1032_1302_354102
Counting sequence:
1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742, 15521467648875090, 85249942588971314, 469286147871837366, 2588758890960637798, 14308406109097843626, 79228031819993134650, 439442782615614361662, 2441263009246175852478, 13582285614213903189954, 75672545337796460900418, 422158527806921249683014, 2358045034996817096518614, 13186762229969911326195738, 73825509266803210054176714, 413744003711584755242223438, 2321083025362608992223726894, 13033522069997514889215092274, 73252943452863199223393858898, 412061442720070604908289934294, 2319824936637513933714881477958, 13070393952625514917631908633482, 73696580719034769214303906556250, 415831259625127007215514095957086, 2347928652146955633301765770354078, 13265947508553602309369175431365026, 75000761566763827145224941186411618, 424283543233691838260433080620759398, 2401593774673792297361446179037614006, 13601477343632400527767268213048769018, 77073779272885977020023254295915628266, 436971024085954796290610303307461466990, 2478653831690076100088720298283149489422, 14066584046529013725085103560520804574738, 79866310879834163229292594665706543602034, 453663534693850195686460667123382923500278, 2578058682623181189697966937739368886054694, 14656630568593973333973106198029483323909994, 83358894098787816613549314525130317456485498, 474286255370429617942243026791925684793786494, 2699569581623203904920541044702174725512879998, 15371234811776523868650878005698910430202961794, 87554469522958377138755995490746080739109617794, 498882798426402159521454478141768350193090899078, 2843576412546208340221194074583339359985310934934, 16213364962102490366103878328244865647555172888538, 92473905425478965452483914141593657771802288922122, 527593095000024778151982091136956400377574686254990, 3010988607092394896417597701043924930186940754864366, 17188802682090899672500146128332285575668045969848818, 98153364535215963782323163906086831829355773017417106, 560640532892262603354460063484591577003970621211357718, 3203172665681192346622816544900896002595156529621124358, 18305841793760424680154621430418780681523533531801673546, 104642864530896737207618717893521194008008527581735690138, 598325164943559373744948766984500352935799706039116059806, 3421920651494217703361052849648731678676812561507875200350, 19575145529594373004334767968613012138269718700842042196322, 112005653162512670274733777484363842197180560245702246829218, 641021117519290914746964286173070817630839957398566690647974, 3669440419831969958422546258088530756063025637290340831875958, 21009716690579236401887583574543083549904081973832685742784954, 120318172177646736618696901545023201244745795730675271890072874, 689177081897978391122217856003853830119110923264764010082913198, 3948362055340350140680020802666740519613808824287558217299724494, 22624953370904018901353934671727048802325911161238183811407020498, 129670474901504706381997527787278405431429527321160644877245020594, 743319221158994216085862924952269488154648087794223144216228112694, 4261757226338042831158975959521897325919311779789998586036272373478, 24438774057583613278048926220772229870922406873153001513488741966634, 140167018025129185868954119576724414060673174921691765624010117079738, 804056104197892430009502735476119485683292523144621098692933804429502, 4613169566706958265933076228065878936195669326617529466206880481490750, 26471802968334898948028447644814364935937000278105670111952646786369346, 151927783773762708731069683108992436724172801785658343831948253505777858, 872085458815060952612778117624832287371627646645575624352952264741298886, 5006655111336460402472381082547036154743871773943263346408958078720471894
Generating function in Maple syntax:
-1/2*x+3/2-1/2*(x^2-6*x+1)^(1/2)
Generating function in latex syntax:
-\frac{x}{2}+\frac{3}{2}-\frac{\sqrt{x^{2}-6 x +1}}{2}
Generating function in sympy syntax:
-x/2 - sqrt(x**2 - 6*x + 1)/2 + 3/2
Implicit equation for the generating function in Maple syntax:
F(x)^2+(x-3)*F(x)+2 = 0
Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{2}+\left(x -3\right) F \! \left(x \right)+2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(n+2) = -(n-1)/(n+2)*a(n)+3*(2*n+1)/(n+2)*a(n+1), n >= 2
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(n +2\right) = -\frac{\left(n -1\right) a \! \left(n \right)}{n +2}+\frac{3 \left(2 n +1\right) a \! \left(n +1\right)}{n +2}, \quad n \geq 2
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/23991/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[19,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x]+F[8,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[5,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]^2*F[18,x]
F[18,x] = x
F[19,x] = F[20,x]
F[20,x] = F[21,x,1]
F[21,x,k[0]] = F[22,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]+F[8,x]
F[24,x,k[0]] = F[18,x]*F[23,x,k[0]]*F[37,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[33,x,k[0]]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[2,x]*F[28,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[18,x]*F[28,x]
F[30,x] = F[16,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[18,x]*F[28,x]*F[5,x]
F[34,x,k[0]] = F[33,x,k[0]]+F[74,x,k[0]]
F[35,x,k[0]] = F[34,x,k[0]]+F[71,x]
F[35,x,k[0]] = F[36,x,k[0]]+F[67,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[41,x,k[0]]
F[37,x,k[0]] = F[1,x]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[37,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = k[0]*x
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[18,x]*F[37,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[4,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[40,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[62,x,k[0]]
F[47,x,k[0]] = F[35,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[18,x]*F[50,x,k[0]]*F[53,x,k[0]]
F[50,x,k[0]] = F[37,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[50,x,k[0]]^2*F[18,x]
F[54,x,k[0]] = F[18,x]*F[37,x,k[0]]*F[53,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[41,x,k[0]]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[18,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[55,x,k[0]]+F[59,x,k[0]]
F[46,x,k[0]] = F[59,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[55,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[37,x,k[0]]*F[4,x]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[18,x]*F[64,x,k[0]]
F[65,x,k[0]] = F[18,x]*F[64,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = (F[22,x,k[0]]-F[22,x,1])/(-1+k[0])
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[18,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[35,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[5,x]*F[50,x,k[0]]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[0,x]*F[28,x]
F[73,x] = F[14,x]*F[31,x]
F[74,x,k[0]] = F[0,x]*F[38,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_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{23}\! \left(x , y\right) F_{37}\! \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 \right)+F_{33}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{71}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = y x
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{37}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{50}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{50}\! \left(x , y\right)^{2} F_{18}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{37}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{38}\! \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_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_19(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_8(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_5(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)**2*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x, 1))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0) + F_8(x))
