02143_02413_20143_20413_24013

Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3509, 21006, 130090, 826970, 5367586, 35437376, 237304847, 1608306876, 11013004242, 76089163650, 529830064433, 3714914793732, 26207612017746, 185905623451824, 1325275268533856, 9489953164435804, 68232319531766121, 492414600357237980, 3565760672882106414, 25902148273830504940, 188702284368541195496, 1378425695350528263076, 10094188018346281969923, 74091232425241046343582, 545007719726541972689695, 4017153043249757878604158, 29666010111135449599196190, 219469954935776555263687774, 1626375067642013063996352136, 12071311673359735224816606764, 89730115101711959527135739785, 667939250717485364537289582482, 4978728218878776484520212836876, 37158040485460851751672569826644, 277659517787668565129859419102212, 2077170595647819575858916718018574, 15556356655635088391101929720533584, 116626617334396779983193653887998548, 875227532359393529689198565598543040, 6574437131133370158869450944105067436, 49430221635878286044018875590523830388, 371968462084615962132360811408211102544, 2801454121937078054765530828188530670553, 21115917729471586437391982618811433630464, 159283783162551957414840788320610846746488, 1202417357564015361067279336461191030171636, 9083404598843575041759252547142565339161528, 68665755007526761015965993857794610347879198, 519420246567791430626405580201360502377266009, 3931644996217474636434489841252365638106872222, 29778076260528873892101628245798833531139414678, 225671431559941368856799613195607364136650457216, 1711217854197117248647170651761207363307556500406, 12982980685039195843917229873040442812917111823436, 98554382955023764867120572531320536775984566936855, 748518132648772132148310942733031074369798663807508, 5687826624307327437423124165381728781423606744580910, 43241539837357067669807674979788988403480652685551280, 328897206287898191241534972841200393333686570220097277, 2502748491633601163899969534356217373209923699777639730, 19053127027057269556235917773174137780674751276849016838, 145111441198841928864089860179702081600444815339728574104, 1105650695744959539448077039769739589923153873899534824920, 8427716564243345395200822336635098698633327105709895561420, 64264717851557329507251013645986478305232945491974385005783, 490231509480197789619088588881745366646190465177905352308102, 3741030051587025657664146560851929927507267070514835720353946, 28558680824656466743478950690731397513639439439886052771750880, 218091053215065853373020173127472006038019479905820106175831114, 1666043269116485414689662804074205286327348206731711430321838740, 12731498987543181263631868654118509437348548469415313505514490853, 97322646143086040991460891353294326009053388628774997296038710460, 744193365949730918544662221159441651582273630955844423852749017324, 5692351950709891106584511678467694193403928077981505806102862673806, 43554038919728354247553901443415934803455168065391892504705824641640, 333344017962270954902690682795942730618367308506229959316677577467006, 2552004014849160451502058113254346522900065600575489350480996360539826, 19543013156221680554015244270066090556245160081233793160755415647062268, 149699487098859279990065897031679791897403902136572723290166662684070676, 1147004049753873982781155011043952342413861379120530027873113807863426962, 8790686079095735865757863793376172207199954783453378156486856802005516452, 67389338729769455610758356485647744556908134140016399128676662133151039424, 516734824544917120780543043516540103580839204470682795146452737481105146588, 3963236361477789129831610462294739381774291053438380477978193287029733227340, 30404341093111324624581996503508906266120979722682592108167386269057359443620, 233304087505204727592521345335586653231404418958506746988950266182445658188392, 1790639051885664896242753560828946936978581215833688054265048053864440533317096, 13746451401082277912731413274796609187775242304943130162009262409340227076216236, 105552361824645703396993853592834525201621121145940305734201763708175330910342101, 810658870451253089217120443458743155361245205803131037160445531537688890632012650, 6227292108411101032665081001286832513227493382654000774675035737685053789739841898, 47846414288719851121782100033594757834937984806363122951647863300456835840364538306, 367694230745857739051754376768936007226676365622399224610388245333517126814001115668, 2826244638263168010133134197105121689214334600061106507660233344257393755450587625248

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25000/
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[24,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[24,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[117,x]*F[12,x]*F[24,x]
F[12,x] = F[13,x,1]
F[14,x,k[0]] = F[13,x,k[0]]*F[25,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[26,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[25,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[22,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[21,x,k[0]]
