01324_02314_03214_04213_12304_13204_14203
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, 4626460910, 28623829932, 178166605469, 1114930402440, 7010385859241, 44268641757686, 280626420185957, 1785180266234336, 11392541408667527, 72916422219043686, 467941980829808259, 3010430527688012228, 19411255413676902257, 125427990832979822646, 812056475420723211783, 5267089205038358557792, 34221205347220552639329, 222696131439707551192690, 1451375382406498882058182, 9472342505150837980903252, 61902740691871232108044808, 405046171027094337860731016, 2653452918572449121584479218, 17402149338897585751600805720, 114249329148950156856234234746, 750827625471004622211463752436, 4939021884727022458842867544952, 32518886411316671674479523832840, 214291873751757716767485377868124, 1413297776087416103371614244161400, 9328318771999552335668313231280520, 61616876783670657420750133354448784, 407294397185839959305030086486523312, 2694116644458775819191900360249028160, 17832454952556194793063448702441218878, 118108456133224054896712281881294073504, 782735441038084181873376174571921204798, 5190423904758211714925623093159987529940, 34437748604324370602921443095806124348670, 228613348802761193819299056898251103103520, 1518429584878699452758715737965618159089146, 10090339156041997714448904165769656482808836, 67085265469182269096371940696225176709087018, 446222470771400760685028301475826338589370968, 2969420268403659855286401721764792630621190430, 19768841311537724731476668187817715104569054612, 131666042922449537951834621280520110053303471010, 877290424015865818346880465873212379701063241152, 5847689920102773395759414557652760546802232350510, 38993408419116618105542020519109120925093028526268, 260111052357004245660027670908389957512466820743597, 1735730220114040026340897099386922165391833947865432, 11586619493088057882327621252793168906633250938259721, 77370938845319382687142128852935924146408932629941190, 516822353108239057057029437902042842148514674662419773, 3453368290932589431853552021684476899062661662140650512, 23082282473781244452295005277856353187419679309190452031, 154328124984472507651335696388666980554258774573424627974, 1032139183592163087017533898200918421374692470046418839071, 6904859429601032747058582816164952948679433476446939199924, 46205266536320181426487310344988988269089878831043923591709, 309275121223940447159630036857060836913341464544421031517550, 2070676670974641920906501287320278905499315655042971674572323, 13867253178811249227450625186077796703068596490980137353842544, 92891635992394003458122289441506064871757100155365375339409781, 622397819827856475992653514365555537205877166359004019148819498, 4171211114683363427571940726311192393941688810523954035950009817, 27961238701882598679447834359486732630441844324338482564095564756, 187477145923724981612292903698648795608425282097227497205342107555, 1257290403354177037223612728961396659821227768162891862633256099738, 8433657178969410678131440011101868721692491889501994028286162049357, 56583157089508627243158990205965857000513916886620191564623491222248, 379705761920781999657270131090422845850991964973181396964885522557739, 2548554599043140363443231873509704126193769692611360247388224330790142, 17109033305191955618097654053809021898880593578369070022649093578663029, 114878795834488059089903096169421685021220278083636011885606402267845476, 771498902416377410624559072179342466876146574738360664788940250559675835, 5182150333600908292783706121488990170282871900048595239396338176644084322, 34814666560135972710263317246810153243233673189827274867799009911758078385, 233932383133868249797258682403495809787396329184028403812999095922175026288, 1572145407395045149670521466060147900287845853819939769693645445770608553567, 10567391028374042932499173915192456572349859271146334217119048908545002501422, 71041812502192814388078254150442949034695626021661148811669323709035335648075, 477672249204505045222596299584128022762033334726637681936105232438962474568012, 3212286643394146533079755798626935388948238393497282286492182058292664002271913, 21605558511504029545830813337448516283122899753151114737788606128423697402175422
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24380/
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,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = (4*x*k[0]-1)*F[8,x,k[0]]^2+F[8,x,k[0]]+k[0]^2*x^2
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,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[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,1,k[0]]
F[19,x,k[0],k[1]] = (F[20,x,k[0]*k[1]]*k[0]-F[20,x,k[1]])/(-1+k[0])
F[20,x,k[0]] = F[2,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[15,x,k[0]]*F[23,x,k[0]]*F[70,x,k[0]]
F[23,x,k[0]] = F[20,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[74,x,k[0]]
F[27,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[28,x,k[0]] = F[29,x]+F[31,x,k[0]]
F[29,x] = 1/F[4,x]*F[30,x]
F[30,x] = F[2,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]*F[70,x,k[0]]
F[33,x,k[0]] = F[28,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[24,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[4,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[54,x,k[0]]
F[39,x,k[0]] = F[26,x,k[0]]+F[38,x,k[0]]
F[39,x,k[0]] = F[40,x]+F[58,x,k[0]]
F[40,x] = -F[57,x]+F[41,x]
