0213_3120
Counting sequence:
1, 1, 2, 6, 22, 86, 336, 1282, 4758, 17234, 61242, 214594, 744594, 2566594, 8809442, 30157826, 103082050, 352045314, 1201795970, 4101913602, 13999868162, 47782800386, 163095158274, 556717514754, 1900427035650, 6487635578882, 22148113283074, 75613356769282, 258148040151042, 881343770902530, 3009028235452418, 10273307556839426, 35074902368206850, 119752373736374274, 408858279849197570, 1395925185058308098, 4765977016529387522, 16272041667182985218, 55556176927315066882, 189680545141337620482, 647609651544774148098, 2211077129967840002050, 7549088369195785650178, 25774197360871834910722, 87998608652295908360194, 300446031060560615833602, 1025786887759968834945026, 3502255447348418485157890, 11957447923960073397731330, 40825280607066460178612226, 139386226162249800387395586, 475894342535835205578522626, 1624804915889048781211041794, 5547430974349094355854163970, 18940114056770395443071811586, 64665594259481785424504946690, 220782148884065623348028112898, 753797406931406270449892458498, 2573625329774764783822583103490, 8786906504848000277714191777794, 30000375359018565012981932883970, 102427688424631871647396126523394, 349710002976792793183158406217730, 1193984635050087162872093128785922, 4076518534230240547039534978695170, 13918104866785914292742605749878786, 47519382398609640437484519128301570, 162241319860711817407721852198977538, 553926514645301924107671480504942594, 1891223418859098359244534286169145346, 6457040646144348787370173025428176898, 22045715746856173460111440342262218754, 75268781695129650290596154053083791362, 256983695286792951335779491737243746306, 877397217756884638667606055425107034114, 2995621480453894321328068832368261070850, 10227691486301685991471878832729798737922, 34919522984298700258772904910905390661634, 119222708964590896208648133864613922996226, 407051789889765071878619089000061210722306, 1389761741629876174035164291908915884457986, 4744943386739969712448900162467640180211714, 16200250063700116415203811838846038437789698, 55311113481320505227204553767423075346808834, 188843953797881744344310141013175200341032962, 644753588228885875929402865763945928886059010, 2201326445319779825805504043308445631502090242, 7515798604821347158065791398117810519425417218, 25660541528645828163592388764389535314480201730, 87610568904940616641641148420708853469820223490, 299121192562470806718098060033019819433352232962, 1021263632440001986284025771467632568614036439042, 3486812144635066316551853675088934901786307723266, 11904721313660261262241489941025374557650670321666, 40645260965370912350810360259535823051493436555266, 138771601234163126744035922560743178533950514528258, 473795883005910681995624982393219175140241690329090, 1617640329555316473917290534616231776292894826037250, 5522969552209444530484072510352610866904978100846594, 18856597549727145171633117884558531684294480346742786, 64380451094489691620461715938960224604993360607838210
Generating function in Maple syntax:
(6*x^7-58*x^6+168*x^5-218*x^4+152*x^3-59*x^2+12*x-1)/(x-1)/(2*x^2-4*x+1)/(2*x-1)^4
Generating function in latex syntax:
\frac{6 x^{7}-58 x^{6}+168 x^{5}-218 x^{4}+152 x^{3}-59 x^{2}+12 x -1}{\left(x -1\right) \left(2 x^{2}-4 x +1\right) \left(2 x -1\right)^{4}}
Generating function in sympy syntax:
(6*x**7 - 58*x**6 + 168*x**5 - 218*x**4 + 152*x**3 - 59*x**2 + 12*x - 1)/((x - 1)*(2*x - 1)**4*(2*x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x^2-4*x+1)*(2*x-1)^4*F(x)-6*x^7+58*x^6-168*x^5+218*x^4-152*x^3+59*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x^{2}-4 x +1\right) \left(2 x -1\right)^{4} F \! \left(x \right)-6 x^{7}+58 x^{6}-168 x^{5}+218 x^{4}-152 x^{3}+59 x^{2}-12 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/96*(12*2^(1/2)+12)*(1-1/2*2^(1/2))^(-n)+1/96*(-12*2^(1/2)+12)*(1+1/2*2^(1/2))^(-n)+2+1/96*(n^3-18*n^2+59*n-138)*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(12 \sqrt{2}+12\right) \left(1-\frac{\sqrt{2}}{2}\right)^{-n}}{96}+\frac{\left(-12 \sqrt{2}+12\right) \left(1+\frac{\sqrt{2}}{2}\right)^{-n}}{96}+2+\\\frac{\left(n^{3}-18 n^{2}+59 n -138\right) 2^{n}}{96} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 86
a(6) = 336
a(7) = 1282
a(n+6) = -32*a(n)+128*a(n+1)-192*a(n+2)+144*a(n+3)-58*a(n+4)+12*a(n+5)-2, n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 86
a \! \left(6\right) = 336
a \! \left(7\right) = 1282
a \! \left(n +6\right) = -32 a \! \left(n \right)+128 a \! \left(n +1\right)-192 a \! \left(n +2\right)+144 a \! \left(n +3\right)-58 a \! \left(n +4\right)+12 a \! \left(n +5\right)-2, \quad n \geq 8
Specification 1
Strategy pack name: point_and_row_placements
Tree: http://permpal.com/tree/128/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[59,x]
F[4,x] = F[13,x]*F[5,x]
F[5,x] = F[3,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[50,x]+F[9,x]
F[9,x] = F[10,x]+F[49,x]
F[10,x] = F[11,x]+F[42,x]
F[11,x] = F[1,x]+F[12,x]+F[14,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[13,x]*F[15,x]
F[15,x] = F[11,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[11,x]+F[17,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[13,x]*F[21,x]*F[35,x]
F[21,x] = F[11,x]+F[22,x]
F[22,x] = F[23,x]*F[29,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]*F[25,x]*F[26,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[26,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[13,x]*F[29,x]*F[32,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[32,x]
F[35,x] = F[26,x]+F[36,x]
F[36,x] = F[33,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[41,x]
F[38,x] = 0
F[39,x] = F[13,x]*F[40,x]
F[40,x] = F[27,x]+F[37,x]
F[41,x] = F[13,x]*F[36,x]
F[42,x] = F[43,x]
F[43,x] = F[13,x]*F[44,x]
F[44,x] = F[11,x]+F[43,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[13,x]*F[35,x]*F[47,x]
F[47,x] = F[11,x]+F[48,x]
F[48,x] = F[25,x]*F[30,x]
F[49,x] = F[7,x]
F[50,x] = F[51,x]*F[54,x]
F[51,x] = F[10,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[32,x]^2*F[13,x]*F[25,x]*F[29,x]
F[54,x] = F[55,x]
F[55,x] = F[13,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[1,x]+F[54,x]
F[58,x] = F[54,x]
F[59,x] = F[13,x]*F[60,x]
F[60,x] = F[3,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[13,x]*F[63,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[15,x]+F[65,x]
F[65,x] = F[62,x]
F[66,x] = F[54,x]*F[67,x]
F[67,x] = F[15,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[26,x]^2*F[13,x]*F[25,x]*F[29,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_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{59}\! \left(x \right)
F_{4}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{50}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right) F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{25}\! \left(x \right) F_{30}\! \left(x \right)
F_{49}\! \left(x \right) = F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{10}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{13}\! \left(x \right) F_{25}\! \left(x \right) F_{29}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{1}\! \left(x \right)+F_{54}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{13}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{3}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{13}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{54}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{26} \left(x \right)^{2} F_{13}\! \left(x \right) F_{25}\! \left(x \right) F_{29}\! \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_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_59(x))
Eq(F_4(x), F_13(x)*F_5(x))
Eq(F_5(x), F_3(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_50(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_49(x))
Eq(F_10(x), F_11(x) + F_42(x))
Eq(F_11(x), F_1(x) + F_12(x) + F_14(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_13(x)*F_15(x))
Eq(F_15(x), F_11(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_13(x)*F_18(x))
Eq(F_18(x), F_11(x) + F_17(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_13(x)*F_21(x)*F_35(x))
Eq(F_21(x), F_11(x) + F_22(x))
Eq(F_22(x), F_23(x)*F_29(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)*F_25(x)*F_26(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_26(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_13(x)*F_29(x)*F_32(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_32(x))
Eq(F_35(x), F_26(x) + F_36(x))
Eq(F_36(x), F_33(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_41(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_27(x) + F_37(x))
Eq(F_41(x), F_13(x)*F_36(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_13(x)*F_44(x))
