01342_01432_04132_10342_10432_13042

Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3297, 18922, 111484, 670089, 4092042, 25314738, 158305369, 999049900, 6354510326, 40693686742, 262152185681, 1697688427557, 11045563841398, 72165671019934, 473266580394343, 3114289217531786, 20556853966300306, 136076492610117639, 903102342949000379, 6007988095149853923, 40057191131620642585, 267621561423650511001, 1791382031034368971888, 12012284420548646755840, 80683111407985231240085, 542767116210118737660818, 3656594093391897036633709, 24668033574414262962875632, 166629686915271659362775313, 1126934668813473526465614549, 7630353545554910631646619045, 51720594876834245944261789158, 350938276725018080996132025335, 2383546675676566628548676462373, 16203964222906269014368615516435, 110256474617073199611689160693105, 750851469530547999678989646505843, 5117457195591200802662115497598866, 34905103791540913883606373975797442, 238255808508071408600245064557643230, 1627436955185350794403569913248294557, 11123926081084238088640268294323273185, 76083973686106457388515097316562956913, 520712627079126703121666318919123411705, 3565842803864014391221478340997235406330, 24432921144810082116335735173740987728081, 167505177016195168997493152695387197025670, 1148978159780978334004715287556710070724411, 7885288009384149442618474628821070025654003, 54142412144672402527261088673154337056362332, 371932665765230997923174075640147780176099004, 2556174814952108788417617940299079467143430970, 17575572409551730282703576410217284867852217397, 120896753085429090054527042085060154448734720618, 831955090002464812019541127910682810691625843213, 5727424462697242754661823798929189082633924949101, 39444597826630962582842690981968600821421577320916, 271755953314462685313927394771574009124715627974544, 1872961787110703180557778577159454175540215549218763, 12913151810824760634690159203260324597486385320806222, 89060366624022244773085500440102162536468388905405690, 614442402862954856715987229313421872849145148712250856, 4240510535631529197378200917009147777136705646471670967, 29274625789430427414980343109157292473693250800070097976, 202160795508971850400883168060604897404360610685868209257, 1396468702446348676767213572783955116337695784147936308900, 9649184603521059185144727182873001133878273498321257906755, 66691696298584248855563149833088751887600190703075721316008, 461074803642836502624103193841278608216001714199526330489508, 3188499553542616369546303772173510490937322309935630444835414, 22055335317320508414676601968457191900777376969011511847005230, 152598550775266721087685849287396546573594746344440441743306612, 1056072684078206493852825027481572945902628315525473383773210296, 7310400782505618523548874355972671437299494302380884150092938616, 50616249616745184255414870330227159862045978923635809114090992359, 350540057240047011650967697608642679021420435312458731559385876405, 2428185510554546490304707745234514772746281672111171918449771675893, 16823652340782717994873122643858994090517700078876145894356608170937, 116587151737377153102495829570357240093714005320224736753290136045268, 808110848544879990905094306936926919520847967422094804383617556698126, 5602462327024126206347449875638010057976297530329757318902380503417709, 38848362102039271961235071091950123833913026859299206503788724005405727, 269432702115317756928288766868887506279363048119134877199561570967842943, 1869002383143868465192518095675853271784324047982589666962788402409709823, 12967299755842361692799302595513640268168207016874782707087050867275751817, 89984486508846736793046309218047483200250091543682745335589825095942822477, 624543136624791554012835882043937772123409867867328304630659611007504436028, 4335431252747524458438156835848609387984740443768174958146356319377011271045, 30100634345437051926786842500315663810295034900143704543422781055187074125630, 209021488330905913266697548896170900263513548411779683127159039801083244313805, 1451699336171321477771077641823216810866767524351294126124047070651220130922333, 10083967383180401577069547869611952400568321252250390885390946600316920635966736, 70057365012462384057283983117341919660993500494707068373302368326739990896691067, 486790865619612849099733865618158535248053178125041698704700441349990186130276652

Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24534/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[151,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[9,x,1]
F[10,x,k[0]] = F[4,x]+F[9,x,k[0]]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[14,x,k[0]]+F[148,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[13,x] = x
F[15,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[140,x,k[0]]+F[142,x,k[0]]+F[90,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[85,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[26,x,k[0]]
F[17,x,k[0]] = F[0,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[24,x,k[0]]
F[20,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]+F[25,x,k[0]]
F[21,x,k[0]] = F[13,x]*F[22,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[23,x,k[0]] = F[9,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[20,x,k[0]]*F[24,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[13,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[129,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[20,x,k[0]]+F[30,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]+F[45,x,k[0]]