F[41,x] = -F[49,x]+F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[48,x]+F[45,x]
F[45,x] = 1/F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[0,x]+F[29,x]
F[48,x] = F[28,x,1]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x,1]
F[52,x,k[0]] = 1/(-1+k[0])*(F[53,x,k[0]]*k[0]-F[53,x,1])
F[53,x,k[0]] = F[39,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[56,x,k[0]] = 1/(-1+k[0])*(F[53,x,k[0]]*k[0]-F[53,x,1])
F[57,x] = F[58,x,1]
F[58,x,k[0]] = F[59,x,k[0]]+F[73,x,k[0]]
F[59,x,k[0]] = -k[0]*(F[60,x,1]-F[60,x,k[0]])/(-1+k[0])
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[15,x,k[0]]*F[62,x,k[0]]*F[70,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[62,x,k[0]]*k[0]-F[62,x,1])
F[64,x,k[0]] = F[63,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[64,x,k[0]]
F[65,x,k[0]] = F[34,x,k[0]]
F[67,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[35,x,k[0]]
F[69,x,k[0]] = F[38,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[70,x,k[0]]^2*F[15,x,k[0]]
F[74,x,k[0]] = F[44,x]+F[73,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[4,x]*F[56,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{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 , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y^{2} x^{2}+4 x F_{8}\! \left(x , y\right)^{2} y -F_{8}\! \left(x , y\right)^{2}+F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \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_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , 1, y\right)
F_{19}\! \left(x , y , z\right) = -\frac{-F_{20}\! \left(x , y z \right) y +F_{20}\! \left(x , z\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{40}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{48}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{52}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{62}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{-y F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{69}\! \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_{35}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{70}\! \left(x , y\right)^{2} F_{15}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_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, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0**2*x**2 + 4*k_0*x + (-8*k_0*x + 2)*(F_8(x, k_0) + 1) + (4*k_0*x - 1)*(F_8(x, k_0) + 1)**2 + F_8(x, k_0) - 1)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(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_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, 1, k_0))
Eq(F_19(x, k_0, k_1), (-k_0*k_1*F_20(x, k_0*k_1) + k_1*F_20(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_20(x, k_0), F_2(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_15(x, k_0)*F_23(x, k_0)*F_70(x, k_0))
Eq(F_23(x, k_0), F_20(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_74(x, k_0))
Eq(F_27(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_29(x) + F_31(x, k_0))
Eq(F_29(x), F_30(x)/F_4(x))
Eq(F_30(x), F_2(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_15(x, k_0)*F_33(x, k_0)*F_70(x, k_0))
Eq(F_33(x, k_0), F_28(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_24(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_4(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_54(x, k_0))
Eq(F_39(x, k_0), F_26(x, k_0) + F_38(x, k_0))
Eq(F_39(x, k_0), F_40(x) + F_58(x, k_0))
Eq(F_40(x), F_41(x) - F_57(x))
Eq(F_41(x), F_42(x) - F_49(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x) - F_48(x))
Eq(F_45(x), F_46(x)/F_4(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), -F_0(x) + F_29(x))
Eq(F_48(x), F_28(x, 1))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x, 1))
Eq(F_52(x, k_0), (-k_0*F_53(x, k_0) + F_53(x, 1))/(1 - k_0))
Eq(F_53(x, k_0), F_39(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_56(x, k_0), (k_0*F_53(x, k_0) - F_53(x, 1))/(k_0 - 1))
Eq(F_57(x), F_58(x, 1))
Eq(F_58(x, k_0), F_59(x, k_0) + F_73(x, k_0))
Eq(F_59(x, k_0), -F_60(x, 1) + (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_15(x, k_0)*F_62(x, k_0)*F_70(x, k_0))
Eq(F_63(x, k_0), (k_0*F_62(x, k_0) - F_62(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_63(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_64(x, k_0))
Eq(F_65(x, k_0), F_34(x, k_0))
Eq(F_67(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_35(x, k_0))
Eq(F_69(x, k_0), F_38(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_15(x, k_0)*F_70(x, k_0)**2)
Eq(F_74(x, k_0), F_44(x) + F_73(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_4(x)*F_56(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"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.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": 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[2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 1], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"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, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 1], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24740/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = (F[12,x,k[0]*k[1]]*k[0]-F[12,x,k[1]])/(-1+k[0])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[36,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[30,x,k[0]]+F[33,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[16,x,k[0]] = F[17,x,1,k[0]]