Eq(F_44(x), F_11(x) + F_43(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_13(x)*F_35(x)*F_47(x))
Eq(F_47(x), F_11(x) + F_48(x))
Eq(F_48(x), F_25(x)*F_30(x))
Eq(F_49(x), F_7(x))
Eq(F_50(x), F_51(x)*F_54(x))
Eq(F_51(x), F_10(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)*F_25(x)*F_29(x)*F_32(x)**2)
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_13(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_1(x) + F_54(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_13(x)*F_60(x))
Eq(F_60(x), F_3(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_13(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_15(x) + F_65(x))
Eq(F_65(x), F_62(x))
Eq(F_66(x), F_54(x)*F_67(x))
Eq(F_67(x), F_15(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_13(x)*F_25(x)*F_26(x)**2*F_29(x))
Pack JSON:
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Specification JSON:
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"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "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"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "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}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 2]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "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"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "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}}]}, {"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 2
Strategy pack name: insertion_row_placements
Tree: http://permpal.com/tree/129/
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[12,x]*F[4,x]
F[4,x] = F[33,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[19,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[14,x]
F[18,x] = F[14,x]
F[19,x] = F[20,x]+F[21,x]+F[22,x]
F[20,x] = 0
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[17,x]*F[24,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[32,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[25,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[1,x]+F[31,x]
F[31,x] = F[12,x]*F[30,x]
F[32,x] = F[12,x]*F[24,x]
F[33,x] = F[34,x]+F[56,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[30,x]+F[41,x]
F[41,x] = F[10,x]+F[42,x]
F[42,x] = F[20,x]+F[43,x]+F[45,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[28,x]+F[42,x]
F[45,x] = F[12,x]*F[41,x]
F[46,x] = F[20,x]+F[47,x]+F[55,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[28,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[49,x]
F[52,x] = F[46,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[28,x]^2*F[38,x]
F[55,x] = F[12,x]*F[37,x]
F[56,x] = F[158,x]+F[20,x]+F[57,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[99,x]
F[59,x] = F[6,x]+F[60,x]
F[60,x] = F[20,x]+F[61,x]+F[82,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[14,x]+F[64,x]
F[64,x] = F[20,x]+F[65,x]+F[66,x]
F[65,x] = F[12,x]*F[63,x]
F[66,x] = F[67,x]
F[67,x] = F[12,x]^2*F[17,x]*F[9,x]
F[68,x] = F[19,x]+F[69,x]
F[69,x] = F[20,x]+F[70,x]+F[72,x]+F[74,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[64,x]+F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[14,x]*F[24,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[17,x]*F[76,x]
F[76,x] = F[25,x]+F[77,x]
F[77,x] = 2*F[20,x]+F[78,x]+F[80,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[50,x]+F[77,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[25,x]+F[77,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[10,x]+F[19,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[10,x]+F[86,x]
F[89,x] = 2*F[20,x]+F[90,x]+F[92,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[19,x]+F[89,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[17,x]*F[94,x]
F[94,x] = F[86,x]+F[95,x]
F[95,x] = 2*F[20,x]+F[96,x]+F[98,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[25,x]+F[95,x]
F[98,x] = F[12,x]*F[94,x]
F[99,x] = F[100,x]+F[56,x]
F[100,x] = 2*F[20,x]+F[101,x]+F[144,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[137,x]
F[103,x] = F[104,x]+F[133,x]
F[104,x] = F[105,x]+F[118,x]+F[20,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[107,x]+F[13,x]
F[107,x] = F[104,x]+F[108,x]
F[108,x] = 2*F[20,x]+F[109,x]+F[110,x]
F[109,x] = F[107,x]*F[12,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[116,x]
F[113,x] = F[108,x]+F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[10,x]*F[38,x]
F[116,x] = F[117,x]
F[117,x] = F[10,x]^2*F[17,x]*F[38,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[104,x]+F[38,x]
F[121,x] = F[122,x]+F[46,x]
F[122,x] = 2*F[20,x]+F[123,x]+F[131,x]
F[123,x] = F[124,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[127,x]
F[127,x] = F[14,x]*F[28,x]*F[30,x]
F[128,x] = F[122,x]+F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[28,x]^2*F[14,x]*F[38,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[104,x]+F[122,x]
F[133,x] = 2*F[20,x]+F[134,x]+F[135,x]
F[134,x] = F[103,x]*F[12,x]
F[135,x] = F[136,x]
F[136,x] = F[12,x]^2*F[17,x]*F[38,x]*F[9,x]
F[137,x] = F[108,x]+F[138,x]
F[138,x] = 2*F[20,x]+F[139,x]+F[141,x]+F[142,x]
F[139,x] = F[12,x]*F[140,x]
F[140,x] = F[133,x]+F[138,x]
F[141,x] = F[12,x]*F[137,x]
F[142,x] = F[143,x]
F[143,x] = F[12,x]^2*F[10,x]*F[17,x]*F[38,x]*F[9,x]
F[144,x] = F[145,x]
F[145,x] = F[12,x]*F[146,x]
F[146,x] = F[113,x]+F[147,x]
F[147,x] = F[148,x]+F[150,x]
F[148,x] = F[149,x]
F[149,x] = F[10,x]^2*F[38,x]
F[150,x] = 3*F[20,x]+F[151,x]+F[153,x]
F[151,x] = F[12,x]*F[152,x]
F[152,x] = F[108,x]+F[150,x]
F[153,x] = F[154,x]
F[154,x] = F[12,x]*F[155,x]
F[155,x] = F[147,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[10,x]^3*F[17,x]*F[38,x]
F[158,x] = F[12,x]*F[159,x]
F[159,x] = F[160,x]+F[33,x]
F[160,x] = F[161,x]+F[182,x]
F[161,x] = F[162,x]+F[174,x]+F[20,x]
F[162,x] = F[163,x]
F[163,x] = F[12,x]*F[164,x]*F[165,x]
F[164,x] = F[1,x]+F[38,x]
F[165,x] = F[166,x]+F[169,x]
F[166,x] = F[167,x]
F[167,x] = F[12,x]*F[168,x]
F[168,x] = F[24,x]+F[30,x]
F[169,x] = F[170,x]+F[172,x]+F[20,x]
F[170,x] = F[12,x]*F[171,x]
F[171,x] = F[49,x]+F[81,x]
F[172,x] = F[12,x]*F[173,x]
F[173,x] = F[24,x]+F[94,x]
F[174,x] = F[175,x]
F[175,x] = F[12,x]*F[176,x]
F[176,x] = F[161,x]+F[177,x]
F[177,x] = F[178,x]+F[180,x]
F[178,x] = F[179,x]*F[38,x]
F[179,x] = F[1,x]+F[166,x]
F[180,x] = F[181,x]
F[181,x] = F[12,x]*F[166,x]*F[30,x]*F[38,x]
F[182,x] = 2*F[20,x]+F[183,x]+F[197,x]
F[183,x] = F[184,x]
F[184,x] = F[12,x]*F[185,x]
F[185,x] = F[126,x]+F[186,x]
F[186,x] = F[122,x]+F[187,x]
F[187,x] = 3*F[20,x]+F[188,x]+F[196,x]
F[188,x] = F[189,x]
F[189,x] = F[12,x]*F[190,x]
F[190,x] = F[191,x]+F[193,x]
F[191,x] = F[192,x]
F[192,x] = F[28,x]^2*F[14,x]*F[30,x]
F[193,x] = F[187,x]+F[194,x]
F[194,x] = F[195,x]
F[195,x] = F[28,x]^3*F[14,x]*F[38,x]
F[196,x] = F[12,x]*F[186,x]
F[197,x] = F[12,x]*F[198,x]
F[198,x] = F[132,x]+F[199,x]
F[199,x] = F[200,x]+F[205,x]
F[200,x] = 2*F[20,x]+F[201,x]+F[203,x]
F[201,x] = F[202,x]
F[202,x] = F[12,x]^2*F[14,x]*F[164,x]*F[30,x]
F[203,x] = F[12,x]*F[204,x]
F[204,x] = F[104,x]+F[200,x]
F[205,x] = 2*F[20,x]+F[206,x]+F[208,x]+F[210,x]
F[206,x] = F[207,x]
F[207,x] = F[12,x]^2*F[14,x]*F[164,x]*F[28,x]*F[30,x]
F[208,x] = F[12,x]*F[209,x]
F[209,x] = F[122,x]+F[205,x]
F[210,x] = F[12,x]*F[199,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{33}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{32}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \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_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{56}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{28}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{38}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{56}\! \left(x \right) = F_{158}\! \left(x \right)+F_{20}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{99}\! \left(x \right)
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right)+F_{61}\! \left(x \right)+F_{82}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right)+F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{17}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{50}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{10}\! \left(x \right)+F_{19}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{10}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{19}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{86}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{25}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{56}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{101}\! \left(x \right)+F_{144}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{137}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{133}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{118}\! \left(x \right)+F_{20}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{13}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{10}\! \left(x \right) F_{38}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{10} \left(x \right)^{2} F_{17}\! \left(x \right) F_{38}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{104}\! \left(x \right)+F_{38}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{46}\! \left(x \right)