F[32,x,k[0]] = F[24,x,k[0]]*F[31,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[34,x,k[0]] = F[18,x,k[0]]+F[33,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[37,x,k[0]]+F[39,x,k[0]]+F[6,x]
F[35,x,k[0]] = F[13,x]*F[36,x,k[0]]
F[36,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[37,x,k[0]] = F[13,x]*F[38,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[24,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]+F[42,x,k[0]]
F[41,x,k[0]] = F[34,x,k[0]]+F[4,x]
F[42,x,k[0]] = k[0]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[13,x]*F[29,x,k[0]]
F[45,x,k[0]] = F[117,x,k[0]]+F[46,x,k[0]]+F[47,x,k[0]]
F[46,x,k[0]] = F[33,x,k[0]]+F[5,x]
F[47,x,k[0]] = F[13,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[13,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[116,x,k[0]]+F[51,x,k[0]]+F[80,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[79,x,k[0]]
F[52,x,k[0]] = F[17,x,k[0]]*F[53,x]
F[53,x] = 1/F[13,x]*F[54,x]
F[54,x] = -F[1,x]-F[73,x]-F[77,x]+F[55,x]
F[55,x] = F[56,x]+F[62,x]
F[56,x] = F[0,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[0,x]*F[13,x]*F[56,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[59,x]^2*F[13,x]
F[62,x] = F[5,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[13,x]*F[59,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[0,x]*F[62,x]
F[67,x] = F[5,x]*F[68,x]
F[68,x] = F[69,x,1]
F[69,x,k[0]] = (F[70,x,k[0]]*k[0]-F[70,x,1])/(-1+k[0])
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[70,x,k[0]]^2*F[24,x,k[0]]
F[73,x] = F[13,x]*F[74,x]
F[74,x] = F[55,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[13,x]*F[55,x]*F[59,x]*F[68,x]
F[77,x] = F[78,x]
F[78,x] = F[13,x]*F[55,x]*F[59,x]
F[79,x,k[0]] = F[26,x,k[0]]*F[55,x]
F[80,x,k[0]] = F[13,x]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[83,x,k[0]]
F[82,x,k[0]] = F[22,x,k[0]]*F[53,x]
F[83,x,k[0]] = F[55,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[112,x,k[0]]+F[85,x,k[0]]+F[93,x,k[0]]
F[85,x,k[0]] = 2*F[6,x]+F[86,x,k[0]]+F[90,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = F[13,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[13,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[22,x,k[0]]+F[84,x,k[0]]
F[90,x,k[0]] = F[13,x]*F[16,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[24,x,k[0]]*F[85,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[13,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[13,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[104,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[20,x,k[0]]*F[99,x]
F[99,x] = 1/F[13,x]*F[100,x]
F[100,x] = -F[1,x]-F[103,x]+F[101,x]
F[101,x] = 1/F[13,x]*F[102,x]
F[102,x] = F[2,x]
F[103,x] = F[13,x]*F[55,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[109,x,k[0]]*F[4,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[26,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[13,x]*F[84,x,k[0]]
F[109,x,k[0]] = F[1,x]+F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[109,x,k[0]]*F[24,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[13,x]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[13,x]*F[20,x,k[0]]*F[55,x]
F[116,x,k[0]] = F[24,x,k[0]]*F[50,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[13,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[123,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[13,x]*F[59,x]
F[122,x,k[0]] = F[121,x,k[0]]*F[13,x]
F[122,x,k[0]] = F[45,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[13,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[20,x,k[0]]*F[74,x]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[30,x,k[0]]*F[59,x]*F[68,x]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[109,x,k[0]]*F[13,x]*F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[139,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[135,x,k[0]]+F[137,x,k[0]]+F[29,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[13,x]*F[50,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[125,x,k[0]]*F[13,x]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[13,x]*F[132,x,k[0]]*F[59,x]
F[139,x,k[0]] = F[129,x,k[0]]*F[59,x]
F[140,x,k[0]] = F[13,x]*F[141,x,k[0]]
F[141,x,k[0]] = F[12,x,k[0]]+F[87,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[24,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[15,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = k[0]*F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[13,x]*F[20,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[24,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[16,x,k[0]]
F[150,x,k[0]] = k[0]*F[85,x,k[0]]
F[151,x] = F[13,x]*F[152,x]
F[152,x] = F[41,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{151}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{142}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{42}\! \left(x , y\right) = y F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{54}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{73}\! \left(x \right)-F_{77}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{0}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{56}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{62}\! \left(x \right) = F_{5}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right) F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x , 1\right)
F_{69}\! \left(x , y\right) = -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{70}\! \left(x , y\right)^{2} F_{24}\! \left(x , y\right)
F_{73}\! \left(x \right) = F_{13}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{55}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{59}\! \left(x \right) F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{59}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{53}\! \left(x \right)