F[20,x,k[0]] = F[0,x]+F[16,x,k[0]]
F[21,x,k[0]] = F[16,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[13,x,k[0]]*F[24,x]
F[24,x] = x
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[24,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[47,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[12,x]*F[24,x]*F[33,x,k[0]]
F[33,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[25,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x]+F[40,x,k[0]]
F[37,x] = F[38,x,1]
F[38,x,k[0]] = (F[39,x,k[0]]*k[0]-F[39,x,1])/(-1+k[0])
F[39,x,k[0]] = (-1+x^3*F[39,x,k[0]]^2*k[0]^3+6*x^2*F[39,x,k[0]]*k[0]^2+(-11*F[39,x,k[0]]+9)*x*k[0])*(x*F[39,x,k[0]]*k[0]-1)
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[25,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,1,k[0]]
F[43,x,k[0],k[1]] = (F[44,x,k[0],k[1]]*k[0]-F[44,x,1,k[1]])/(-1+k[0])
F[44,x,k[0],k[1]] = F[38,x,k[0]]+F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[25,x,k[1]]*F[43,x,k[0],k[1]]
F[47,x,k[0]] = F[101,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[13,x,k[0]]*F[25,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[34,x,k[0]]+F[52,x]
F[52,x] = (-1+x^3*F[52,x]^2+6*x^2*F[52,x]+(-11*F[52,x]+9)*x)*(x*F[52,x]-1)
F[53,x,k[0]] = F[54,x,k[0],1]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[0]*k[1]]
F[56,x,k[0],k[1]] = F[51,x,k[0]]+F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[57,x,k[0],k[1]]+F[68,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[58,x,k[1]]+F[61,x,k[0],k[1]]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[25,x,k[0]]*F[58,x,k[0]]
F[61,x,k[0],k[1]] = F[62,x,k[0]]+F[63,x,k[0],k[1]]
F[62,x,k[0]] = F[59,x,k[0]]
F[63,x,k[0],k[1]] = F[64,x]+F[65,x,k[0],k[1]]+F[67,x,k[1],k[0]]
F[64,x] = 0
F[65,x,k[0],k[1]] = F[25,x,k[0]]*F[66,x,k[0],k[1]]
F[66,x,k[0],k[1]] = F[59,x,k[1]]+F[63,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[25,x,k[0]]*F[61,x,k[1],k[0]]
F[68,x,k[0],k[1]] = F[69,x,k[0],k[1]]
F[69,x,k[0],k[1]] = F[24,x]*F[57,x,k[0],k[1]]*F[70,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[56,x,k[0],k[1]]+F[71,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[24,x]*F[73,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[74,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,1,k[0],k[1]]
F[75,x,k[0],k[1],k[2]] = (F[76,x,k[0],k[1],k[2]]*k[2]-F[76,x,k[0],k[1],1])/(-1+k[2])
F[76,x,k[0],k[1],k[2]] = F[77,x,k[0],k[2],k[1]]+F[97,x,k[0],k[1],k[2]]
F[77,x,k[0],k[1],k[2]] = F[78,x,k[1]]*F[95,x,k[0],k[2]]
F[78,x,k[0]] = F[79,x,k[0]]+F[82,x,k[0]]
F[79,x,k[0]] = F[58,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[24,x]*F[58,x,k[0]]*F[78,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[24,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[78,x,k[0]]*F[79,x,k[0]]
F[86,x,k[0]] = F[52,x]*F[87,x,k[0]]
F[87,x,k[0]] = (F[88,x,k[0]]-F[88,x,1])/(-1+k[0])
F[78,x,k[0]] = F[88,x,k[0]]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[52,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[24,x]*F[52,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[78,x,1]
F[95,x,k[0],k[1]] = F[52,x]+F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = k[0]*F[34,x,k[1]]
F[97,x,k[0],k[1],k[2]] = k[0]*F[98,x,k[2],k[2]]
F[98,x,k[0],k[1]] = F[51,x,k[0]]*F[99,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[78,x,k[1]]+F[99,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[55,x,k[0],k[1]]*F[70,x,k[0],k[1]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[25,x,k[0]]*F[51,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]*F[116,x,k[0]]*F[25,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]+F[110,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[108,x,k[0]]
F[107,x,k[0]] = (F[15,x,k[0]]-F[15,x,1])/(-1+k[0])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[106,x,k[0]]*F[25,x,k[0]]
F[110,x,k[0]] = F[111,x,1,k[0]]
F[111,x,k[0],k[1]] = F[112,x]*F[114,x,k[0],k[1]]
F[112,x] = F[113,x]
F[113,x] = F[12,x]*F[24,x]
F[114,x,k[0],k[1]] = F[1,x]+F[115,x,k[0],k[1]]
F[115,x,k[0],k[1]] = k[0]*F[62,x,k[1]]
F[116,x,k[0]] = F[58,x,k[0]]
F[117,x] = F[118,x]+F[52,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[24,x]
F[120,x] = F[121,x]+F[37,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[24,x]
F[123,x] = F[124,x,1]
F[124,x,k[0]] = (F[125,x,k[0]]*k[0]-F[125,x,1])/(-1+k[0])
F[125,x,k[0]] = F[126,x,k[0]]+F[38,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[127,x,k[0]] = F[124,x,k[0]]*F[24,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_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{14}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = x
F_{25}\! \left(x , y_{0}\right) = y_{0} x
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)+F_{47}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y_{0}\right) = F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right) F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)