F_{122}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{123}\! \left(x \right)+F_{131}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{30}\! \left(x \right)
F_{128}\! \left(x \right) = F_{122}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{104}\! \left(x \right)+F_{122}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{17}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{137}\! \left(x \right) = F_{108}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{139}\! \left(x \right)+F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{133}\! \left(x \right)+F_{138}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{10}\! \left(x \right) F_{17}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{113}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{150}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{10} \left(x \right)^{2} F_{38}\! \left(x \right)
F_{150}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{151}\! \left(x \right)+F_{153}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{108}\! \left(x \right)+F_{150}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{147}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{10} \left(x \right)^{3} F_{17}\! \left(x \right) F_{38}\! \left(x \right)
F_{158}\! \left(x \right) = F_{12}\! \left(x \right) F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{33}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{182}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{174}\! \left(x \right)+F_{20}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{12}\! \left(x \right) F_{164}\! \left(x \right) F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{169}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{12}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{172}\! \left(x \right)+F_{20}\! \left(x \right)
F_{170}\! \left(x \right) = F_{12}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{49}\! \left(x \right)+F_{81}\! \left(x \right)
F_{172}\! \left(x \right) = F_{12}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{24}\! \left(x \right)+F_{94}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{12}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{161}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{180}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{38}\! \left(x \right)
F_{179}\! \left(x \right) = F_{1}\! \left(x \right)+F_{166}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{12}\! \left(x \right) F_{166}\! \left(x \right) F_{30}\! \left(x \right) F_{38}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{183}\! \left(x \right)+F_{197}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{12}\! \left(x \right) F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{126}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{122}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{188}\! \left(x \right)+F_{196}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{12}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{193}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{14}\! \left(x \right) F_{30}\! \left(x \right)
F_{193}\! \left(x \right) = F_{187}\! \left(x \right)+F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{28} \left(x \right)^{3} F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{196}\! \left(x \right) = F_{12}\! \left(x \right) F_{186}\! \left(x \right)
F_{197}\! \left(x \right) = F_{12}\! \left(x \right) F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{132}\! \left(x \right)+F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{205}\! \left(x \right)
F_{200}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{14}\! \left(x \right) F_{164}\! \left(x \right) F_{30}\! \left(x \right)
F_{203}\! \left(x \right) = F_{12}\! \left(x \right) F_{204}\! \left(x \right)
F_{204}\! \left(x \right) = F_{104}\! \left(x \right)+F_{200}\! \left(x \right)
F_{205}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{206}\! \left(x \right)+F_{208}\! \left(x \right)+F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{14}\! \left(x \right) F_{164}\! \left(x \right) F_{28}\! \left(x \right) F_{30}\! \left(x \right)
F_{208}\! \left(x \right) = F_{12}\! \left(x \right) F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{122}\! \left(x \right)+F_{205}\! \left(x \right)
F_{210}\! \left(x \right) = F_{12}\! \left(x \right) F_{199}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_33(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_19(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_14(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_22(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_17(x)*F_24(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_32(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_25(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_1(x) + F_31(x))
Eq(F_31(x), F_12(x)*F_30(x))
Eq(F_32(x), F_12(x)*F_24(x))
Eq(F_33(x), F_34(x) + F_56(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_30(x) + F_41(x))
Eq(F_41(x), F_10(x) + F_42(x))
Eq(F_42(x), F_20(x) + F_43(x) + F_45(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_28(x) + F_42(x))
Eq(F_45(x), F_12(x)*F_41(x))
Eq(F_46(x), F_20(x) + F_47(x) + F_55(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_28(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_49(x))
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_28(x)**2*F_38(x))
Eq(F_55(x), F_12(x)*F_37(x))
Eq(F_56(x), F_158(x) + F_20(x) + F_57(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_99(x))
Eq(F_59(x), F_6(x) + F_60(x))
Eq(F_60(x), F_20(x) + F_61(x) + F_82(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_14(x) + F_64(x))
Eq(F_64(x), F_20(x) + F_65(x) + F_66(x))
Eq(F_65(x), F_12(x)*F_63(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_12(x)**2*F_17(x)*F_9(x))
Eq(F_68(x), F_19(x) + F_69(x))
Eq(F_69(x), F_20(x) + F_70(x) + F_72(x) + F_74(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_64(x) + F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_14(x)*F_24(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_17(x)*F_76(x))
Eq(F_76(x), F_25(x) + F_77(x))
Eq(F_77(x), 2*F_20(x) + F_78(x) + F_80(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_50(x) + F_77(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_25(x) + F_77(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_10(x) + F_19(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_10(x) + F_86(x))
Eq(F_89(x), 2*F_20(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_19(x) + F_89(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_17(x)*F_94(x))
Eq(F_94(x), F_86(x) + F_95(x))
Eq(F_95(x), 2*F_20(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_25(x) + F_95(x))
Eq(F_98(x), F_12(x)*F_94(x))
Eq(F_99(x), F_100(x) + F_56(x))
Eq(F_100(x), F_101(x) + F_144(x) + 2*F_20(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_137(x))
Eq(F_103(x), F_104(x) + F_133(x))
Eq(F_104(x), F_105(x) + F_118(x) + F_20(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_107(x) + F_13(x))
Eq(F_107(x), F_104(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_110(x) + 2*F_20(x))
Eq(F_109(x), F_107(x)*F_12(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_116(x))
Eq(F_113(x), F_108(x) + F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_10(x)*F_38(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_10(x)**2*F_17(x)*F_38(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_104(x) + F_38(x))
Eq(F_121(x), F_122(x) + F_46(x))
Eq(F_122(x), F_123(x) + F_131(x) + 2*F_20(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_14(x)*F_28(x)*F_30(x))
Eq(F_128(x), F_122(x) + F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_14(x)*F_28(x)**2*F_38(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_104(x) + F_122(x))
Eq(F_133(x), F_134(x) + F_135(x) + 2*F_20(x))
Eq(F_134(x), F_103(x)*F_12(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_12(x)**2*F_17(x)*F_38(x)*F_9(x))
Eq(F_137(x), F_108(x) + F_138(x))
Eq(F_138(x), F_139(x) + F_141(x) + F_142(x) + 2*F_20(x))
Eq(F_139(x), F_12(x)*F_140(x))