Eq(F_24(x, k_0), F_18(x)*F_23(x, k_0)*F_37(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_33(x, k_0))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_2(x)*F_28(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_18(x)*F_28(x))
Eq(F_30(x), F_16(x)*F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_18(x)*F_28(x)*F_5(x))
Eq(F_34(x, k_0), F_33(x, k_0) + F_74(x, k_0))
Eq(F_35(x, k_0), F_34(x, k_0) + F_71(x))
Eq(F_35(x, k_0), F_36(x, k_0) + F_67(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_41(x, k_0))
Eq(F_37(x, k_0), F_1(x) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_37(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), k_0*x)
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_18(x)*F_37(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_4(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_40(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_62(x, k_0))
Eq(F_47(x, k_0), F_35(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_18(x)*F_50(x, k_0)*F_53(x, k_0))
Eq(F_50(x, k_0), F_37(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_18(x)*F_50(x, k_0)**2)
Eq(F_54(x, k_0), F_18(x)*F_37(x, k_0)*F_53(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_41(x, k_0) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_18(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_55(x, k_0) + F_59(x, k_0))
Eq(F_46(x, k_0), F_59(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_55(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_37(x, k_0)*F_4(x))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_18(x)*F_64(x, k_0))
Eq(F_65(x, k_0), F_18(x)*F_64(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), -F_22(x, k_0) + (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_18(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_35(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_5(x)*F_50(x, k_0))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_0(x)*F_28(x))
Eq(F_73(x), F_14(x)*F_31(x))
Eq(F_74(x, k_0), F_0(x)*F_38(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [1, 1], [1, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [1, 1], [1, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 2], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [1, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 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"pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 0], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 2], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 0], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 3], [1, 1], [1, 1]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [1, 1], [1, 1]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 3], [0, 3], [0, 3], [1, 1], [1, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 0], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [1, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": 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4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/23992/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = -F[194,x]+F[10,x]
F[10,x] = 1/F[22,x]*F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[22,x]
F[14,x] = F[15,x]+F[37,x]
F[15,x] = F[16,x]+F[28,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[18,x]*F[2,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]^2*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]*F[25,x]
F[24,x] = -F[18,x]+F[0,x]
F[25,x] = F[26,x]
F[26,x] = F[22,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]+F[31,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[2,x]*F[20,x]
F[31,x] = F[32,x]
F[32,x] = F[22,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[12,x]+F[31,x]
F[35,x] = F[36,x]
F[36,x] = F[20,x]^2*F[5,x]
F[37,x] = F[192,x]+F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[0,x]*F[25,x]
F[40,x] = F[183,x]+F[41,x]
F[41,x] = F[42,x]+F[43,x]+F[45,x]
F[42,x] = 0
F[43,x] = F[22,x]*F[44,x]
F[44,x] = F[2,x]+F[41,x]
F[45,x] = F[22,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[25,x]+F[41,x]
F[48,x] = F[41,x]+F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[22,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[73,x,k[0]]
F[54,x,k[0]] = F[22,x]*F[53,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[42,x]+F[56,x,k[0]]+F[59,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]*F[58,x,k[0]]
F[57,x,k[0]] = F[29,x]+F[55,x,k[0]]
F[58,x,k[0]] = k[0]*x
F[59,x,k[0]] = F[20,x]*F[22,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[22,x]*F[60,x,k[0]]
F[62,x,k[0]] = F[42,x]+F[61,x,k[0]]+F[72,x,k[0]]
F[62,x,k[0]] = F[42,x]+F[63,x,k[0]]+F[65,x,k[0]]
F[63,x,k[0]] = F[58,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[2,x]+F[62,x,k[0]]
F[65,x,k[0]] = F[22,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[71,x,k[0]]
F[67,x,k[0]] = F[62,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[58,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[68,x,k[0]]
F[71,x,k[0]] = F[50,x,k[0]]+F[62,x,k[0]]
F[72,x,k[0]] = F[58,x,k[0]]*F[64,x,k[0]]
F[73,x,k[0]] = F[116,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[98,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[77,x,k[0]]
F[76,x,k[0]] = F[64,x,k[0]]*F[68,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[95,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[22,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]+F[93,x,k[0]]
F[81,x,k[0]] = F[62,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = F[2,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[58,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[42,x]+F[86,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[22,x]*F[88,x,k[0]]*F[90,x,k[0]]
F[88,x,k[0]] = F[18,x]+F[89,x,k[0]]
F[89,x,k[0]] = F[58,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[70,x,k[0]]+F[86,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[18,x]*F[22,x]*F[90,x,k[0]]
F[93,x,k[0]] = F[78,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[12,x]*F[83,x,k[0]]
F[95,x,k[0]] = F[42,x]+F[96,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[58,x,k[0]]*F[77,x,k[0]]
F[97,x,k[0]] = F[22,x]*F[60,x,k[0]]*F[83,x,k[0]]
F[98,x,k[0]] = F[77,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]+F[78,x,k[0]]
F[102,x,k[0]] = F[101,x,k[0]]+F[106,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[22,x]
F[78,x,k[0]] = F[103,x,k[0]]+F[104,x,k[0]]+F[42,x]
F[104,x,k[0]] = F[105,x,k[0]]*F[58,x,k[0]]
F[105,x,k[0]] = F[29,x]+F[78,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[78,x,k[0]]
F[107,x,k[0]] = F[2,x]*F[68,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]+F[95,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]+F[114,x,k[0]]
F[111,x,k[0]] = F[110,x,k[0]]*F[22,x]
F[95,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]+F[42,x]
F[112,x,k[0]] = F[113,x,k[0]]*F[58,x,k[0]]
F[113,x,k[0]] = F[55,x,k[0]]+F[95,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[95,x,k[0]]
F[115,x,k[0]] = F[62,x,k[0]]*F[68,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[163,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[120,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[0,x]*F[25,x]*F[68,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[147,x,k[0]]
F[121,x,k[0]] = (-F[122,x,1]*k[0]+F[122,x,k[0]])/(-1+k[0])
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[58,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[62,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[2,x]*F[68,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[130,x,k[0]]+F[42,x]
F[128,x,k[0]] = F[129,x,k[0]]*F[58,x,k[0]]
F[129,x,k[0]] = F[127,x,k[0]]+F[6,x]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[22,x]
F[132,x,k[0]] = F[125,x,k[0]]+F[133,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]+F[146,x,k[0]]
F[134,x,k[0]] = F[125,x,k[0]]+F[135,x,k[0]]
F[136,x,k[0]] = F[135,x,k[0]]+F[143,x]
F[137,x,k[0]] = F[136,x,k[0]]+F[141,x,k[0]]
F[138,x,k[0]] = F[137,x,k[0]]+F[140,x,k[0]]
F[139,x,k[0]] = F[138,x,k[0]]*F[58,x,k[0]]
F[139,x,k[0]] = F[50,x,k[0]]
F[140,x,k[0]] = F[12,x]+F[50,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]*F[20,x]