F[17,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[18,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[25,x,k[1],k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[3,x]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,1,k[0],k[1]]
F[23,x,k[0],k[1],k[2]] = (F[24,x,k[0]*k[1],k[2]]*k[0]-F[24,x,k[1],k[2]])/(-1+k[0])
F[24,x,k[0],k[1]] = (F[12,x,k[0]]*k[0]-F[12,x,k[1]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[24,x,k[1],k[0]]*F[27,x,k[0]]*F[9,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x,k[0]]^2*F[9,x,k[0]]
F[30,x,k[0]] = F[3,x]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,1,k[0]]
F[32,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]-F[24,x,1,k[1]])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]*F[9,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{12}\! \left(x , y_{1}\right)}{-1+y_{0}}
F_{12}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , 1, y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{1}, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , 1, y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{24}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{24}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}\right)-F_{12}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}, y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)^{2} F_{9}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{32}\! \left(x , 1, y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{12}\! \left(x , y_{0}\right)+F_{12}\! \left(x , 1\right)}{-1+y_{0}}
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), (-k_0*k_1*F_12(x, k_0*k_1) + k_1*F_12(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_36(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_30(x, k_0) + F_33(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_16(x, k_0), F_17(x, 1, k_0))
Eq(F_17(x, k_0, k_1), (-k_0*F_18(x, k_0, k_1) + F_18(x, 1, k_1))/(1 - k_0))
Eq(F_18(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_25(x, k_1, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_3(x))
Eq(F_20(x, k_0, k_1), (k_0*F_18(x, k_0, k_1) - F_18(x, 1, k_1))/(k_0 - 1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, 1, k_0, k_1))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*k_1*F_24(x, k_0*k_1, k_2) + k_1*F_24(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_12(x, k_0) + k_1*F_12(x, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_24(x, k_1, k_0)*F_27(x, k_0)*F_9(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_27(x, k_0)**2*F_9(x, k_0))
Eq(F_30(x, k_0), F_3(x)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, 1, k_0))
Eq(F_32(x, k_0, k_1), (-k_0*F_24(x, k_0, k_1) + F_24(x, 1, k_1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_27(x, k_0)*F_35(x, k_0)*F_9(x, k_0))
Eq(F_35(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_12(x, k_0)*F_27(x, k_0)*F_9(x, k_0))
Pack JSON:
{"name": "col_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "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.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], 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0], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 0], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 2]]}, {"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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24853/
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,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = (4*x*k[0]-1)*F[8,x,k[0]]^2+F[8,x,k[0]]+k[0]^2*x^2
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,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[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,1,k[0]]
F[19,x,k[0],k[1]] = (F[20,x,k[0]*k[1]]*k[0]-F[20,x,k[1]])/(-1+k[0])
F[20,x,k[0]] = F[2,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[15,x,k[0]]*F[23,x,k[0]]*F[70,x,k[0]]
F[23,x,k[0]] = F[20,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[74,x,k[0]]
F[27,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[28,x,k[0]] = F[29,x]+F[31,x,k[0]]
F[29,x] = 1/F[4,x]*F[30,x]
F[30,x] = F[2,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]*F[70,x,k[0]]
F[33,x,k[0]] = F[28,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[24,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[4,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[54,x,k[0]]
F[39,x,k[0]] = F[26,x,k[0]]+F[38,x,k[0]]
F[39,x,k[0]] = F[40,x]+F[58,x,k[0]]
F[40,x] = -F[57,x]+F[41,x]
F[41,x] = -F[49,x]+F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[48,x]+F[45,x]
F[45,x] = 1/F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[0,x]+F[29,x]
F[48,x] = F[28,x,1]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x,1]
F[52,x,k[0]] = 1/(-1+k[0])*(F[53,x,k[0]]*k[0]-F[53,x,1])
F[53,x,k[0]] = F[39,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[56,x,k[0]] = 1/(-1+k[0])*(F[53,x,k[0]]*k[0]-F[53,x,1])
F[57,x] = F[58,x,1]
F[58,x,k[0]] = F[59,x,k[0]]+F[73,x,k[0]]
F[59,x,k[0]] = -k[0]*(F[60,x,1]-F[60,x,k[0]])/(-1+k[0])
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[15,x,k[0]]*F[62,x,k[0]]*F[70,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[62,x,k[0]]*k[0]-F[62,x,1])
F[64,x,k[0]] = F[63,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[64,x,k[0]]