Eq(F_140(x), F_133(x) + F_138(x))
Eq(F_141(x), F_12(x)*F_137(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_10(x)*F_12(x)**2*F_17(x)*F_38(x)*F_9(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_12(x)*F_146(x))
Eq(F_146(x), F_113(x) + F_147(x))
Eq(F_147(x), F_148(x) + F_150(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_10(x)**2*F_38(x))
Eq(F_150(x), F_151(x) + F_153(x) + 3*F_20(x))
Eq(F_151(x), F_12(x)*F_152(x))
Eq(F_152(x), F_108(x) + F_150(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_12(x)*F_155(x))
Eq(F_155(x), F_147(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_10(x)**3*F_17(x)*F_38(x))
Eq(F_158(x), F_12(x)*F_159(x))
Eq(F_159(x), F_160(x) + F_33(x))
Eq(F_160(x), F_161(x) + F_182(x))
Eq(F_161(x), F_162(x) + F_174(x) + F_20(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_12(x)*F_164(x)*F_165(x))
Eq(F_164(x), F_1(x) + F_38(x))
Eq(F_165(x), F_166(x) + F_169(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_12(x)*F_168(x))
Eq(F_168(x), F_24(x) + F_30(x))
Eq(F_169(x), F_170(x) + F_172(x) + F_20(x))
Eq(F_170(x), F_12(x)*F_171(x))
Eq(F_171(x), F_49(x) + F_81(x))
Eq(F_172(x), F_12(x)*F_173(x))
Eq(F_173(x), F_24(x) + F_94(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_12(x)*F_176(x))
Eq(F_176(x), F_161(x) + F_177(x))
Eq(F_177(x), F_178(x) + F_180(x))
Eq(F_178(x), F_179(x)*F_38(x))
Eq(F_179(x), F_1(x) + F_166(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_12(x)*F_166(x)*F_30(x)*F_38(x))
Eq(F_182(x), F_183(x) + F_197(x) + 2*F_20(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_12(x)*F_185(x))
Eq(F_185(x), F_126(x) + F_186(x))
Eq(F_186(x), F_122(x) + F_187(x))
Eq(F_187(x), F_188(x) + F_196(x) + 3*F_20(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_12(x)*F_190(x))
Eq(F_190(x), F_191(x) + F_193(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_14(x)*F_28(x)**2*F_30(x))
Eq(F_193(x), F_187(x) + F_194(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_14(x)*F_28(x)**3*F_38(x))
Eq(F_196(x), F_12(x)*F_186(x))
Eq(F_197(x), F_12(x)*F_198(x))
Eq(F_198(x), F_132(x) + F_199(x))
Eq(F_199(x), F_200(x) + F_205(x))
Eq(F_200(x), 2*F_20(x) + F_201(x) + F_203(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_12(x)**2*F_14(x)*F_164(x)*F_30(x))
Eq(F_203(x), F_12(x)*F_204(x))
Eq(F_204(x), F_104(x) + F_200(x))
Eq(F_205(x), 2*F_20(x) + F_206(x) + F_208(x) + F_210(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_12(x)**2*F_14(x)*F_164(x)*F_28(x)*F_30(x))
Eq(F_208(x), F_12(x)*F_209(x))
Eq(F_209(x), F_122(x) + F_205(x))
Eq(F_210(x), F_12(x)*F_199(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.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_row_placements", "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": 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false, "indices": [1], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}]]}, "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}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 3
Strategy pack name: row_and_col_placements
Tree: http://permpal.com/tree/130/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[75,x]
F[4,x] = F[13,x]*F[5,x]
F[5,x] = F[3,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[69,x]+F[9,x]
F[9,x] = F[10,x]+F[68,x]
F[10,x] = F[11,x]+F[51,x]
F[11,x] = F[1,x]+F[12,x]+F[14,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[13,x]*F[15,x]
F[15,x] = F[11,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[19,x]+F[39,x]+F[40,x]
F[19,x] = F[1,x]+F[20,x]+F[38,x]
F[20,x] = F[21,x]
F[21,x] = F[13,x]*F[22,x]*F[35,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]*F[23,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[29,x]
F[29,x] = F[1,x]+F[27,x]
F[30,x] = F[31,x]+F[32,x]+F[34,x]
F[31,x] = 0
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[24,x]+F[30,x]
F[34,x] = F[13,x]*F[26,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[13,x]*F[29,x]*F[35,x]
F[38,x] = F[13,x]*F[19,x]
F[39,x] = F[10,x]*F[13,x]*F[22,x]
F[40,x] = F[13,x]*F[41,x]
F[41,x] = F[15,x]+F[42,x]+F[50,x]
F[42,x] = F[43,x]
F[43,x] = F[13,x]*F[22,x]*F[44,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[23,x]^2*F[13,x]*F[35,x]*F[47,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[13,x]*F[23,x]*F[47,x]
F[50,x] = F[13,x]*F[41,x]
F[51,x] = F[52,x]
F[52,x] = F[13,x]*F[53,x]
F[53,x] = F[54,x]+F[58,x]+F[67,x]
F[54,x] = F[1,x]+F[55,x]+F[56,x]
F[55,x] = F[13,x]*F[54,x]
F[56,x] = F[57,x]
F[57,x] = F[13,x]*F[22,x]*F[47,x]
F[58,x] = F[13,x]*F[59,x]
F[59,x] = F[10,x]+F[60,x]+F[61,x]
F[60,x] = F[13,x]*F[59,x]
F[61,x] = F[62,x]
F[62,x] = F[13,x]*F[22,x]*F[63,x]
F[63,x] = F[10,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[13,x]*F[29,x]*F[35,x]*F[66,x]
F[66,x] = F[47,x]+F[48,x]
F[67,x] = F[13,x]*F[15,x]*F[22,x]
F[68,x] = F[7,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[63,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[1,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[13,x]*F[22,x]
F[75,x] = F[13,x]*F[76,x]
F[76,x] = F[3,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[13,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[15,x]+F[81,x]
F[81,x] = F[78,x]
F[82,x] = F[13,x]*F[22,x]*F[44,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_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{4}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{69}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{68}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \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_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{50}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{44}\! \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_{46}\! \left(x \right) = F_{23} \left(x \right)^{2} F_{13}\! \left(x \right) F_{35}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right) F_{41}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{58}\! \left(x \right)+F_{67}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right) F_{54}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{10}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{10}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right) F_{35}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{68}\! \left(x \right) = F_{7}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{63}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{3}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{44}\! \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_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_75(x))
Eq(F_4(x), F_13(x)*F_5(x))
Eq(F_5(x), F_3(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_69(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_68(x))
Eq(F_10(x), F_11(x) + F_51(x))
Eq(F_11(x), F_1(x) + F_12(x) + F_14(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_13(x)*F_15(x))
Eq(F_15(x), F_11(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_13(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_39(x) + F_40(x))
Eq(F_19(x), F_1(x) + F_20(x) + F_38(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_13(x)*F_22(x)*F_35(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x)*F_23(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_27(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_34(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_24(x) + F_30(x))
Eq(F_34(x), F_13(x)*F_26(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_13(x)*F_29(x)*F_35(x))
Eq(F_38(x), F_13(x)*F_19(x))
Eq(F_39(x), F_10(x)*F_13(x)*F_22(x))
Eq(F_40(x), F_13(x)*F_41(x))
Eq(F_41(x), F_15(x) + F_42(x) + F_50(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_13(x)*F_22(x)*F_44(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_13(x)*F_23(x)**2*F_35(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_13(x)*F_23(x)*F_47(x))
Eq(F_50(x), F_13(x)*F_41(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_13(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_58(x) + F_67(x))
Eq(F_54(x), F_1(x) + F_55(x) + F_56(x))
Eq(F_55(x), F_13(x)*F_54(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_13(x)*F_22(x)*F_47(x))
Eq(F_58(x), F_13(x)*F_59(x))
Eq(F_59(x), F_10(x) + F_60(x) + F_61(x))
Eq(F_60(x), F_13(x)*F_59(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_13(x)*F_22(x)*F_63(x))
Eq(F_63(x), F_10(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_13(x)*F_29(x)*F_35(x)*F_66(x))
Eq(F_66(x), F_47(x) + F_48(x))
Eq(F_67(x), F_13(x)*F_15(x)*F_22(x))
Eq(F_68(x), F_7(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_63(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_1(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_13(x)*F_22(x))