F[142,x,k[0]] = F[125,x,k[0]]+F[5,x]
F[143,x] = -F[5,x]+F[144,x]
F[144,x] = -F[145,x]+F[9,x]
F[145,x] = F[20,x]*F[5,x]
F[146,x,k[0]] = F[125,x,k[0]]*F[20,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[22,x]
F[149,x,k[0]] = F[120,x,k[0]]+F[150,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]*F[5,x]
F[151,x,k[0]] = (-F[152,x,1]*k[0]+F[152,x,k[0]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]*F[58,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[160,x,k[0]]+F[42,x]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]*F[22,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[162,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[18,x]
F[159,x,k[0]] = F[155,x,k[0]]+F[160,x,k[0]]+F[68,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[159,x,k[0]]*F[18,x]*F[22,x]
F[162,x,k[0]] = F[90,x,k[0]]^2*F[58,x,k[0]]
F[163,x,k[0]] = F[120,x,k[0]]+F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[174,x,k[0]]
F[165,x,k[0]] = (-F[166,x,1]*k[0]+F[166,x,k[0]])/(-1+k[0])
F[167,x,k[0]] = F[122,x,k[0]]+F[166,x,k[0]]
F[168,x,k[0]] = F[167,x,k[0]]+F[171,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]*F[22,x]
F[122,x,k[0]] = F[169,x,k[0]]+F[170,x,k[0]]+F[42,x]
F[170,x,k[0]] = F[58,x,k[0]]*F[62,x,k[0]]
F[171,x,k[0]] = F[122,x,k[0]]+F[172,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[58,x,k[0]]*F[68,x,k[0]]
F[175,x,k[0]] = F[147,x,k[0]]+F[174,x,k[0]]
F[176,x,k[0]] = F[175,x,k[0]]+F[180,x,k[0]]
F[177,x,k[0]] = F[176,x,k[0]]*F[22,x]
F[147,x,k[0]] = 2*F[42,x]+F[177,x,k[0]]+F[178,x,k[0]]
F[178,x,k[0]] = -k[0]*(F[179,x,1]-F[179,x,k[0]])/(-1+k[0])
F[179,x,k[0]] = F[22,x]*F[78,x,k[0]]
F[180,x,k[0]] = F[147,x,k[0]]+F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]
F[182,x,k[0]] = F[2,x]*F[25,x]*F[68,x,k[0]]
F[183,x] = F[184,x]+F[186,x]+F[42,x]
F[184,x] = F[185,x]*F[22,x]
F[185,x] = F[183,x]+F[29,x]
F[186,x] = F[187,x]*F[22,x]
F[187,x] = F[188,x]+F[190,x]
F[188,x] = F[183,x]+F[189,x]
F[189,x] = F[2,x]*F[25,x]
F[190,x] = F[183,x]+F[191,x]
F[191,x] = F[100,x,1]
F[192,x] = F[193,x]+F[40,x]
F[193,x] = F[191,x]+F[49,x]
F[194,x] = F[12,x]+F[2,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = -F_{194}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{28}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{18}\! \left(x \right)+F_{0}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{22}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{5}\! \left(x \right)
F_{37}\! \left(x \right) = F_{192}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{25}\! \left(x \right)
F_{40}\! \left(x \right) = F_{183}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = 0
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{41}\! \left(x \right)
F_{48}\! \left(x \right) = F_{41}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = y x
F_{59}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{88}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{18}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{60}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{95}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{62}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{25}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = -\frac{F_{122}\! \left(x , 1\right) y -F_{122}\! \left(x , y\right)}{-1+y}
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{143}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{143}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{9}\! \left(x \right)
F_{145}\! \left(x \right) = F_{20}\! \left(x \right) F_{5}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{151}\! \left(x , y\right) = -\frac{F_{152}\! \left(x , 1\right) y -F_{152}\! \left(x , y\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{90}\! \left(x , y\right)^{2} F_{58}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = -\frac{F_{166}\! \left(x , 1\right) y -F_{166}\! \left(x , y\right)}{-1+y}
F_{167}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{42}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{62}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{147}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = -\frac{y \left(F_{179}\! \left(x , 1\right)-F_{179}\! \left(x , y\right)\right)}{-1+y}
F_{179}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{186}\! \left(x \right)+F_{42}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{22}\! \left(x \right)
F_{185}\! \left(x \right) = F_{183}\! \left(x \right)+F_{29}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{22}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{190}\! \left(x \right)
F_{188}\! \left(x \right) = F_{183}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right)
F_{190}\! \left(x \right) = F_{183}\! \left(x \right)+F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{40}\! \left(x \right)
F_{193}\! \left(x \right) = F_{191}\! \left(x \right)+F_{49}\! \left(x \right)
F_{194}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) - F_194(x))
Eq(F_10(x), F_11(x)/F_22(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_22(x))
Eq(F_14(x), F_15(x) + F_37(x))
Eq(F_15(x), F_16(x) + F_28(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_18(x)*F_2(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_18(x)**2*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x)*F_25(x))
Eq(F_24(x), F_0(x) - F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_22(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x) + F_31(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_2(x)*F_20(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_22(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_12(x) + F_31(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_20(x)**2*F_5(x))
Eq(F_37(x), F_192(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_0(x)*F_25(x))
Eq(F_40(x), F_183(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_43(x) + F_45(x))
Eq(F_42(x), 0)
Eq(F_43(x), F_22(x)*F_44(x))
Eq(F_44(x), F_2(x) + F_41(x))
Eq(F_45(x), F_22(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_25(x) + F_41(x))
Eq(F_48(x), F_41(x) + F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_22(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_73(x, k_0))
Eq(F_54(x, k_0), F_22(x)*F_53(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_42(x) + F_56(x, k_0) + F_59(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0)*F_58(x, k_0))
Eq(F_57(x, k_0), F_29(x) + F_55(x, k_0))
Eq(F_58(x, k_0), k_0*x)
Eq(F_59(x, k_0), F_20(x)*F_22(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_22(x)*F_60(x, k_0))
Eq(F_62(x, k_0), F_42(x) + F_61(x, k_0) + F_72(x, k_0))
Eq(F_62(x, k_0), F_42(x) + F_63(x, k_0) + F_65(x, k_0))
Eq(F_63(x, k_0), F_58(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_2(x) + F_62(x, k_0))
Eq(F_65(x, k_0), F_22(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_71(x, k_0))
Eq(F_67(x, k_0), F_62(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_58(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_68(x, k_0))
Eq(F_71(x, k_0), F_50(x, k_0) + F_62(x, k_0))
Eq(F_72(x, k_0), F_58(x, k_0)*F_64(x, k_0))
Eq(F_73(x, k_0), F_116(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_98(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_77(x, k_0))
Eq(F_76(x, k_0), F_64(x, k_0)*F_68(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_95(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_22(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0) + F_93(x, k_0))
Eq(F_81(x, k_0), F_62(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), F_2(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_58(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_42(x) + F_86(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_22(x)*F_88(x, k_0)*F_90(x, k_0))
Eq(F_88(x, k_0), F_18(x) + F_89(x, k_0))
Eq(F_89(x, k_0), F_58(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_70(x, k_0) + F_86(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_18(x)*F_22(x)*F_90(x, k_0))