F_{37}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{38}\! \left(x , y_{0}\right) = -\frac{-F_{39}\! \left(x , y_{0}\right) y_{0}+F_{39}\! \left(x , 1\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}\right) = y_{0}^{4} x^{4} F_{39}\! \left(x , y_{0}\right)^{3}+5 x^{3} F_{39}\! \left(x , y_{0}\right)^{2} y_{0}^{3}-11 y_{0}^{2} x^{2} F_{39}\! \left(x , y_{0}\right)^{2}+3 x^{2} F_{39}\! \left(x , y_{0}\right) y_{0}^{2}+10 x F_{39}\! \left(x , y_{0}\right) y_{0}-9 y_{0} x +1
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = x^{4} F_{52} \left(x \right)^{3}+5 x^{3} F_{52} \left(x \right)^{2}-11 x^{2} F_{52} \left(x \right)^{2}+3 x^{2} F_{52}\! \left(x \right)+10 x F_{52}\! \left(x \right)-9 x +1
F_{53}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}, 1\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{1}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{62}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{64}\! \left(x \right)+F_{65}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}, y_{0}\right)
F_{64}\! \left(x \right) = 0
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}, y_{1}\right)
F_{66}\! \left(x , y_{0}, y_{1}\right) = F_{59}\! \left(x , y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{67}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}\right) F_{61}\! \left(x , y_{1}, y_{0}\right)
F_{68}\! \left(x , y_{0}, y_{1}\right) = F_{69}\! \left(x , y_{0}, y_{1}\right)
F_{69}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x \right) F_{57}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = F_{72}\! \left(x , y_{0}, y_{1}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , 1, y_{0}, y_{1}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{76}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{77}\! \left(x , y_{0}, y_{2}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{78}\! \left(x , y_{1}\right) F_{95}\! \left(x , y_{0}, y_{2}\right)
F_{78}\! \left(x , y_{0}\right) = F_{79}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{81}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{58}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{85}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{52}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = -\frac{-F_{88}\! \left(x , y_{0}\right)+F_{88}\! \left(x , 1\right)}{-1+y_{0}}
F_{78}\! \left(x , y_{0}\right) = F_{88}\! \left(x , y_{0}\right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{52}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{24}\! \left(x \right) F_{52}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{52}\! \left(x \right)+F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{34}\! \left(x , y_{1}\right)
F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{98}\! \left(x , y_{2}, y_{2}\right)
F_{98}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right) F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{78}\! \left(x , y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{116}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{110}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x , y_{0}\right)+F_{108}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = -\frac{-F_{15}\! \left(x , y_{0}\right)+F_{15}\! \left(x , 1\right)}{-1+y_{0}}
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , y_{0}\right)
F_{109}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , 1, y_{0}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x \right) F_{114}\! \left(x , y_{0}, y_{1}\right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{115}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{62}\! \left(x , y_{1}\right)
F_{116}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{52}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{24}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{37}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{24}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x , 1\right)
F_{124}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{125}\! \left(x , y_{0}\right)+F_{125}\! \left(x , 1\right)}{-1+y_{0}}
F_{125}\! \left(x , y_{0}\right) = F_{126}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)
F_{127}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right) F_{24}\! \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_24(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_24(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_117(x)*F_12(x)*F_24(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_14(x, k_0), F_13(x, k_0)*F_25(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_26(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_25(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_22(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_21(x, k_0))
Eq(F_20(x, k_0), F_0(x) + F_16(x, k_0))
Eq(F_21(x, k_0), F_16(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_13(x, k_0)*F_24(x))
Eq(F_24(x), x)