Eq(F_75(x), F_13(x)*F_76(x))
Eq(F_76(x), F_3(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_13(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_15(x) + F_81(x))
Eq(F_81(x), F_78(x))
Eq(F_82(x), F_13(x)*F_22(x)*F_44(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"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_and_col_placements", "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:
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"comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], 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1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"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_col_placements_req_corrob
Tree: http://permpal.com/tree/131/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[32,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[8,x]
F[13,x] = F[14,x]+F[19,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[14,x]
F[18,x] = F[14,x]
F[19,x] = F[20,x]+F[21,x]+F[22,x]
F[20,x] = 0
F[21,x] = F[13,x]*F[8,x]
F[22,x] = F[23,x]
F[23,x] = F[17,x]*F[24,x]*F[8,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[31,x]
F[26,x] = F[27,x]*F[8,x]
F[27,x] = F[25,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[1,x]+F[28,x]
F[31,x] = F[24,x]*F[8,x]
F[32,x] = F[33,x]+F[55,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[8,x]
F[35,x] = F[30,x]+F[36,x]
F[36,x] = F[37,x]+F[45,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[8,x]
F[39,x] = F[30,x]+F[40,x]
F[40,x] = F[11,x]+F[41,x]
F[41,x] = F[20,x]+F[42,x]+F[44,x]
F[42,x] = F[43,x]*F[8,x]
F[43,x] = F[28,x]+F[41,x]
F[44,x] = F[40,x]*F[8,x]
F[45,x] = F[20,x]+F[46,x]+F[54,x]
F[46,x] = F[47,x]*F[8,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[28,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[48,x]*F[8,x]
F[51,x] = F[45,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[28,x]^2*F[37,x]
F[54,x] = F[36,x]*F[8,x]
F[55,x] = F[147,x]+F[20,x]+F[56,x]
F[56,x] = F[57,x]*F[8,x]
F[57,x] = F[58,x]+F[88,x]
F[58,x] = F[59,x]+F[6,x]
F[59,x] = F[20,x]+F[60,x]+F[67,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]*F[8,x]
F[62,x] = F[58,x]+F[63,x]
F[63,x] = F[14,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]*F[8,x]
F[66,x] = F[24,x]+F[30,x]
F[67,x] = F[68,x]
F[68,x] = F[17,x]*F[69,x]*F[8,x]
F[69,x] = F[64,x]+F[70,x]
F[70,x] = F[20,x]+F[71,x]+F[78,x]
F[71,x] = F[72,x]*F[8,x]
F[72,x] = F[48,x]+F[73,x]
F[73,x] = F[25,x]+F[74,x]
F[74,x] = 2*F[20,x]+F[75,x]+F[77,x]
F[75,x] = F[76,x]*F[8,x]
F[76,x] = F[49,x]+F[74,x]
F[77,x] = F[73,x]*F[8,x]
F[78,x] = F[79,x]*F[8,x]
F[79,x] = F[24,x]+F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[82,x]
F[82,x] = F[8,x]*F[83,x]
F[83,x] = F[11,x]+F[81,x]
F[84,x] = 2*F[20,x]+F[85,x]+F[87,x]
F[85,x] = F[8,x]*F[86,x]
F[86,x] = F[25,x]+F[84,x]
F[87,x] = F[8,x]*F[80,x]
F[88,x] = F[55,x]+F[89,x]
F[89,x] = 2*F[20,x]+F[133,x]+F[90,x]
F[90,x] = F[8,x]*F[91,x]
F[91,x] = F[126,x]+F[92,x]
F[92,x] = F[122,x]+F[93,x]
F[93,x] = F[107,x]+F[20,x]+F[94,x]
F[94,x] = F[8,x]*F[95,x]
F[95,x] = F[13,x]+F[96,x]
F[96,x] = F[93,x]+F[97,x]
F[97,x] = 2*F[20,x]+F[98,x]+F[99,x]
F[98,x] = F[8,x]*F[96,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[8,x]
F[101,x] = F[102,x]+F[105,x]
F[102,x] = F[103,x]+F[97,x]
F[103,x] = F[104,x]
F[104,x] = F[11,x]*F[37,x]
F[105,x] = F[106,x]
F[106,x] = F[11,x]^2*F[17,x]*F[37,x]
F[107,x] = F[108,x]*F[8,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[37,x]+F[93,x]
F[110,x] = F[111,x]+F[45,x]
F[111,x] = 2*F[20,x]+F[112,x]+F[120,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[8,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]
F[116,x] = F[14,x]*F[28,x]*F[30,x]
F[117,x] = F[111,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[28,x]^2*F[14,x]*F[37,x]
F[120,x] = F[121,x]*F[8,x]
F[121,x] = F[111,x]+F[93,x]
F[122,x] = 2*F[20,x]+F[123,x]+F[124,x]
F[123,x] = F[8,x]*F[92,x]
F[124,x] = F[125,x]
F[125,x] = F[8,x]^2*F[10,x]*F[17,x]*F[37,x]
F[126,x] = F[127,x]+F[97,x]
F[127,x] = 2*F[20,x]+F[128,x]+F[130,x]+F[131,x]
F[128,x] = F[129,x]*F[8,x]
F[129,x] = F[122,x]+F[127,x]
F[130,x] = F[126,x]*F[8,x]
F[131,x] = F[132,x]
F[132,x] = F[8,x]^2*F[10,x]*F[11,x]*F[17,x]*F[37,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[8,x]
F[135,x] = F[102,x]+F[136,x]
F[136,x] = F[137,x]+F[139,x]
F[137,x] = F[138,x]
F[138,x] = F[11,x]^2*F[37,x]
F[139,x] = 3*F[20,x]+F[140,x]+F[142,x]
F[140,x] = F[141,x]*F[8,x]
F[141,x] = F[139,x]+F[97,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[8,x]
F[144,x] = F[136,x]+F[145,x]
F[145,x] = F[146,x]
F[146,x] = F[11,x]^3*F[17,x]*F[37,x]
F[147,x] = F[148,x]*F[8,x]
F[148,x] = F[149,x]+F[32,x]
F[149,x] = F[150,x]+F[175,x]
F[150,x] = F[151,x]+F[160,x]+F[20,x]
F[151,x] = F[152,x]*F[8,x]
F[152,x] = F[153,x]+F[48,x]
F[153,x] = F[154,x]+F[45,x]
F[154,x] = 2*F[20,x]+F[155,x]+F[158,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[76,x]*F[8,x]
F[157,x] = F[1,x]+F[37,x]
F[158,x] = F[159,x]*F[8,x]
F[159,x] = F[154,x]+F[45,x]
F[160,x] = F[161,x]*F[8,x]
F[161,x] = F[162,x]+F[36,x]
F[162,x] = F[163,x]+F[168,x]
F[163,x] = F[164,x]+F[166,x]+F[20,x]
F[164,x] = F[165,x]
F[165,x] = F[10,x]*F[11,x]*F[157,x]*F[8,x]
F[166,x] = F[167,x]
F[167,x] = F[10,x]*F[37,x]*F[8,x]
F[168,x] = F[169,x]+F[172,x]+F[174,x]+F[20,x]
F[169,x] = F[170,x]
F[170,x] = F[157,x]*F[171,x]*F[8,x]
F[171,x] = F[25,x]+F[84,x]
F[172,x] = F[173,x]
F[173,x] = F[27,x]*F[37,x]*F[8,x]
F[174,x] = F[162,x]*F[8,x]
F[175,x] = 2*F[20,x]+F[176,x]+F[190,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[8,x]
F[178,x] = F[115,x]+F[179,x]
F[179,x] = F[111,x]+F[180,x]
F[180,x] = 3*F[20,x]+F[181,x]+F[189,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[8,x]
F[183,x] = F[184,x]+F[186,x]
F[184,x] = F[185,x]
F[185,x] = F[28,x]^2*F[14,x]*F[30,x]
F[186,x] = F[180,x]+F[187,x]
F[187,x] = F[188,x]
F[188,x] = F[28,x]^3*F[14,x]*F[37,x]
F[189,x] = F[179,x]*F[8,x]
F[190,x] = F[191,x]*F[8,x]
F[191,x] = F[121,x]+F[192,x]
F[192,x] = F[193,x]+F[198,x]
F[193,x] = 2*F[20,x]+F[194,x]+F[196,x]
F[194,x] = F[195,x]
F[195,x] = F[8,x]^2*F[14,x]*F[157,x]*F[30,x]
F[196,x] = F[197,x]*F[8,x]
F[197,x] = F[193,x]+F[93,x]
F[198,x] = 2*F[20,x]+F[199,x]+F[201,x]+F[203,x]
F[199,x] = F[200,x]
F[200,x] = F[8,x]^2*F[14,x]*F[157,x]*F[28,x]*F[30,x]
F[201,x] = F[202,x]*F[8,x]
F[202,x] = F[111,x]+F[198,x]
F[203,x] = F[192,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{32}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right) F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{55}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{30}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right) F_{8}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{28}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{37}\! \left(x \right)
F_{54}\! \left(x \right) = F_{36}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{147}\! \left(x \right)+F_{20}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right) F_{8}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{88}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{6}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{8}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right) F_{8}\! \left(x \right)
F_{66}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{17}\! \left(x \right) F_{69}\! \left(x \right) F_{8}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right)+F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{25}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{76}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right) F_{8}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right) F_{8}\! \left(x \right)
F_{79}\! \left(x \right) = F_{24}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{8}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{8}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{25}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{8}\! \left(x \right) F_{80}\! \left(x \right)
F_{88}\! \left(x \right) = F_{55}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{133}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{8}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{126}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{122}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{107}\! \left(x \right)+F_{20}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{8}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{8}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{37}\! \left(x \right)+F_{93}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{45}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{112}\! \left(x \right)+F_{120}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{8}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{30}\! \left(x \right)