Eq(F_93(x, k_0), F_78(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_12(x)*F_83(x, k_0))
Eq(F_95(x, k_0), F_42(x) + F_96(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_58(x, k_0)*F_77(x, k_0))
Eq(F_97(x, k_0), F_22(x)*F_60(x, k_0)*F_83(x, k_0))
Eq(F_98(x, k_0), F_77(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_108(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0) + F_78(x, k_0))
Eq(F_102(x, k_0), F_101(x, k_0) + F_106(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_22(x))
Eq(F_78(x, k_0), F_103(x, k_0) + F_104(x, k_0) + F_42(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_58(x, k_0))
Eq(F_105(x, k_0), F_29(x) + F_78(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_78(x, k_0))
Eq(F_107(x, k_0), F_2(x)*F_68(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0) + F_95(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0) + F_114(x, k_0))
Eq(F_111(x, k_0), F_110(x, k_0)*F_22(x))
Eq(F_95(x, k_0), F_111(x, k_0) + F_112(x, k_0) + F_42(x))
Eq(F_112(x, k_0), F_113(x, k_0)*F_58(x, k_0))
Eq(F_113(x, k_0), F_55(x, k_0) + F_95(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_95(x, k_0))
Eq(F_115(x, k_0), F_62(x, k_0)*F_68(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_163(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_120(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_0(x)*F_25(x)*F_68(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_147(x, k_0))
Eq(F_121(x, k_0), -F_122(x, 1) - F_122(x, k_0) + (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0)*F_58(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_62(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_2(x)*F_68(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_130(x, k_0) + F_42(x))
Eq(F_128(x, k_0), F_129(x, k_0)*F_58(x, k_0))
Eq(F_129(x, k_0), F_127(x, k_0) + F_6(x))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_22(x))
Eq(F_132(x, k_0), F_125(x, k_0) + F_133(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_146(x, k_0))
Eq(F_134(x, k_0), F_125(x, k_0) + F_135(x, k_0))
Eq(F_136(x, k_0), F_135(x, k_0) + F_143(x))
Eq(F_137(x, k_0), F_136(x, k_0) + F_141(x, k_0))
Eq(F_138(x, k_0), F_137(x, k_0) + F_140(x, k_0))
Eq(F_139(x, k_0), F_138(x, k_0)*F_58(x, k_0))
Eq(F_139(x, k_0), F_50(x, k_0))
Eq(F_140(x, k_0), F_12(x) + F_50(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0)*F_20(x))
Eq(F_142(x, k_0), F_125(x, k_0) + F_5(x))
Eq(F_143(x), F_144(x) - F_5(x))
Eq(F_144(x), -F_145(x) + F_9(x))
Eq(F_145(x), F_20(x)*F_5(x))
Eq(F_146(x, k_0), F_125(x, k_0)*F_20(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_22(x))
Eq(F_149(x, k_0), F_120(x, k_0) + F_150(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_5(x))
Eq(F_151(x, k_0), -F_152(x, 1) - F_152(x, k_0) + (-k_0*F_152(x, k_0) + F_152(x, 1))/(1 - k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0)*F_58(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_160(x, k_0) + F_42(x))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0)*F_22(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_162(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_18(x))
Eq(F_159(x, k_0), F_155(x, k_0) + F_160(x, k_0) + F_68(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_159(x, k_0)*F_18(x)*F_22(x))
Eq(F_162(x, k_0), F_58(x, k_0)*F_90(x, k_0)**2)
Eq(F_163(x, k_0), F_120(x, k_0) + F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_174(x, k_0))
Eq(F_165(x, k_0), -F_166(x, 1) - F_166(x, k_0) + (-k_0*F_166(x, k_0) + F_166(x, 1))/(1 - k_0))
Eq(F_167(x, k_0), F_122(x, k_0) + F_166(x, k_0))
Eq(F_168(x, k_0), F_167(x, k_0) + F_171(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0)*F_22(x))
Eq(F_122(x, k_0), F_169(x, k_0) + F_170(x, k_0) + F_42(x))
Eq(F_170(x, k_0), F_58(x, k_0)*F_62(x, k_0))
Eq(F_171(x, k_0), F_122(x, k_0) + F_172(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_58(x, k_0)*F_68(x, k_0))
Eq(F_175(x, k_0), F_147(x, k_0) + F_174(x, k_0))
Eq(F_176(x, k_0), F_175(x, k_0) + F_180(x, k_0))
Eq(F_177(x, k_0), F_176(x, k_0)*F_22(x))
Eq(F_147(x, k_0), F_177(x, k_0) + F_178(x, k_0) + 2*F_42(x))
Eq(F_178(x, k_0), -F_179(x, 1) + (-k_0*F_179(x, k_0) + F_179(x, 1))/(1 - k_0))
Eq(F_179(x, k_0), F_22(x)*F_78(x, k_0))
Eq(F_180(x, k_0), F_147(x, k_0) + F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0))
Eq(F_182(x, k_0), F_2(x)*F_25(x)*F_68(x, k_0))
Eq(F_183(x), F_184(x) + F_186(x) + F_42(x))
Eq(F_184(x), F_185(x)*F_22(x))
Eq(F_185(x), F_183(x) + F_29(x))
Eq(F_186(x), F_187(x)*F_22(x))
Eq(F_187(x), F_188(x) + F_190(x))
Eq(F_188(x), F_183(x) + F_189(x))
Eq(F_189(x), F_2(x)*F_25(x))
Eq(F_190(x), F_183(x) + F_191(x))
Eq(F_191(x), F_100(x, 1))
Eq(F_192(x), F_193(x) + F_40(x))
Eq(F_193(x), F_191(x) + F_49(x))
Eq(F_194(x), F_12(x) + F_2(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [1, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 0], [2, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0], [2, 0]]}, 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2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[2, 2]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: insertion_point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/23993/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[37,x]+F[9,x]
F[9,x] = F[10,x]+F[21,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]*F[2,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]*F[18,x]
F[17,x] = -F[12,x]+F[0,x]
F[18,x] = F[19,x]
F[19,x] = F[15,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[31,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[18,x]*F[2,x]
F[24,x] = F[13,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = F[25,x]+F[28,x]
F[28,x] = -F[0,x]+F[29,x]
F[29,x] = 1/F[15,x]*F[30,x]
F[30,x] = F[2,x]
F[31,x] = F[32,x]
F[32,x] = F[15,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[31,x]+F[6,x]
F[35,x] = F[36,x]
F[36,x] = F[13,x]^2*F[28,x]
F[37,x] = F[193,x]+F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[0,x]*F[18,x]
F[40,x] = F[178,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[18,x]*F[4,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[18,x]+F[41,x]
F[48,x] = F[41,x]+F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[15,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[76,x,k[0]]
F[54,x,k[0]] = F[15,x]*F[53,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]*F[69,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[22,x]+F[55,x,k[0]]
F[59,x,k[0]] = F[13,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[60,x,k[0]]+F[75,x,k[0]]
F[62,x,k[0]] = F[61,x,k[0]]*F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[15,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]+F[71,x,k[0]]
F[66,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]*F[70,x,k[0]]
F[69,x,k[0]] = k[0]*x
F[70,x,k[0]] = F[1,x]+F[67,x,k[0]]
F[71,x,k[0]] = F[70,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[74,x,k[0]]
F[73,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[74,x,k[0]] = F[50,x,k[0]]+F[63,x,k[0]]
F[75,x,k[0]] = F[2,x]+F[63,x,k[0]]
F[76,x,k[0]] = F[123,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[103,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[67,x,k[0]]*F[75,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]+F[99,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[15,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[97,x,k[0]]
F[84,x,k[0]] = F[63,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[2,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[69,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x]+F[90,x,k[0]]+F[95,x,k[0]]
F[89,x] = 0
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[15,x]*F[92,x,k[0]]*F[94,x,k[0]]
F[92,x,k[0]] = F[12,x]+F[93,x,k[0]]
F[93,x,k[0]] = F[69,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[70,x,k[0]]+F[90,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[12,x]*F[15,x]*F[94,x,k[0]]