F_{83}\! \left(x , y\right) = F_{55}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{85}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{100}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{103}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{2}\! \left(x \right)
F_{103}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{20}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{74}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{59}\! \left(x \right) F_{68}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{13}\! \left(x \right) F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{132}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = y F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = y F_{85}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{13}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{41}\! \left(x , 1\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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_151(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_10(x, k_0), F_4(x) + F_9(x, k_0))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_14(x, k_0) + F_148(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_12(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_13(x), x)
Eq(F_15(x, k_0), F_1(x) + F_14(x, k_0) + F_140(x, k_0) + F_142(x, k_0) + F_90(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_85(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_26(x, k_0))
Eq(F_17(x, k_0), F_0(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_24(x, k_0))
Eq(F_20(x, k_0), F_17(x, k_0) + F_21(x, k_0) + F_25(x, k_0))
Eq(F_21(x, k_0), F_13(x)*F_22(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_23(x, k_0), F_9(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_20(x, k_0)*F_24(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_13(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_129(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_20(x, k_0) + F_30(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0) + F_45(x, k_0))
Eq(F_32(x, k_0), F_24(x, k_0)*F_31(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_34(x, k_0), F_18(x, k_0) + F_33(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_37(x, k_0) + F_39(x, k_0) + F_6(x))
Eq(F_35(x, k_0), F_13(x)*F_36(x, k_0))
Eq(F_36(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_13(x)*F_38(x, k_0))
Eq(F_38(x, k_0), -F_34(x, 1) + (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_24(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0) + F_42(x, k_0))
Eq(F_41(x, k_0), F_34(x, k_0) + F_4(x))
Eq(F_42(x, k_0), k_0*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_13(x)*F_29(x, k_0))
Eq(F_45(x, k_0), F_117(x, k_0) + F_46(x, k_0) + F_47(x, k_0))
Eq(F_46(x, k_0), F_33(x, k_0) + F_5(x))
Eq(F_47(x, k_0), F_13(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_13(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_116(x, k_0) + F_51(x, k_0) + F_80(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_79(x, k_0))
Eq(F_52(x, k_0), F_17(x, k_0)*F_53(x))
Eq(F_53(x), F_54(x)/F_13(x))
Eq(F_54(x), -F_1(x) + F_55(x) - F_73(x) - F_77(x))
Eq(F_55(x), F_56(x) + F_62(x))
Eq(F_56(x), F_0(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_0(x)*F_13(x)*F_56(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_13(x)*F_59(x)**2)
Eq(F_62(x), F_5(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_13(x)*F_59(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_0(x)*F_62(x))
Eq(F_67(x), F_5(x)*F_68(x))
Eq(F_68(x), F_69(x, 1))
Eq(F_69(x, k_0), (-k_0*F_70(x, k_0) + F_70(x, 1))/(1 - k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_24(x, k_0)*F_70(x, k_0)**2)
Eq(F_73(x), F_13(x)*F_74(x))
Eq(F_74(x), F_55(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_13(x)*F_55(x)*F_59(x)*F_68(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_13(x)*F_55(x)*F_59(x))
Eq(F_79(x, k_0), F_26(x, k_0)*F_55(x))
Eq(F_80(x, k_0), F_13(x)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_83(x, k_0))
Eq(F_82(x, k_0), F_22(x, k_0)*F_53(x))
Eq(F_83(x, k_0), F_55(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_112(x, k_0) + F_85(x, k_0) + F_93(x, k_0))
Eq(F_85(x, k_0), 2*F_6(x) + F_86(x, k_0) + F_90(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), F_13(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_13(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_22(x, k_0) + F_84(x, k_0))
Eq(F_90(x, k_0), F_13(x)*F_16(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_24(x, k_0)*F_85(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_13(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_13(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_104(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_20(x, k_0)*F_99(x))
Eq(F_99(x), F_100(x)/F_13(x))
Eq(F_100(x), -F_1(x) + F_101(x) - F_103(x))
Eq(F_101(x), F_102(x)/F_13(x))
Eq(F_102(x), F_2(x))
Eq(F_103(x), F_13(x)*F_55(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_109(x, k_0)*F_4(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_26(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_13(x)*F_84(x, k_0))
Eq(F_109(x, k_0), F_1(x) + F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_109(x, k_0)*F_24(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_13(x))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_13(x)*F_20(x, k_0)*F_55(x))