F_{117}\! \left(x \right) = F_{111}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{8}\! \left(x \right)
F_{121}\! \left(x \right) = F_{111}\! \left(x \right)+F_{93}\! \left(x \right)
F_{122}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{8}\! \left(x \right) F_{92}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{10}\! \left(x \right) F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{97}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{128}\! \left(x \right)+F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{8}\! \left(x \right)
F_{129}\! \left(x \right) = F_{122}\! \left(x \right)+F_{127}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right) F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{8}\! \left(x \right)
F_{135}\! \left(x \right) = F_{102}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{139}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{37}\! \left(x \right)
F_{139}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{140}\! \left(x \right)+F_{142}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{8}\! \left(x \right)
F_{141}\! \left(x \right) = F_{139}\! \left(x \right)+F_{97}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{8}\! \left(x \right)
F_{144}\! \left(x \right) = F_{136}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11} \left(x \right)^{3} F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{8}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{32}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{175}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{160}\! \left(x \right)+F_{20}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{8}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{48}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{45}\! \left(x \right)
F_{154}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{155}\! \left(x \right)+F_{158}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{157}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{8}\! \left(x \right)
F_{159}\! \left(x \right) = F_{154}\! \left(x \right)+F_{45}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{8}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{36}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{168}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{166}\! \left(x \right)+F_{20}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{157}\! \left(x \right) F_{8}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{10}\! \left(x \right) F_{37}\! \left(x \right) F_{8}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{172}\! \left(x \right)+F_{174}\! \left(x \right)+F_{20}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{157}\! \left(x \right) F_{171}\! \left(x \right) F_{8}\! \left(x \right)
F_{171}\! \left(x \right) = F_{25}\! \left(x \right)+F_{84}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{27}\! \left(x \right) F_{37}\! \left(x \right) F_{8}\! \left(x \right)
F_{174}\! \left(x \right) = F_{162}\! \left(x \right) F_{8}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{176}\! \left(x \right)+F_{190}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{8}\! \left(x \right)
F_{178}\! \left(x \right) = F_{115}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{111}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{181}\! \left(x \right)+F_{189}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{8}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{186}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{28} \left(x \right)^{2} F_{14}\! \left(x \right) F_{30}\! \left(x \right)
F_{186}\! \left(x \right) = F_{180}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{28} \left(x \right)^{3} F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{189}\! \left(x \right) = F_{179}\! \left(x \right) F_{8}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{8}\! \left(x \right)
F_{191}\! \left(x \right) = F_{121}\! \left(x \right)+F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{198}\! \left(x \right)
F_{193}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{194}\! \left(x \right)+F_{196}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{14}\! \left(x \right) F_{157}\! \left(x \right) F_{30}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right) F_{8}\! \left(x \right)
F_{197}\! \left(x \right) = F_{193}\! \left(x \right)+F_{93}\! \left(x \right)
F_{198}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{199}\! \left(x \right)+F_{201}\! \left(x \right)+F_{203}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{14}\! \left(x \right) F_{157}\! \left(x \right) F_{28}\! \left(x \right) F_{30}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right) F_{8}\! \left(x \right)
F_{202}\! \left(x \right) = F_{111}\! \left(x \right)+F_{198}\! \left(x \right)
F_{203}\! \left(x \right) = F_{192}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_32(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_19(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_14(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_22(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_13(x)*F_8(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_17(x)*F_24(x)*F_8(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_31(x))
Eq(F_26(x), F_27(x)*F_8(x))
Eq(F_27(x), F_25(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_1(x) + F_28(x))
Eq(F_31(x), F_24(x)*F_8(x))
Eq(F_32(x), F_33(x) + F_55(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_8(x))
Eq(F_35(x), F_30(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_45(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_8(x))
Eq(F_39(x), F_30(x) + F_40(x))
Eq(F_40(x), F_11(x) + F_41(x))
Eq(F_41(x), F_20(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_43(x)*F_8(x))
Eq(F_43(x), F_28(x) + F_41(x))
Eq(F_44(x), F_40(x)*F_8(x))
Eq(F_45(x), F_20(x) + F_46(x) + F_54(x))
Eq(F_46(x), F_47(x)*F_8(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_28(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_48(x)*F_8(x))
Eq(F_51(x), F_45(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_28(x)**2*F_37(x))
Eq(F_54(x), F_36(x)*F_8(x))
Eq(F_55(x), F_147(x) + F_20(x) + F_56(x))
Eq(F_56(x), F_57(x)*F_8(x))
Eq(F_57(x), F_58(x) + F_88(x))
Eq(F_58(x), F_59(x) + F_6(x))
Eq(F_59(x), F_20(x) + F_60(x) + F_67(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x)*F_8(x))
Eq(F_62(x), F_58(x) + F_63(x))
Eq(F_63(x), F_14(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x)*F_8(x))
Eq(F_66(x), F_24(x) + F_30(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_17(x)*F_69(x)*F_8(x))
Eq(F_69(x), F_64(x) + F_70(x))
Eq(F_70(x), F_20(x) + F_71(x) + F_78(x))
Eq(F_71(x), F_72(x)*F_8(x))
Eq(F_72(x), F_48(x) + F_73(x))
Eq(F_73(x), F_25(x) + F_74(x))
Eq(F_74(x), 2*F_20(x) + F_75(x) + F_77(x))
Eq(F_75(x), F_76(x)*F_8(x))
Eq(F_76(x), F_49(x) + F_74(x))
Eq(F_77(x), F_73(x)*F_8(x))
Eq(F_78(x), F_79(x)*F_8(x))
Eq(F_79(x), F_24(x) + F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_8(x)*F_83(x))
Eq(F_83(x), F_11(x) + F_81(x))
Eq(F_84(x), 2*F_20(x) + F_85(x) + F_87(x))
Eq(F_85(x), F_8(x)*F_86(x))
Eq(F_86(x), F_25(x) + F_84(x))
Eq(F_87(x), F_8(x)*F_80(x))
Eq(F_88(x), F_55(x) + F_89(x))
Eq(F_89(x), F_133(x) + 2*F_20(x) + F_90(x))
Eq(F_90(x), F_8(x)*F_91(x))
Eq(F_91(x), F_126(x) + F_92(x))
Eq(F_92(x), F_122(x) + F_93(x))
Eq(F_93(x), F_107(x) + F_20(x) + F_94(x))
Eq(F_94(x), F_8(x)*F_95(x))
Eq(F_95(x), F_13(x) + F_96(x))
Eq(F_96(x), F_93(x) + F_97(x))
Eq(F_97(x), 2*F_20(x) + F_98(x) + F_99(x))
Eq(F_98(x), F_8(x)*F_96(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_8(x))
Eq(F_101(x), F_102(x) + F_105(x))
Eq(F_102(x), F_103(x) + F_97(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_11(x)*F_37(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_11(x)**2*F_17(x)*F_37(x))
Eq(F_107(x), F_108(x)*F_8(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_37(x) + F_93(x))
Eq(F_110(x), F_111(x) + F_45(x))
Eq(F_111(x), F_112(x) + F_120(x) + 2*F_20(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_8(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_14(x)*F_28(x)*F_30(x))
Eq(F_117(x), F_111(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_14(x)*F_28(x)**2*F_37(x))
Eq(F_120(x), F_121(x)*F_8(x))
Eq(F_121(x), F_111(x) + F_93(x))
Eq(F_122(x), F_123(x) + F_124(x) + 2*F_20(x))