F[97,x,k[0]] = F[81,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[6,x]*F[86,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[69,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[80,x,k[0]]
F[102,x,k[0]] = F[60,x,k[0]]*F[86,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[80,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[114,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]+F[81,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]+F[112,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[70,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]+F[111,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]*F[15,x]
F[110,x,k[0]] = F[81,x,k[0]]
F[111,x,k[0]] = F[67,x,k[0]]*F[9,x]
F[112,x,k[0]] = F[113,x,k[0]]+F[81,x,k[0]]
F[113,x,k[0]] = F[2,x]*F[67,x,k[0]]
F[115,x,k[0]] = F[114,x,k[0]]+F[99,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]+F[121,x,k[0]]
F[117,x,k[0]] = F[116,x,k[0]]*F[70,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = F[118,x,k[0]]*F[15,x]
F[119,x,k[0]] = F[99,x,k[0]]
F[120,x,k[0]] = F[53,x,k[0]]*F[67,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[99,x,k[0]]
F[122,x,k[0]] = F[63,x,k[0]]*F[67,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[151,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[127,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]
F[126,x,k[0]] = F[0,x]*F[18,x]*F[67,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[135,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = -k[0]*(F[130,x,1]-F[130,x,k[0]])/(-1+k[0])
F[130,x,k[0]] = F[131,x,k[0]]*F[15,x]
F[132,x,k[0]] = F[131,x,k[0]]+F[134,x]
F[133,x,k[0]] = F[132,x,k[0]]*F[69,x,k[0]]
F[133,x,k[0]] = F[63,x,k[0]]
F[134,x] = F[2,x]+F[28,x]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[15,x]
F[137,x,k[0]] = F[127,x,k[0]]+F[138,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[28,x]
F[139,x,k[0]] = (-F[140,x,1]*k[0]+F[140,x,k[0]])/(-1+k[0])
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]*F[69,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]+F[148,x,k[0]]+F[89,x]
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]*F[15,x]
F[145,x,k[0]] = F[146,x,k[0]]+F[150,x,k[0]]
F[146,x,k[0]] = F[12,x]*F[147,x,k[0]]
F[147,x,k[0]] = F[143,x,k[0]]+F[148,x,k[0]]+F[67,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[12,x]*F[147,x,k[0]]*F[15,x]
F[150,x,k[0]] = F[94,x,k[0]]^2*F[69,x,k[0]]
F[151,x,k[0]] = F[127,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]+F[166,x,k[0]]
F[154,x,k[0]] = F[128,x,k[0]]+F[153,x,k[0]]
F[155,x,k[0]] = F[154,x,k[0]]+F[162,x,k[0]]
F[156,x,k[0]] = F[155,x,k[0]]*F[20,x]
F[157,x,k[0]] = F[156,x,k[0]]+F[161,x,k[0]]
F[158,x,k[0]] = F[157,x,k[0]]+F[160,x,k[0]]
F[159,x,k[0]] = F[15,x]*F[158,x,k[0]]
F[159,x,k[0]] = F[128,x,k[0]]
F[160,x,k[0]] = F[18,x]*F[4,x]*F[67,x,k[0]]
F[161,x,k[0]] = F[18,x]*F[70,x,k[0]]*F[72,x,k[0]]
F[162,x,k[0]] = F[128,x,k[0]]+F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[69,x,k[0]]
F[165,x,k[0]] = F[163,x,k[0]]+F[18,x]
F[167,x,k[0]] = F[135,x,k[0]]+F[166,x,k[0]]
F[168,x,k[0]] = F[167,x,k[0]]+F[175,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]*F[20,x]
F[170,x,k[0]] = F[169,x,k[0]]+F[174,x,k[0]]
F[171,x,k[0]] = F[170,x,k[0]]+F[173,x,k[0]]
F[172,x,k[0]] = F[15,x]*F[171,x,k[0]]
F[172,x,k[0]] = F[135,x,k[0]]
F[173,x,k[0]] = F[18,x]*F[67,x,k[0]]*F[9,x]
F[174,x,k[0]] = F[107,x,k[0]]*F[18,x]*F[70,x,k[0]]
F[175,x,k[0]] = F[135,x,k[0]]+F[176,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = F[18,x]*F[2,x]*F[67,x,k[0]]
F[178,x] = F[179,x]
F[179,x] = F[15,x]*F[180,x]
F[180,x] = F[181,x]+F[40,x]
F[181,x] = F[182,x]*F[28,x]
F[182,x] = F[183,x]
F[183,x] = F[15,x]*F[184,x]
F[184,x] = F[185,x]+F[191,x]+F[89,x]
F[185,x] = F[186,x]
F[186,x] = F[15,x]*F[187,x]*F[190,x]
F[187,x] = F[188,x]+F[20,x]
F[188,x] = F[189,x]
F[189,x] = F[187,x]^2*F[15,x]
F[190,x] = F[185,x]+F[191,x]+F[20,x]
F[191,x] = F[192,x]
F[192,x] = F[12,x]*F[15,x]*F[190,x]
F[193,x] = F[194,x]+F[40,x]
F[194,x] = F[195,x]+F[49,x]
F[195,x] = F[196,x]
F[196,x] = F[197,x,1]
F[197,x,k[0]] = F[105,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{37}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{0}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{31}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{28}\! \left(x \right)
F_{37}\! \left(x \right) = F_{193}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{40}\! \left(x \right) = F_{178}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{48}\! \left(x \right) = F_{41}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{61}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = y x
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{89}\! \left(x \right) = 0
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{92}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = -\frac{y \left(F_{130}\! \left(x , 1\right)-F_{130}\! \left(x , y\right)\right)}{-1+y}
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{134}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{139}\! \left(x , y\right) = -\frac{F_{140}\! \left(x , 1\right) y -F_{140}\! \left(x , y\right)}{-1+y}
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{89}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{147}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{94}\! \left(x , y\right)^{2} F_{69}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{70}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{18}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{170}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{171}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{67}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{174}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{18}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{15}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{40}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{28}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{15}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{191}\! \left(x \right)+F_{89}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{15}\! \left(x \right) F_{187}\! \left(x \right) F_{190}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{20}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{187} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{190}\! \left(x \right) = F_{185}\! \left(x \right)+F_{191}\! \left(x \right)+F_{20}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{190}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{40}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{49}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x , 1\right)
F_{197}\! \left(x , y\right) = F_{105}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_37(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_21(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x)*F_2(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)**2*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x)*F_18(x))
Eq(F_17(x), F_0(x) - F_12(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_15(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_31(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_18(x)*F_2(x))
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), F_25(x) + F_28(x))
Eq(F_28(x), -F_0(x) + F_29(x))
Eq(F_29(x), F_30(x)/F_15(x))
Eq(F_30(x), F_2(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_15(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_31(x) + F_6(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_13(x)**2*F_28(x))
Eq(F_37(x), F_193(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_0(x)*F_18(x))
Eq(F_40(x), F_178(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_18(x)*F_4(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_18(x) + F_41(x))
Eq(F_48(x), F_41(x) + F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_15(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_76(x, k_0))
Eq(F_54(x, k_0), F_15(x)*F_53(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0)*F_69(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_22(x) + F_55(x, k_0))