Eq(F_116(x, k_0), F_24(x, k_0)*F_50(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_13(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_123(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_13(x)*F_59(x))
Eq(F_122(x, k_0), F_121(x, k_0)*F_13(x))
Eq(F_122(x, k_0), F_45(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_13(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_20(x, k_0)*F_74(x))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_30(x, k_0)*F_59(x)*F_68(x))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_109(x, k_0)*F_13(x)*F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_139(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_135(x, k_0) + F_137(x, k_0) + F_29(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_13(x)*F_50(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_125(x, k_0)*F_13(x))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_13(x)*F_132(x, k_0)*F_59(x))
Eq(F_139(x, k_0), F_129(x, k_0)*F_59(x))
Eq(F_140(x, k_0), F_13(x)*F_141(x, k_0))
Eq(F_141(x, k_0), F_12(x, k_0) + F_87(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_24(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_15(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), k_0*F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_13(x)*F_20(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_24(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_16(x, k_0))
Eq(F_150(x, k_0), k_0*F_85(x, k_0))
Eq(F_151(x), F_13(x)*F_152(x))
Eq(F_152(x), F_41(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": 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{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 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[0, 4], [0, 4], [6, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [1, 4], [1, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [1, 4], [6, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [6, 4], [6, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 4], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 1], [0, 4], [6, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 2], [0, 4], [1, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 2], [0, 4], [6, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [1, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [6, 4]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[6, 2]]}, {"patt": [0], "pos": [[6, 4]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}

Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25005/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[151,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[9,x,1]
F[10,x,k[0]] = F[4,x]+F[9,x,k[0]]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[14,x,k[0]]+F[148,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[13,x] = x
F[15,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[140,x,k[0]]+F[142,x,k[0]]+F[90,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[85,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[26,x,k[0]]
F[17,x,k[0]] = F[0,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[24,x,k[0]]
F[20,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]+F[25,x,k[0]]
F[21,x,k[0]] = F[13,x]*F[22,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[23,x,k[0]] = F[9,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[20,x,k[0]]*F[24,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[13,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[129,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[20,x,k[0]]+F[30,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]+F[45,x,k[0]]
F[32,x,k[0]] = F[24,x,k[0]]*F[31,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[34,x,k[0]] = F[18,x,k[0]]+F[33,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[37,x,k[0]]+F[39,x,k[0]]+F[6,x]
F[35,x,k[0]] = F[13,x]*F[36,x,k[0]]
F[36,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[37,x,k[0]] = F[13,x]*F[38,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[24,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]+F[42,x,k[0]]
F[41,x,k[0]] = F[34,x,k[0]]+F[4,x]
F[42,x,k[0]] = k[0]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[13,x]*F[29,x,k[0]]
F[45,x,k[0]] = F[117,x,k[0]]+F[46,x,k[0]]+F[47,x,k[0]]
F[46,x,k[0]] = F[33,x,k[0]]+F[5,x]
F[47,x,k[0]] = F[13,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[13,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[116,x,k[0]]+F[51,x,k[0]]+F[80,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[79,x,k[0]]
F[52,x,k[0]] = F[17,x,k[0]]*F[53,x]
F[53,x] = 1/F[13,x]*F[54,x]
F[54,x] = -F[1,x]-F[73,x]-F[77,x]+F[55,x]
F[55,x] = F[56,x]+F[62,x]
F[56,x] = F[0,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[0,x]*F[13,x]*F[56,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[59,x]^2*F[13,x]
F[62,x] = F[5,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[13,x]*F[59,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[0,x]*F[62,x]
F[67,x] = F[5,x]*F[68,x]
F[68,x] = F[69,x,1]
F[69,x,k[0]] = (F[70,x,k[0]]*k[0]-F[70,x,1])/(-1+k[0])
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[70,x,k[0]]^2*F[24,x,k[0]]
F[73,x] = F[13,x]*F[74,x]
F[74,x] = F[55,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[13,x]*F[55,x]*F[59,x]*F[68,x]
F[77,x] = F[78,x]
F[78,x] = F[13,x]*F[55,x]*F[59,x]
F[79,x,k[0]] = F[26,x,k[0]]*F[55,x]
F[80,x,k[0]] = F[13,x]*F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[83,x,k[0]]
F[82,x,k[0]] = F[22,x,k[0]]*F[53,x]