F[65,x,k[0]] = F[34,x,k[0]]
F[67,x,k[0]] = F[66,x,k[0]]+F[69,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[35,x,k[0]]
F[69,x,k[0]] = F[38,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[70,x,k[0]]^2*F[15,x,k[0]]
F[74,x,k[0]] = F[44,x]+F[73,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[4,x]*F[56,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{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 , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y^{2} x^{2}+4 x F_{8}\! \left(x , y\right)^{2} y -F_{8}\! \left(x , y\right)^{2}+F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \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_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , 1, y\right)
F_{19}\! \left(x , y , z\right) = -\frac{-F_{20}\! \left(x , y z \right) y +F_{20}\! \left(x , z\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{40}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{48}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{52}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{62}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{-y F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{69}\! \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_{35}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{70}\! \left(x , y\right)^{2} F_{15}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_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, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0**2*x**2 + 4*k_0*x + (-8*k_0*x + 2)*(F_8(x, k_0) + 1) + (4*k_0*x - 1)*(F_8(x, k_0) + 1)**2 + F_8(x, k_0) - 1)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(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_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, 1, k_0))
Eq(F_19(x, k_0, k_1), (-k_0*k_1*F_20(x, k_0*k_1) + k_1*F_20(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_20(x, k_0), F_2(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_15(x, k_0)*F_23(x, k_0)*F_70(x, k_0))
Eq(F_23(x, k_0), F_20(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_74(x, k_0))
Eq(F_27(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_29(x) + F_31(x, k_0))
Eq(F_29(x), F_30(x)/F_4(x))
Eq(F_30(x), F_2(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_15(x, k_0)*F_33(x, k_0)*F_70(x, k_0))
Eq(F_33(x, k_0), F_28(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_24(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_4(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_54(x, k_0))
Eq(F_39(x, k_0), F_26(x, k_0) + F_38(x, k_0))
Eq(F_39(x, k_0), F_40(x) + F_58(x, k_0))
Eq(F_40(x), F_41(x) - F_57(x))
Eq(F_41(x), F_42(x) - F_49(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x) - F_48(x))
Eq(F_45(x), F_46(x)/F_4(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), -F_0(x) + F_29(x))
Eq(F_48(x), F_28(x, 1))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x, 1))
Eq(F_52(x, k_0), (-k_0*F_53(x, k_0) + F_53(x, 1))/(1 - k_0))
Eq(F_53(x, k_0), F_39(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_56(x, k_0), (k_0*F_53(x, k_0) - F_53(x, 1))/(k_0 - 1))
Eq(F_57(x), F_58(x, 1))
Eq(F_58(x, k_0), F_59(x, k_0) + F_73(x, k_0))
Eq(F_59(x, k_0), -F_60(x, 1) + (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_15(x, k_0)*F_62(x, k_0)*F_70(x, k_0))
Eq(F_63(x, k_0), (k_0*F_62(x, k_0) - F_62(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_63(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_64(x, k_0))
Eq(F_65(x, k_0), F_34(x, k_0))
Eq(F_67(x, k_0), F_66(x, k_0) + F_69(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_35(x, k_0))
Eq(F_69(x, k_0), F_38(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_15(x, k_0)*F_70(x, k_0)**2)
Eq(F_74(x, k_0), F_44(x) + F_73(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_4(x)*F_56(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"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.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": 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{"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 3]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 3]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 3]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 1], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 3], [3, 0], [3, 0], [3, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 2]]}]}]}, "children": [{"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": [[1, 2]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 0], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 0], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 1], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 1], [3, 0], [3, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 1], [3, 0], [3, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"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, 2, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[2, 0], [2, 1], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 4
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/25037/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = (F[12,x,k[0]*k[1]]*k[0]-F[12,x,k[1]])/(-1+k[0])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[36,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[30,x,k[0]]+F[33,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[16,x,k[0]] = F[17,x,1,k[0]]