Eq(F_59(x, k_0), F_13(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_60(x, k_0) + F_75(x, k_0))
Eq(F_62(x, k_0), F_61(x, k_0)*F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_15(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0) + F_71(x, k_0))
Eq(F_66(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0)*F_70(x, k_0))
Eq(F_69(x, k_0), k_0*x)
Eq(F_70(x, k_0), F_1(x) + F_67(x, k_0))
Eq(F_71(x, k_0), F_70(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_74(x, k_0))
Eq(F_73(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_74(x, k_0), F_50(x, k_0) + F_63(x, k_0))
Eq(F_75(x, k_0), F_2(x) + F_63(x, k_0))
Eq(F_76(x, k_0), F_123(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_103(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_67(x, k_0)*F_75(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0) + F_99(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_15(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_97(x, k_0))
Eq(F_84(x, k_0), F_63(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_2(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_69(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x) + F_90(x, k_0) + F_95(x, k_0))
Eq(F_89(x), 0)
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_15(x)*F_92(x, k_0)*F_94(x, k_0))
Eq(F_92(x, k_0), F_12(x) + F_93(x, k_0))
Eq(F_93(x, k_0), F_69(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_70(x, k_0) + F_90(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_12(x)*F_15(x)*F_94(x, k_0))
Eq(F_97(x, k_0), F_81(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_6(x)*F_86(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_69(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_80(x, k_0))
Eq(F_102(x, k_0), F_60(x, k_0)*F_86(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_80(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_114(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0) + F_81(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0) + F_112(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_70(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0) + F_111(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0)*F_15(x))
Eq(F_110(x, k_0), F_81(x, k_0))
Eq(F_111(x, k_0), F_67(x, k_0)*F_9(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_81(x, k_0))
Eq(F_113(x, k_0), F_2(x)*F_67(x, k_0))
Eq(F_115(x, k_0), F_114(x, k_0) + F_99(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0) + F_121(x, k_0))
Eq(F_117(x, k_0), F_116(x, k_0)*F_70(x, k_0))
Eq(F_118(x, k_0), F_117(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), F_118(x, k_0)*F_15(x))
Eq(F_119(x, k_0), F_99(x, k_0))
Eq(F_120(x, k_0), F_53(x, k_0)*F_67(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_99(x, k_0))
Eq(F_122(x, k_0), F_63(x, k_0)*F_67(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_151(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_127(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0))
Eq(F_126(x, k_0), F_0(x)*F_18(x)*F_67(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_135(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), -F_130(x, 1) + (-k_0*F_130(x, k_0) + F_130(x, 1))/(1 - k_0))
Eq(F_130(x, k_0), F_131(x, k_0)*F_15(x))
Eq(F_132(x, k_0), F_131(x, k_0) + F_134(x))
Eq(F_133(x, k_0), F_132(x, k_0)*F_69(x, k_0))
Eq(F_133(x, k_0), F_63(x, k_0))
Eq(F_134(x), F_2(x) + F_28(x))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_15(x))
Eq(F_137(x, k_0), F_127(x, k_0) + F_138(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_28(x))
Eq(F_139(x, k_0), -F_140(x, 1) - F_140(x, k_0) + (-k_0*F_140(x, k_0) + F_140(x, 1))/(1 - k_0))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0)*F_69(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_148(x, k_0) + F_89(x))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0)*F_15(x))
Eq(F_145(x, k_0), F_146(x, k_0) + F_150(x, k_0))
Eq(F_146(x, k_0), F_12(x)*F_147(x, k_0))
Eq(F_147(x, k_0), F_143(x, k_0) + F_148(x, k_0) + F_67(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_12(x)*F_147(x, k_0)*F_15(x))
Eq(F_150(x, k_0), F_69(x, k_0)*F_94(x, k_0)**2)
Eq(F_151(x, k_0), F_127(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_166(x, k_0))
Eq(F_154(x, k_0), F_128(x, k_0) + F_153(x, k_0))
Eq(F_155(x, k_0), F_154(x, k_0) + F_162(x, k_0))
Eq(F_156(x, k_0), F_155(x, k_0)*F_20(x))
Eq(F_157(x, k_0), F_156(x, k_0) + F_161(x, k_0))
Eq(F_158(x, k_0), F_157(x, k_0) + F_160(x, k_0))
Eq(F_159(x, k_0), F_15(x)*F_158(x, k_0))
Eq(F_159(x, k_0), F_128(x, k_0))
Eq(F_160(x, k_0), F_18(x)*F_4(x)*F_67(x, k_0))
Eq(F_161(x, k_0), F_18(x)*F_70(x, k_0)*F_72(x, k_0))
Eq(F_162(x, k_0), F_128(x, k_0) + F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_69(x, k_0))
Eq(F_165(x, k_0), F_163(x, k_0) + F_18(x))
Eq(F_167(x, k_0), F_135(x, k_0) + F_166(x, k_0))
Eq(F_168(x, k_0), F_167(x, k_0) + F_175(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0)*F_20(x))
Eq(F_170(x, k_0), F_169(x, k_0) + F_174(x, k_0))
Eq(F_171(x, k_0), F_170(x, k_0) + F_173(x, k_0))
Eq(F_172(x, k_0), F_15(x)*F_171(x, k_0))
Eq(F_172(x, k_0), F_135(x, k_0))
Eq(F_173(x, k_0), F_18(x)*F_67(x, k_0)*F_9(x))
Eq(F_174(x, k_0), F_107(x, k_0)*F_18(x)*F_70(x, k_0))
Eq(F_175(x, k_0), F_135(x, k_0) + F_176(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_18(x)*F_2(x)*F_67(x, k_0))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_15(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_40(x))
Eq(F_181(x), F_182(x)*F_28(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_15(x)*F_184(x))
Eq(F_184(x), F_185(x) + F_191(x) + F_89(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_15(x)*F_187(x)*F_190(x))
Eq(F_187(x), F_188(x) + F_20(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_15(x)*F_187(x)**2)
Eq(F_190(x), F_185(x) + F_191(x) + F_20(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_12(x)*F_15(x)*F_190(x))
Eq(F_193(x), F_194(x) + F_40(x))
Eq(F_194(x), F_195(x) + F_49(x))
Eq(F_195(x), F_196(x))
Eq(F_196(x), F_197(x, 1))
Eq(F_197(x, k_0), F_105(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 0], [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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], 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{"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "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, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: insertion_point_placements_tracked_fusion
Tree: http://permpal.com/tree/23994/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[36,x]+F[9,x]
F[9,x] = F[10,x]+F[26,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[0,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[15,x]
F[14,x] = x
F[15,x] = F[1,x]+F[12,x]
F[16,x] = F[17,x]*F[20,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]^2*F[14,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[20,x]+F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[14,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[12,x]*F[2,x]
F[29,x] = F[18,x]*F[20,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[30,x]+F[6,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[23,x]
F[36,x] = F[192,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[0,x]*F[12,x]
F[39,x] = F[177,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[12,x]*F[4,x]
F[44,x] = F[15,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[12,x]+F[40,x]
F[47,x] = F[40,x]+F[48,x]
F[48,x] = F[49,x,1]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[14,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[75,x,k[0]]
F[53,x,k[0]] = F[14,x]*F[52,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[68,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[27,x]+F[54,x,k[0]]
F[58,x,k[0]] = F[18,x]*F[59,x,k[0]]
F[60,x,k[0]] = F[59,x,k[0]]+F[74,x,k[0]]
F[61,x,k[0]] = F[60,x,k[0]]*F[68,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[14,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[70,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[69,x,k[0]]