F[83,x,k[0]] = F[55,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[112,x,k[0]]+F[85,x,k[0]]+F[93,x,k[0]]
F[85,x,k[0]] = 2*F[6,x]+F[86,x,k[0]]+F[90,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = F[13,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[13,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[22,x,k[0]]+F[84,x,k[0]]
F[90,x,k[0]] = F[13,x]*F[16,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[24,x,k[0]]*F[85,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[13,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[13,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[104,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[20,x,k[0]]*F[99,x]
F[99,x] = 1/F[13,x]*F[100,x]
F[100,x] = -F[1,x]-F[103,x]+F[101,x]
F[101,x] = 1/F[13,x]*F[102,x]
F[102,x] = F[2,x]
F[103,x] = F[13,x]*F[55,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[109,x,k[0]]*F[4,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[26,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[13,x]*F[84,x,k[0]]
F[109,x,k[0]] = F[1,x]+F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[109,x,k[0]]*F[24,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[13,x]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[13,x]*F[20,x,k[0]]*F[55,x]
F[116,x,k[0]] = F[24,x,k[0]]*F[50,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[13,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[123,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[13,x]*F[59,x]
F[122,x,k[0]] = F[121,x,k[0]]*F[13,x]
F[122,x,k[0]] = F[45,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[13,x]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[20,x,k[0]]*F[74,x]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[30,x,k[0]]*F[59,x]*F[68,x]
F[129,x,k[0]] = F[130,x,k[0]]
F[130,x,k[0]] = F[109,x,k[0]]*F[13,x]*F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[139,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[135,x,k[0]]+F[137,x,k[0]]+F[29,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[13,x]*F[50,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[125,x,k[0]]*F[13,x]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[13,x]*F[132,x,k[0]]*F[59,x]
F[139,x,k[0]] = F[129,x,k[0]]*F[59,x]
F[140,x,k[0]] = F[13,x]*F[141,x,k[0]]
F[141,x,k[0]] = F[12,x,k[0]]+F[87,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[24,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[15,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = k[0]*F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[13,x]*F[20,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[24,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[16,x,k[0]]
F[150,x,k[0]] = k[0]*F[85,x,k[0]]
F[151,x] = F[13,x]*F[152,x]
F[152,x] = F[41,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{151}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{142}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{42}\! \left(x , y\right) = y F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{54}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{73}\! \left(x \right)-F_{77}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{0}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{56}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{62}\! \left(x \right) = F_{5}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right) F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x , 1\right)
F_{69}\! \left(x , y\right) = -\frac{-y F_{70}\! \left(x , y\right)+F_{70}\! \left(x , 1\right)}{-1+y}
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{70}\! \left(x , y\right)^{2} F_{24}\! \left(x , y\right)
F_{73}\! \left(x \right) = F_{13}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{55}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{59}\! \left(x \right) F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{59}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{53}\! \left(x \right)
F_{83}\! \left(x , y\right) = F_{55}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{85}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = 2 F_{6}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{100}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{103}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{2}\! \left(x \right)
F_{103}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{20}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{74}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{59}\! \left(x \right) F_{68}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{13}\! \left(x \right) F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{132}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{59}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = y F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = y F_{85}\! \left(x , y\right)
F_{151}\! \left(x \right) = F_{13}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{41}\! \left(x , 1\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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_151(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_10(x, k_0), F_4(x) + F_9(x, k_0))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_14(x, k_0) + F_148(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_12(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_13(x), x)
Eq(F_15(x, k_0), F_1(x) + F_14(x, k_0) + F_140(x, k_0) + F_142(x, k_0) + F_90(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_85(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_26(x, k_0))