F[17,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[18,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[25,x,k[1],k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[3,x]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,1,k[0],k[1]]
F[23,x,k[0],k[1],k[2]] = (F[24,x,k[0]*k[1],k[2]]*k[0]-F[24,x,k[1],k[2]])/(-1+k[0])
F[24,x,k[0],k[1]] = (F[12,x,k[0]]*k[0]-F[12,x,k[1]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[24,x,k[1],k[0]]*F[27,x,k[0]]*F[9,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x,k[0]]^2*F[9,x,k[0]]
F[30,x,k[0]] = F[3,x]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,1,k[0]]
F[32,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]-F[24,x,1,k[1]])/(-1+k[0])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]*F[9,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{12}\! \left(x , y_{1}\right)}{-1+y_{0}}
F_{12}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , 1, y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{1}, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , 1, y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{24}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{24}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}\right)-F_{12}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}, y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)^{2} F_{9}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{32}\! \left(x , 1, y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{12}\! \left(x , y_{0}\right)+F_{12}\! \left(x , 1\right)}{-1+y_{0}}
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), (-k_0*k_1*F_12(x, k_0*k_1) + k_1*F_12(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_36(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_30(x, k_0) + F_33(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_16(x, k_0), F_17(x, 1, k_0))
Eq(F_17(x, k_0, k_1), (-k_0*F_18(x, k_0, k_1) + F_18(x, 1, k_1))/(1 - k_0))
Eq(F_18(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_25(x, k_1, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_3(x))
Eq(F_20(x, k_0, k_1), (k_0*F_18(x, k_0, k_1) - F_18(x, 1, k_1))/(k_0 - 1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, 1, k_0, k_1))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*k_1*F_24(x, k_0*k_1, k_2) + k_1*F_24(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_12(x, k_0) + k_1*F_12(x, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_24(x, k_1, k_0)*F_27(x, k_0)*F_9(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_27(x, k_0)**2*F_9(x, k_0))
Eq(F_30(x, k_0), F_3(x)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, 1, k_0))
Eq(F_32(x, k_0, k_1), (-k_0*F_24(x, k_0, k_1) + F_24(x, 1, k_1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_27(x, k_0)*F_35(x, k_0)*F_9(x, k_0))
Eq(F_35(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_12(x, k_0)*F_27(x, k_0)*F_9(x, k_0))
Pack JSON:
{"name": "col_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 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"pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 3]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 3]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 3]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 0], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 2]]}, {"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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"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, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 4, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25972/
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[6,x,1]
F[6,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[45,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[49,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = (F[12,x,k[0]*k[1]]*k[0]-F[12,x,k[1]])/(-1+k[0])
F[12,x,k[0]] = F[0,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[42,x,k[0]]*F[45,x,k[0]]
F[15,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[18,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[19,x,k[0]] = F[15,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[47,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[42,x,k[0]]*F[45,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[26,x,k[0]] = F[25,x,k[0]]+F[46,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[28,x,k[0]]
F[27,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[30,x,k[0]] = F[31,x,1,k[0]]
F[31,x,k[0],k[1]] = 1/(-1+k[0])*(F[32,x,k[0],k[1]]*k[0]-F[32,x,1,k[1]])
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]+F[38,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[34,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[34,x,k[0],k[1]] = (F[12,x,k[0]]*k[0]-F[12,x,k[1]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[1]]*F[4,x]
F[37,x,k[0],k[1]] = 1/(-1+k[0])*(F[32,x,k[0],k[1]]*k[0]-F[32,x,1,k[1]])
F[38,x,k[0],k[1]] = F[39,x,k[1],k[0]]
F[39,x,k[0],k[1]] = F[4,x]*F[40,x,k[1]]*F[42,x,k[0]]
F[41,x,k[0]] = F[4,x]*F[40,x,k[0]]
F[41,x,k[0]] = F[20,x,k[0]]
F[42,x,k[0]] = F[1,x]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]^2*F[45,x,k[0]]
F[45,x,k[0]] = k[0]*x