Eq(F_123(x), F_8(x)*F_92(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_10(x)*F_17(x)*F_37(x)*F_8(x)**2)
Eq(F_126(x), F_127(x) + F_97(x))
Eq(F_127(x), F_128(x) + F_130(x) + F_131(x) + 2*F_20(x))
Eq(F_128(x), F_129(x)*F_8(x))
Eq(F_129(x), F_122(x) + F_127(x))
Eq(F_130(x), F_126(x)*F_8(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_10(x)*F_11(x)*F_17(x)*F_37(x)*F_8(x)**2)
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_8(x))
Eq(F_135(x), F_102(x) + F_136(x))
Eq(F_136(x), F_137(x) + F_139(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_11(x)**2*F_37(x))
Eq(F_139(x), F_140(x) + F_142(x) + 3*F_20(x))
Eq(F_140(x), F_141(x)*F_8(x))
Eq(F_141(x), F_139(x) + F_97(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_8(x))
Eq(F_144(x), F_136(x) + F_145(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_11(x)**3*F_17(x)*F_37(x))
Eq(F_147(x), F_148(x)*F_8(x))
Eq(F_148(x), F_149(x) + F_32(x))
Eq(F_149(x), F_150(x) + F_175(x))
Eq(F_150(x), F_151(x) + F_160(x) + F_20(x))
Eq(F_151(x), F_152(x)*F_8(x))
Eq(F_152(x), F_153(x) + F_48(x))
Eq(F_153(x), F_154(x) + F_45(x))
Eq(F_154(x), F_155(x) + F_158(x) + 2*F_20(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_76(x)*F_8(x))
Eq(F_157(x), F_1(x) + F_37(x))
Eq(F_158(x), F_159(x)*F_8(x))
Eq(F_159(x), F_154(x) + F_45(x))
Eq(F_160(x), F_161(x)*F_8(x))
Eq(F_161(x), F_162(x) + F_36(x))
Eq(F_162(x), F_163(x) + F_168(x))
Eq(F_163(x), F_164(x) + F_166(x) + F_20(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_10(x)*F_11(x)*F_157(x)*F_8(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_10(x)*F_37(x)*F_8(x))
Eq(F_168(x), F_169(x) + F_172(x) + F_174(x) + F_20(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_157(x)*F_171(x)*F_8(x))
Eq(F_171(x), F_25(x) + F_84(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_27(x)*F_37(x)*F_8(x))
Eq(F_174(x), F_162(x)*F_8(x))
Eq(F_175(x), F_176(x) + F_190(x) + 2*F_20(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_8(x))
Eq(F_178(x), F_115(x) + F_179(x))
Eq(F_179(x), F_111(x) + F_180(x))
Eq(F_180(x), F_181(x) + F_189(x) + 3*F_20(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_8(x))
Eq(F_183(x), F_184(x) + F_186(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_14(x)*F_28(x)**2*F_30(x))
Eq(F_186(x), F_180(x) + F_187(x))
Eq(F_187(x), F_188(x))
Eq(F_188(x), F_14(x)*F_28(x)**3*F_37(x))
Eq(F_189(x), F_179(x)*F_8(x))
Eq(F_190(x), F_191(x)*F_8(x))
Eq(F_191(x), F_121(x) + F_192(x))
Eq(F_192(x), F_193(x) + F_198(x))
Eq(F_193(x), F_194(x) + F_196(x) + 2*F_20(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_14(x)*F_157(x)*F_30(x)*F_8(x)**2)
Eq(F_196(x), F_197(x)*F_8(x))
Eq(F_197(x), F_193(x) + F_93(x))
Eq(F_198(x), F_199(x) + 2*F_20(x) + F_201(x) + F_203(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_14(x)*F_157(x)*F_28(x)*F_30(x)*F_8(x)**2)
Eq(F_201(x), F_202(x)*F_8(x))
Eq(F_202(x), F_111(x) + F_198(x))
Eq(F_203(x), F_192(x)*F_8(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": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.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_col_placements_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:
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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 3]], [[1, 2]], [[2, 0]], [[3, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "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, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [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": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "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"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "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"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 5
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/132/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[31,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[1,x]+F[10,x]+F[11,x]
F[10,x] = F[4,x]*F[9,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[26,x]*F[4,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[15,x]+F[21,x]
F[25,x] = F[17,x]*F[4,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[26,x]+F[30,x]
F[30,x] = F[27,x]
F[31,x] = F[32,x]+F[45,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[1,x]+F[32,x]
F[36,x] = F[26,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[20,x]+F[40,x]
F[40,x] = F[15,x]+F[41,x]
F[41,x] = F[22,x]+F[42,x]+F[44,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[18,x]+F[41,x]
F[44,x] = F[4,x]*F[40,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[152,x]+F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[45,x]+F[7,x]
F[50,x] = F[51,x]+F[76,x]
F[51,x] = F[52,x]+F[57,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[1,x]+F[52,x]
F[56,x] = F[52,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[74,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[27,x]+F[62,x]
F[62,x] = F[63,x]+F[7,x]
F[63,x] = F[27,x]*F[52,x]
F[64,x] = F[63,x]+F[65,x]
F[65,x] = F[57,x]+F[66,x]
F[66,x] = F[27,x]*F[67,x]
F[67,x] = F[22,x]+F[68,x]+F[71,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[52,x]+F[67,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[56,x]+F[73,x]
F[73,x] = F[67,x]
F[74,x] = F[52,x]*F[75,x]
F[75,x] = 2*F[27,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[32,x]*F[52,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[138,x]+F[81,x]
F[81,x] = F[135,x]+F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[27,x]*F[37,x]
F[84,x] = F[45,x]+F[85,x]
F[85,x] = F[27,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[37,x]+F[86,x]
F[91,x] = F[37,x]*F[52,x]
F[92,x] = F[127,x]+F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[37,x]*F[55,x]
F[95,x] = F[117,x]+F[96,x]
F[96,x] = F[107,x]+F[22,x]+F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[102,x]+F[99,x]
F[99,x] = F[100,x]+F[18,x]
F[100,x] = F[101,x]
F[101,x] = F[4,x]*F[99,x]
F[102,x] = F[103,x]+F[41,x]
F[103,x] = 2*F[22,x]+F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[100,x]+F[103,x]
F[106,x] = F[102,x]*F[4,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[40,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[110,x]+F[15,x]
F[113,x] = 2*F[22,x]+F[114,x]+F[116,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[113,x]+F[41,x]
F[116,x] = F[109,x]*F[4,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[125,x]
F[120,x] = F[121,x]+F[124,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[18,x]*F[52,x]
F[123,x] = F[20,x]*F[86,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[18,x]*F[37,x]*F[52,x]
F[126,x] = F[117,x]*F[20,x]
F[127,x] = F[128,x]+F[86,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[123,x]+F[131,x]
F[131,x] = F[132,x]*F[40,x]
F[132,x] = F[133,x]+F[86,x]
F[133,x] = F[134,x]*F[52,x]
F[134,x] = F[1,x]+F[37,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[52,x]
F[137,x] = 2*F[83,x]
F[138,x] = F[139,x]+F[148,x]
F[139,x] = F[140,x]+F[145,x]
F[140,x] = F[141,x]*F[37,x]
F[141,x] = F[142,x]
F[142,x] = F[143,x]*F[26,x]*F[4,x]
F[143,x] = F[144,x]+F[17,x]
F[144,x] = F[13,x]*F[18,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[18,x]*F[45,x]
F[147,x] = F[141,x]*F[86,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[52,x]
F[150,x] = F[140,x]+F[151,x]
F[151,x] = F[18,x]*F[27,x]*F[37,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[37,x]*F[62,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[26,x]*F[86,x]
F[157,x] = F[158,x]+F[174,x]
F[158,x] = F[159,x]
F[159,x] = F[160,x]*F[4,x]
F[160,x] = F[161,x]+F[173,x]
F[161,x] = F[136,x]+F[162,x]
F[162,x] = F[163,x]+F[164,x]
F[163,x] = F[37,x]*F[61,x]
F[164,x] = F[165,x]+F[85,x]
F[165,x] = F[158,x]+F[166,x]
F[166,x] = F[167,x]*F[27,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[14,x]*F[86,x]
F[171,x] = F[17,x]*F[172,x]
F[172,x] = F[86,x]+F[94,x]
F[173,x] = F[27,x]*F[92,x]
F[174,x] = F[175,x]
F[175,x] = F[18,x]*F[27,x]*F[37,x]*F[52,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \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_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \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_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{45}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{20}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{152}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{76}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{27}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{63}\! \left(x \right) = F_{27}\! \left(x \right) F_{52}\! \left(x \right)
