! \left(x , y\right)^{2} F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{48}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = 0
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{40}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{5}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{56}\! \left(x , y\right) = -\frac{y \left(F_{55}\! \left(x , 1\right)-F_{55}\! \left(x , y\right)\right)}{-1+y}
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_17(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_16(x, k_0)*F_9(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_13(x, k_0)**2*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_69(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_26(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0) + F_23(x, k_0))
Eq(F_22(x, k_0), (-k_0*F_10(x, k_0) + F_10(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_29(x)*F_4(x))
Eq(F_28(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_29(x) + F_67(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x) + F_66(x, k_0))
Eq(F_33(x), F_34(x) + F_48(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_35(x) + F_39(x))
Eq(F_39(x), F_1(x) + F_36(x))
Eq(F_40(x), F_41(x) + F_42(x) + F_44(x))
Eq(F_41(x), 0)
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_34(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_36(x))
Eq(F_47(x), F_40(x))
Eq(F_48(x), F_49(x) - F_53(x))
Eq(F_49(x), F_50(x) - F_54(x))
Eq(F_50(x), F_51(x)/F_4(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_2(x) + F_53(x))
Eq(F_53(x), -F_39(x) + F_5(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_56(x, k_0), -F_55(x, 1) + (-k_0*F_55(x, k_0) + F_55(x, 1))/(1 - k_0))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_58(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_5(x) + F_59(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_64(x, k_0))
Eq(F_61(x, k_0), F_0(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_13(x, k_0)*F_16(x, k_0)*F_60(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_55(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_66(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_25(x, k_0)*F_4(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, 2, 3, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, "idx": 1}, {"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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": 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