F[68,x,k[0]] = k[0]*x
F[69,x,k[0]] = F[1,x]+F[66,x,k[0]]
F[70,x,k[0]] = F[69,x,k[0]]*F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[73,x,k[0]]
F[72,x,k[0]] = F[62,x,k[0]]+F[66,x,k[0]]
F[73,x,k[0]] = F[49,x,k[0]]+F[62,x,k[0]]
F[74,x,k[0]] = F[2,x]+F[62,x,k[0]]
F[75,x,k[0]] = F[122,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[102,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[66,x,k[0]]*F[74,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[98,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[14,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[96,x,k[0]]
F[83,x,k[0]] = F[62,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[2,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[68,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x]+F[89,x,k[0]]+F[94,x,k[0]]
F[88,x] = 0
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[14,x]*F[91,x,k[0]]*F[93,x,k[0]]
F[91,x,k[0]] = F[17,x]+F[92,x,k[0]]
F[92,x,k[0]] = F[68,x,k[0]]*F[93,x,k[0]]
F[93,x,k[0]] = F[69,x,k[0]]+F[89,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]
F[95,x,k[0]] = F[14,x]*F[17,x]*F[93,x,k[0]]
F[96,x,k[0]] = F[80,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[6,x]*F[85,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[68,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[79,x,k[0]]
F[101,x,k[0]] = F[59,x,k[0]]*F[85,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[79,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[113,x,k[0]]
F[105,x,k[0]] = F[104,x,k[0]]+F[80,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]+F[111,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]*F[69,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]+F[110,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]*F[14,x]
F[109,x,k[0]] = F[80,x,k[0]]
F[110,x,k[0]] = F[66,x,k[0]]*F[9,x]
F[111,x,k[0]] = F[112,x,k[0]]+F[80,x,k[0]]
F[112,x,k[0]] = F[2,x]*F[66,x,k[0]]
F[114,x,k[0]] = F[113,x,k[0]]+F[98,x,k[0]]
F[115,x,k[0]] = F[114,x,k[0]]+F[120,x,k[0]]
F[116,x,k[0]] = F[115,x,k[0]]*F[69,x,k[0]]
F[117,x,k[0]] = F[116,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = F[117,x,k[0]]*F[14,x]
F[118,x,k[0]] = F[98,x,k[0]]
F[119,x,k[0]] = F[52,x,k[0]]*F[66,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[98,x,k[0]]
F[121,x,k[0]] = F[62,x,k[0]]*F[66,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[150,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[126,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[0,x]*F[12,x]*F[66,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[134,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = -k[0]*(F[129,x,1]-F[129,x,k[0]])/(-1+k[0])
F[129,x,k[0]] = F[130,x,k[0]]*F[14,x]
F[131,x,k[0]] = F[130,x,k[0]]+F[133,x]
F[132,x,k[0]] = F[131,x,k[0]]*F[68,x,k[0]]
F[132,x,k[0]] = F[62,x,k[0]]
F[133,x] = F[2,x]+F[23,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[14,x]
F[136,x,k[0]] = F[126,x,k[0]]+F[137,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]*F[23,x]
F[138,x,k[0]] = (-F[139,x,1]*k[0]+F[139,x,k[0]])/(-1+k[0])
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[68,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[147,x,k[0]]+F[88,x]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[14,x]*F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]+F[149,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]*F[17,x]
F[146,x,k[0]] = F[142,x,k[0]]+F[147,x,k[0]]+F[66,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[14,x]*F[146,x,k[0]]*F[17,x]
F[149,x,k[0]] = F[93,x,k[0]]^2*F[68,x,k[0]]
F[150,x,k[0]] = F[126,x,k[0]]+F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]+F[165,x,k[0]]
F[153,x,k[0]] = F[127,x,k[0]]+F[152,x,k[0]]
F[154,x,k[0]] = F[153,x,k[0]]+F[161,x,k[0]]
F[155,x,k[0]] = F[15,x]*F[154,x,k[0]]
F[156,x,k[0]] = F[155,x,k[0]]+F[160,x,k[0]]
F[157,x,k[0]] = F[156,x,k[0]]+F[159,x,k[0]]
F[158,x,k[0]] = F[14,x]*F[157,x,k[0]]
F[158,x,k[0]] = F[127,x,k[0]]
F[159,x,k[0]] = F[12,x]*F[4,x]*F[66,x,k[0]]
F[160,x,k[0]] = F[12,x]*F[69,x,k[0]]*F[71,x,k[0]]
F[161,x,k[0]] = F[127,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[68,x,k[0]]
F[164,x,k[0]] = F[12,x]+F[162,x,k[0]]
F[166,x,k[0]] = F[134,x,k[0]]+F[165,x,k[0]]
F[167,x,k[0]] = F[166,x,k[0]]+F[174,x,k[0]]
F[168,x,k[0]] = F[15,x]*F[167,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]+F[173,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]+F[172,x,k[0]]
F[171,x,k[0]] = F[14,x]*F[170,x,k[0]]
F[171,x,k[0]] = F[134,x,k[0]]
F[172,x,k[0]] = F[12,x]*F[66,x,k[0]]*F[9,x]
F[173,x,k[0]] = F[106,x,k[0]]*F[12,x]*F[69,x,k[0]]
F[174,x,k[0]] = F[134,x,k[0]]+F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]
F[176,x,k[0]] = F[12,x]*F[2,x]*F[66,x,k[0]]
F[177,x] = F[178,x]
F[178,x] = F[14,x]*F[179,x]
F[179,x] = F[180,x]+F[39,x]
F[180,x] = F[181,x]*F[23,x]
F[181,x] = F[182,x]
F[182,x] = F[14,x]*F[183,x]
F[183,x] = F[184,x]+F[190,x]+F[88,x]
F[184,x] = F[185,x]
F[185,x] = F[14,x]*F[186,x]*F[189,x]
F[186,x] = F[15,x]+F[187,x]
F[187,x] = F[188,x]
F[188,x] = F[186,x]^2*F[14,x]
F[189,x] = F[15,x]+F[184,x]+F[190,x]
F[190,x] = F[191,x]
F[191,x] = F[14,x]*F[17,x]*F[189,x]
F[192,x] = F[193,x]+F[39,x]
F[193,x] = F[194,x]+F[48,x]
F[194,x] = F[195,x]
F[195,x] = F[196,x,1]
F[196,x,k[0]] = F[104,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{36}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{23}\! \left(x \right)
F_{36}\! \left(x \right) = F_{192}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = F_{177}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right)+F_{40}\! \left(x \right)
F_{47}\! \left(x \right) = F_{40}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{53}\! \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_{56}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = y x
F_{69}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{66}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{88}\! \left(x \right) = 0
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{91}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{89}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{66}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{62}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = -\frac{y \left(F_{129}\! \left(x , 1\right)-F_{129}\! \left(x , y\right)\right)}{-1+y}
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{133}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{133}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{138}\! \left(x , y\right) = -\frac{F_{139}\! \left(x , 1\right) y -F_{139}\! \left(x , y\right)}{-1+y}
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{147}\! \left(x , y\right)+F_{88}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{147}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{146}\! \left(x , y\right) F_{17}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{93}\! \left(x , y\right)^{2} F_{68}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{154}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{159}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{157}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{127}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{69}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{162}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{170}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{66}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{12}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{14}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{39}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{23}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{14}\! \left(x \right) F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{190}\! \left(x \right)+F_{88}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{14}\! \left(x \right) F_{186}\! \left(x \right) F_{189}\! \left(x \right)