F_{64}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{57}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{27}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right)+F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{56}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{67}\! \left(x \right)
F_{74}\! \left(x \right) = F_{52}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{27}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{32}\! \left(x \right) F_{52}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{138}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{135}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{27}\! \left(x \right) F_{37}\! \left(x \right)
F_{84}\! \left(x \right) = F_{45}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{27}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{37}\! \left(x \right)+F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{37}\! \left(x \right) F_{52}\! \left(x \right)
F_{92}\! \left(x \right) = F_{127}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{37}\! \left(x \right) F_{55}\! \left(x \right)
F_{95}\! \left(x \right) = F_{117}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{102}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{18}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{41}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{40}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{110}\! \left(x \right)+F_{15}\! \left(x \right)
F_{113}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{114}\! \left(x \right)+F_{116}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{41}\! \left(x \right)
F_{116}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{125}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{123}\! \left(x \right) = F_{20}\! \left(x \right) F_{86}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{18}\! \left(x \right) F_{37}\! \left(x \right) F_{52}\! \left(x \right)
F_{126}\! \left(x \right) = F_{117}\! \left(x \right) F_{20}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{86}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{123}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{40}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{86}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{52}\! \left(x \right)
F_{134}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{52}\! \left(x \right)
F_{137}\! \left(x \right) = 2 F_{83}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{148}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{37}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{17}\! \left(x \right)
F_{144}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right)
F_{147}\! \left(x \right) = F_{141}\! \left(x \right) F_{86}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{52}\! \left(x \right)
F_{150}\! \left(x \right) = F_{140}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{37}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{37}\! \left(x \right) F_{62}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{26}\! \left(x \right) F_{86}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{174}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{173}\! \left(x \right)
F_{161}\! \left(x \right) = F_{136}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{164}\! \left(x \right)
F_{163}\! \left(x \right) = F_{37}\! \left(x \right) F_{61}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{85}\! \left(x \right)
F_{165}\! \left(x \right) = F_{158}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{27}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right)
F_{171}\! \left(x \right) = F_{17}\! \left(x \right) F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{86}\! \left(x \right)+F_{94}\! \left(x \right)
F_{173}\! \left(x \right) = F_{27}\! \left(x \right) F_{92}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{37}\! \left(x \right) F_{52}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_31(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_1(x) + F_10(x) + F_11(x))
Eq(F_10(x), F_4(x)*F_9(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_26(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_15(x) + F_21(x))
Eq(F_25(x), F_17(x)*F_4(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_26(x) + F_30(x))
Eq(F_30(x), F_27(x))
Eq(F_31(x), F_32(x) + F_45(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_1(x) + F_32(x))
Eq(F_36(x), F_26(x)*F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_20(x) + F_40(x))
Eq(F_40(x), F_15(x) + F_41(x))
Eq(F_41(x), F_22(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_18(x) + F_41(x))
Eq(F_44(x), F_4(x)*F_40(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_152(x) + F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_45(x) + F_7(x))
Eq(F_50(x), F_51(x) + F_76(x))
Eq(F_51(x), F_52(x) + F_57(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_1(x) + F_52(x))
Eq(F_56(x), F_52(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_74(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_27(x) + F_62(x))
Eq(F_62(x), F_63(x) + F_7(x))
Eq(F_63(x), F_27(x)*F_52(x))
Eq(F_64(x), F_63(x) + F_65(x))
Eq(F_65(x), F_57(x) + F_66(x))
Eq(F_66(x), F_27(x)*F_67(x))
Eq(F_67(x), F_22(x) + F_68(x) + F_71(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_52(x) + F_67(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_56(x) + F_73(x))
Eq(F_73(x), F_67(x))
Eq(F_74(x), F_52(x)*F_75(x))
Eq(F_75(x), 2*F_27(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_32(x)*F_52(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_138(x) + F_81(x))
Eq(F_81(x), F_135(x) + F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_27(x)*F_37(x))
Eq(F_84(x), F_45(x) + F_85(x))
Eq(F_85(x), F_27(x)*F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_37(x) + F_86(x))
Eq(F_91(x), F_37(x)*F_52(x))
Eq(F_92(x), F_127(x) + F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_37(x)*F_55(x))
Eq(F_95(x), F_117(x) + F_96(x))
Eq(F_96(x), F_107(x) + F_22(x) + F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_102(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_18(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_4(x)*F_99(x))
Eq(F_102(x), F_103(x) + F_41(x))
Eq(F_103(x), F_104(x) + F_106(x) + 2*F_22(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_100(x) + F_103(x))
Eq(F_106(x), F_102(x)*F_4(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_40(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_110(x) + F_15(x))
Eq(F_113(x), F_114(x) + F_116(x) + 2*F_22(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_113(x) + F_41(x))
Eq(F_116(x), F_109(x)*F_4(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_125(x))
Eq(F_120(x), F_121(x) + F_124(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_18(x)*F_52(x))
Eq(F_123(x), F_20(x)*F_86(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_18(x)*F_37(x)*F_52(x))
Eq(F_126(x), F_117(x)*F_20(x))
Eq(F_127(x), F_128(x) + F_86(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_123(x) + F_131(x))
Eq(F_131(x), F_132(x)*F_40(x))
Eq(F_132(x), F_133(x) + F_86(x))
Eq(F_133(x), F_134(x)*F_52(x))
Eq(F_134(x), F_1(x) + F_37(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_52(x))
Eq(F_137(x), 2*F_83(x))
Eq(F_138(x), F_139(x) + F_148(x))
Eq(F_139(x), F_140(x) + F_145(x))
Eq(F_140(x), F_141(x)*F_37(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_143(x)*F_26(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_17(x))
Eq(F_144(x), F_13(x)*F_18(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_18(x)*F_45(x))
Eq(F_147(x), F_141(x)*F_86(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_52(x))
Eq(F_150(x), F_140(x) + F_151(x))
Eq(F_151(x), F_18(x)*F_27(x)*F_37(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_37(x)*F_62(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_26(x)*F_86(x))
Eq(F_157(x), F_158(x) + F_174(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x)*F_4(x))
Eq(F_160(x), F_161(x) + F_173(x))
Eq(F_161(x), F_136(x) + F_162(x))
Eq(F_162(x), F_163(x) + F_164(x))
Eq(F_163(x), F_37(x)*F_61(x))
Eq(F_164(x), F_165(x) + F_85(x))
Eq(F_165(x), F_158(x) + F_166(x))
Eq(F_166(x), F_167(x)*F_27(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_14(x)*F_86(x))
Eq(F_171(x), F_17(x)*F_172(x))
Eq(F_172(x), F_86(x) + F_94(x))
Eq(F_173(x), F_27(x)*F_92(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_18(x)*F_27(x)*F_37(x)*F_52(x))
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.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", "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], 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