F[46,x] = F[15,x,1]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[38,x,1,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[4,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,1,k[0]]
F[52,x,k[0],k[1]] = (-F[53,x,1,k[1]]*k[1]+F[53,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[53,x,k[0],k[1]] = F[32,x,k[0]*k[1],k[1]]
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_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = -\frac{-F_{12}\! \left(x , y z \right) y +F_{12}\! \left(x , z\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , 1, y\right)
F_{31}\! \left(x , y , z\right) = -\frac{-F_{32}\! \left(x , y , z\right) y +F_{32}\! \left(x , 1, z\right)}{-1+y}
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{34}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , z\right) z}{-z +y}
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y , z\right) = -\frac{-F_{32}\! \left(x , y , z\right) y +F_{32}\! \left(x , 1, z\right)}{-1+y}
F_{38}\! \left(x , y , z\right) = F_{39}\! \left(x , z , y\right)
F_{39}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{40}\! \left(x , z\right) F_{42}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{42}\! \left(x , y\right)^{2} F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = y x
F_{46}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{38}\! \left(x , 1, y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , 1, y\right)
F_{52}\! \left(x , y , z\right) = -\frac{z F_{53}\! \left(x , 1, z\right)-y F_{53}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{53}\! \left(x , y , z\right) = F_{32}\! \left(x , y z , z\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_6(x, 1))
Eq(F_6(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_45(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_49(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), (-k_0*k_1*F_12(x, k_0*k_1) + k_1*F_12(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_12(x, k_0), F_0(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_42(x, k_0)*F_45(x, k_0))
Eq(F_15(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_18(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_15(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_47(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_42(x, k_0)*F_45(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_26(x, k_0), F_25(x, k_0) + F_46(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_28(x, k_0))
Eq(F_27(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_30(x, k_0), F_31(x, 1, k_0))
Eq(F_31(x, k_0, k_1), (-k_0*F_32(x, k_0, k_1) + F_32(x, 1, k_1))/(1 - k_0))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_34(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (-k_0*F_12(x, k_0) + k_1*F_12(x, k_1))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_1)*F_4(x))
Eq(F_37(x, k_0, k_1), (k_0*F_32(x, k_0, k_1) - F_32(x, 1, k_1))/(k_0 - 1))
Eq(F_38(x, k_0, k_1), F_39(x, k_1, k_0))
Eq(F_39(x, k_0, k_1), F_4(x)*F_40(x, k_1)*F_42(x, k_0))
Eq(F_41(x, k_0), F_4(x)*F_40(x, k_0))
Eq(F_41(x, k_0), F_20(x, k_0))
Eq(F_42(x, k_0), F_1(x) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0)**2*F_45(x, k_0))
Eq(F_45(x, k_0), k_0*x)
Eq(F_46(x), F_15(x, 1))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_38(x, 1, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_4(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, 1, k_0))
Eq(F_52(x, k_0, k_1), (-k_0*F_53(x, k_0/k_1, k_1) + k_1*F_53(x, 1, k_1))/(-k_0 + k_1))
Eq(F_53(x, k_0, k_1), F_32(x, k_0*k_1, k_1))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "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, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 0, 3], "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, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [4, 0], [4, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [4, 2], [4, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [4, 0], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [4, 0], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [4, 0], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [4, 2], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 0], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 0], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 2], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 3], [4, 0], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 3], [4, 2], [4, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 3], [4, 3], [4, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [4, 2], [4, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [4, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [4, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [4, 2], [4, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [4, 0], [4, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [4, 0], [4, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [4, 0], [4, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [4, 0], [4, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [4, 2], [4, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 3]]}, {"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, 3, 0, 2], "pos": [[0, 0], [0, 2], [4, 0], [4, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 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