F_{186}\! \left(x \right) = F_{15}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{186} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{189}\! \left(x \right) = F_{15}\! \left(x \right)+F_{184}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{189}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{39}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{48}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x , 1\right)
F_{196}\! \left(x , y\right) = F_{104}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_36(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_26(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_0(x)*F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_1(x) + F_12(x))
Eq(F_16(x), F_17(x)*F_20(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_17(x)**2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_20(x) + F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_14(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_12(x)*F_2(x))
Eq(F_29(x), F_18(x)*F_20(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_30(x) + F_6(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_18(x)**2*F_23(x))
Eq(F_36(x), F_192(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_0(x)*F_12(x))
Eq(F_39(x), F_177(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_12(x)*F_4(x))
Eq(F_44(x), F_15(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_12(x) + F_40(x))
Eq(F_47(x), F_40(x) + F_48(x))
Eq(F_48(x), F_49(x, 1))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_14(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_75(x, k_0))
Eq(F_53(x, k_0), F_14(x)*F_52(x, k_0))
Eq(F_53(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_56(x, k_0)*F_68(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_27(x) + F_54(x, k_0))
Eq(F_58(x, k_0), F_18(x)*F_59(x, k_0))
Eq(F_60(x, k_0), F_59(x, k_0) + F_74(x, k_0))
Eq(F_61(x, k_0), F_60(x, k_0)*F_68(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_14(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_70(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_69(x, k_0))
Eq(F_68(x, k_0), k_0*x)
Eq(F_69(x, k_0), F_1(x) + F_66(x, k_0))
Eq(F_70(x, k_0), F_69(x, k_0)*F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_73(x, k_0))
Eq(F_72(x, k_0), F_62(x, k_0) + F_66(x, k_0))
Eq(F_73(x, k_0), F_49(x, k_0) + F_62(x, k_0))
Eq(F_74(x, k_0), F_2(x) + F_62(x, k_0))
Eq(F_75(x, k_0), F_122(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_102(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_66(x, k_0)*F_74(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_98(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_14(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_96(x, k_0))
Eq(F_83(x, k_0), F_62(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_2(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_68(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x) + F_89(x, k_0) + F_94(x, k_0))
Eq(F_88(x), 0)
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_14(x)*F_91(x, k_0)*F_93(x, k_0))
Eq(F_91(x, k_0), F_17(x) + F_92(x, k_0))
Eq(F_92(x, k_0), F_68(x, k_0)*F_93(x, k_0))
Eq(F_93(x, k_0), F_69(x, k_0) + F_89(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0))
Eq(F_95(x, k_0), F_14(x)*F_17(x)*F_93(x, k_0))
Eq(F_96(x, k_0), F_80(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_6(x)*F_85(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_68(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_79(x, k_0))
Eq(F_101(x, k_0), F_59(x, k_0)*F_85(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_79(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_113(x, k_0))
Eq(F_105(x, k_0), F_104(x, k_0) + F_80(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0) + F_111(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0)*F_69(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0) + F_110(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0)*F_14(x))
Eq(F_109(x, k_0), F_80(x, k_0))
Eq(F_110(x, k_0), F_66(x, k_0)*F_9(x))
Eq(F_111(x, k_0), F_112(x, k_0) + F_80(x, k_0))
Eq(F_112(x, k_0), F_2(x)*F_66(x, k_0))
Eq(F_114(x, k_0), F_113(x, k_0) + F_98(x, k_0))
Eq(F_115(x, k_0), F_114(x, k_0) + F_120(x, k_0))
Eq(F_116(x, k_0), F_115(x, k_0)*F_69(x, k_0))
Eq(F_117(x, k_0), F_116(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), F_117(x, k_0)*F_14(x))
Eq(F_118(x, k_0), F_98(x, k_0))
Eq(F_119(x, k_0), F_52(x, k_0)*F_66(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_98(x, k_0))
Eq(F_121(x, k_0), F_62(x, k_0)*F_66(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_150(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_126(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_0(x)*F_12(x)*F_66(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_134(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), -F_129(x, 1) + (-k_0*F_129(x, k_0) + F_129(x, 1))/(1 - k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_14(x))
Eq(F_131(x, k_0), F_130(x, k_0) + F_133(x))
Eq(F_132(x, k_0), F_131(x, k_0)*F_68(x, k_0))
Eq(F_132(x, k_0), F_62(x, k_0))
Eq(F_133(x), F_2(x) + F_23(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_14(x))
Eq(F_136(x, k_0), F_126(x, k_0) + F_137(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0)*F_23(x))
Eq(F_138(x, k_0), -F_139(x, 1) - F_139(x, k_0) + (-k_0*F_139(x, k_0) + F_139(x, 1))/(1 - k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_68(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_147(x, k_0) + F_88(x))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_14(x)*F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_149(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0)*F_17(x))
Eq(F_146(x, k_0), F_142(x, k_0) + F_147(x, k_0) + F_66(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_14(x)*F_146(x, k_0)*F_17(x))
Eq(F_149(x, k_0), F_68(x, k_0)*F_93(x, k_0)**2)
Eq(F_150(x, k_0), F_126(x, k_0) + F_151(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0) + F_165(x, k_0))
Eq(F_153(x, k_0), F_127(x, k_0) + F_152(x, k_0))
Eq(F_154(x, k_0), F_153(x, k_0) + F_161(x, k_0))
Eq(F_155(x, k_0), F_15(x)*F_154(x, k_0))
Eq(F_156(x, k_0), F_155(x, k_0) + F_160(x, k_0))
Eq(F_157(x, k_0), F_156(x, k_0) + F_159(x, k_0))
Eq(F_158(x, k_0), F_14(x)*F_157(x, k_0))
Eq(F_158(x, k_0), F_127(x, k_0))
Eq(F_159(x, k_0), F_12(x)*F_4(x)*F_66(x, k_0))
Eq(F_160(x, k_0), F_12(x)*F_69(x, k_0)*F_71(x, k_0))
Eq(F_161(x, k_0), F_127(x, k_0) + F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_68(x, k_0))
Eq(F_164(x, k_0), F_12(x) + F_162(x, k_0))
Eq(F_166(x, k_0), F_134(x, k_0) + F_165(x, k_0))
Eq(F_167(x, k_0), F_166(x, k_0) + F_174(x, k_0))
Eq(F_168(x, k_0), F_15(x)*F_167(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0) + F_173(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0) + F_172(x, k_0))
Eq(F_171(x, k_0), F_14(x)*F_170(x, k_0))
Eq(F_171(x, k_0), F_134(x, k_0))
Eq(F_172(x, k_0), F_12(x)*F_66(x, k_0)*F_9(x))
Eq(F_173(x, k_0), F_106(x, k_0)*F_12(x)*F_69(x, k_0))
Eq(F_174(x, k_0), F_134(x, k_0) + F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_176(x, k_0), F_12(x)*F_2(x)*F_66(x, k_0))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_14(x)*F_179(x))
Eq(F_179(x), F_180(x) + F_39(x))
Eq(F_180(x), F_181(x)*F_23(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_14(x)*F_183(x))
Eq(F_183(x), F_184(x) + F_190(x) + F_88(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_14(x)*F_186(x)*F_189(x))
Eq(F_186(x), F_15(x) + F_187(x))
Eq(F_187(x), F_188(x))
Eq(F_188(x), F_14(x)*F_186(x)**2)
Eq(F_189(x), F_15(x) + F_184(x) + F_190(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_14(x)*F_17(x)*F_189(x))
Eq(F_192(x), F_193(x) + F_39(x))
Eq(F_193(x), F_194(x) + F_48(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_196(x, 1))
Eq(F_196(x, k_0), F_104(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[1, 0], [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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], 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