Eq(F_17(x, k_0), F_0(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_24(x, k_0))
Eq(F_20(x, k_0), F_17(x, k_0) + F_21(x, k_0) + F_25(x, k_0))
Eq(F_21(x, k_0), F_13(x)*F_22(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_23(x, k_0), F_9(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_20(x, k_0)*F_24(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_13(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_129(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_20(x, k_0) + F_30(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0) + F_45(x, k_0))
Eq(F_32(x, k_0), F_24(x, k_0)*F_31(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_34(x, k_0), F_18(x, k_0) + F_33(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_37(x, k_0) + F_39(x, k_0) + F_6(x))
Eq(F_35(x, k_0), F_13(x)*F_36(x, k_0))
Eq(F_36(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_13(x)*F_38(x, k_0))
Eq(F_38(x, k_0), -F_34(x, 1) + (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_24(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0) + F_42(x, k_0))
Eq(F_41(x, k_0), F_34(x, k_0) + F_4(x))
Eq(F_42(x, k_0), k_0*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_13(x)*F_29(x, k_0))
Eq(F_45(x, k_0), F_117(x, k_0) + F_46(x, k_0) + F_47(x, k_0))
Eq(F_46(x, k_0), F_33(x, k_0) + F_5(x))
Eq(F_47(x, k_0), F_13(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_13(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_116(x, k_0) + F_51(x, k_0) + F_80(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_79(x, k_0))
Eq(F_52(x, k_0), F_17(x, k_0)*F_53(x))
Eq(F_53(x), F_54(x)/F_13(x))
Eq(F_54(x), -F_1(x) + F_55(x) - F_73(x) - F_77(x))
Eq(F_55(x), F_56(x) + F_62(x))
Eq(F_56(x), F_0(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_0(x)*F_13(x)*F_56(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_13(x)*F_59(x)**2)
Eq(F_62(x), F_5(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_13(x)*F_59(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_0(x)*F_62(x))
Eq(F_67(x), F_5(x)*F_68(x))
Eq(F_68(x), F_69(x, 1))
Eq(F_69(x, k_0), (-k_0*F_70(x, k_0) + F_70(x, 1))/(1 - k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_24(x, k_0)*F_70(x, k_0)**2)
Eq(F_73(x), F_13(x)*F_74(x))
Eq(F_74(x), F_55(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_13(x)*F_55(x)*F_59(x)*F_68(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_13(x)*F_55(x)*F_59(x))
Eq(F_79(x, k_0), F_26(x, k_0)*F_55(x))
Eq(F_80(x, k_0), F_13(x)*F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_83(x, k_0))
Eq(F_82(x, k_0), F_22(x, k_0)*F_53(x))
Eq(F_83(x, k_0), F_55(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_112(x, k_0) + F_85(x, k_0) + F_93(x, k_0))
Eq(F_85(x, k_0), 2*F_6(x) + F_86(x, k_0) + F_90(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), F_13(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_13(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_22(x, k_0) + F_84(x, k_0))
Eq(F_90(x, k_0), F_13(x)*F_16(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_24(x, k_0)*F_85(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_13(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_13(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_104(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_20(x, k_0)*F_99(x))
Eq(F_99(x), F_100(x)/F_13(x))
Eq(F_100(x), -F_1(x) + F_101(x) - F_103(x))
Eq(F_101(x), F_102(x)/F_13(x))
Eq(F_102(x), F_2(x))
Eq(F_103(x), F_13(x)*F_55(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_109(x, k_0)*F_4(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_26(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_13(x)*F_84(x, k_0))
Eq(F_109(x, k_0), F_1(x) + F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_109(x, k_0)*F_24(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_13(x))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_13(x)*F_20(x, k_0)*F_55(x))
Eq(F_116(x, k_0), F_24(x, k_0)*F_50(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_13(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_123(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_13(x)*F_59(x))
Eq(F_122(x, k_0), F_121(x, k_0)*F_13(x))
Eq(F_122(x, k_0), F_45(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_13(x))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_20(x, k_0)*F_74(x))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_30(x, k_0)*F_59(x)*F_68(x))
Eq(F_129(x, k_0), F_130(x, k_0))
Eq(F_130(x, k_0), F_109(x, k_0)*F_13(x)*F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_139(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_135(x, k_0) + F_137(x, k_0) + F_29(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_13(x)*F_50(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_125(x, k_0)*F_13(x))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_13(x)*F_132(x, k_0)*F_59(x))
Eq(F_139(x, k_0), F_129(x, k_0)*F_59(x))
Eq(F_140(x, k_0), F_13(x)*F_141(x, k_0))
Eq(F_141(x, k_0), F_12(x, k_0) + F_87(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_24(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_15(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), k_0*F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_13(x)*F_20(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_24(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_16(x, k_0))
Eq(F_150(x, k_0), k_0*F_85(x, k_0))
Eq(F_151(x), F_13(x)*F_152(x))
Eq(F_152(x), F_41(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], 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