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_24(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_47(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_12(x)*F_24(x)*F_33(x, k_0))
Eq(F_33(x, k_0), -F_34(x, 1) + (-k_0*F_34(x, k_0) + F_34(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_25(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x) + F_40(x, k_0))
Eq(F_37(x), F_38(x, 1))
Eq(F_38(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), k_0**4*x**4*F_39(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_39(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_39(x, k_0) + 1)
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_25(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, 1, k_0))
Eq(F_43(x, k_0, k_1), (-k_0*F_44(x, k_0, k_1) + F_44(x, 1, k_1))/(1 - k_0))
Eq(F_44(x, k_0, k_1), F_38(x, k_0) + F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_25(x, k_1)*F_43(x, k_0, k_1))
Eq(F_47(x, k_0), F_101(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_13(x, k_0)*F_25(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_34(x, k_0) + F_52(x))
Eq(F_52(x), x**4*F_52(x)**3 + x**2*(5*x - 11)*F_52(x)**2 - 9*x + (3*x**2 + 10*x)*F_52(x) + 1)
Eq(F_53(x, k_0), F_54(x, k_0, 1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_0*k_1))
Eq(F_56(x, k_0, k_1), F_51(x, k_0) + F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0, k_1) + F_68(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_1) + F_61(x, k_0, k_1))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_25(x, k_0)*F_58(x, k_0))
Eq(F_61(x, k_0, k_1), F_62(x, k_0) + F_63(x, k_0, k_1))
Eq(F_62(x, k_0), F_59(x, k_0))
Eq(F_63(x, k_0, k_1), F_64(x) + F_65(x, k_0, k_1) + F_67(x, k_1, k_0))
Eq(F_64(x), 0)
Eq(F_65(x, k_0, k_1), F_25(x, k_0)*F_66(x, k_0, k_1))
Eq(F_66(x, k_0, k_1), F_59(x, k_1) + F_63(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_25(x, k_0)*F_61(x, k_1, k_0))
Eq(F_68(x, k_0, k_1), F_69(x, k_0, k_1))
Eq(F_69(x, k_0, k_1), F_24(x)*F_57(x, k_0, k_1)*F_70(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_56(x, k_0, k_1) + F_71(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_24(x)*F_73(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_100(x, k_0, k_1) + F_74(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, 1, k_0, k_1))
Eq(F_75(x, k_0, k_1, k_2), (-k_2*F_76(x, k_0, k_1, k_2) + F_76(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_76(x, k_0, k_1, k_2), F_77(x, k_0, k_2, k_1) + F_97(x, k_0, k_1, k_2))
Eq(F_77(x, k_0, k_1, k_2), F_78(x, k_1)*F_95(x, k_0, k_2))
Eq(F_78(x, k_0), F_79(x, k_0) + F_82(x, k_0))
Eq(F_79(x, k_0), F_58(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_24(x)*F_58(x, k_0)*F_78(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_24(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_78(x, k_0)*F_79(x, k_0))
Eq(F_86(x, k_0), F_52(x)*F_87(x, k_0))
Eq(F_87(x, k_0), -F_88(x, k_0) + (-k_0*F_88(x, k_0) + F_88(x, 1))/(1 - k_0))
Eq(F_78(x, k_0), F_88(x, k_0) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_52(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_24(x)*F_52(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_78(x, 1))
Eq(F_95(x, k_0, k_1), F_52(x) + F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), k_0*F_34(x, k_1))
Eq(F_97(x, k_0, k_1, k_2), k_0*F_98(x, k_2, k_2))
Eq(F_98(x, k_0, k_1), F_51(x, k_0)*F_99(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_78(x, k_1) + F_99(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_55(x, k_0, k_1)*F_70(x, k_0, k_1))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_25(x, k_0)*F_51(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0)*F_116(x, k_0)*F_25(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0) + F_110(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_108(x, k_0))
Eq(F_107(x, k_0), -F_15(x, k_0) + (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_106(x, k_0)*F_25(x, k_0))
Eq(F_110(x, k_0), F_111(x, 1, k_0))
Eq(F_111(x, k_0, k_1), F_112(x)*F_114(x, k_0, k_1))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_12(x)*F_24(x))
Eq(F_114(x, k_0, k_1), F_1(x) + F_115(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), k_0*F_62(x, k_1))
Eq(F_116(x, k_0), F_58(x, k_0))
Eq(F_117(x), F_118(x) + F_52(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_24(x))
Eq(F_120(x), F_121(x) + F_37(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_24(x))
Eq(F_123(x), F_124(x, 1))
Eq(F_124(x, k_0), (-k_0*F_125(x, k_0) + F_125(x, 1))/(1 - k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_38(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_127(x, k_0), F_124(x, k_0)*F_24(x))
Pack JSON:
{"name": "point_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, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]]}], "iterative": false}
Specification JSON:
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"pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": true}}, {"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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25816/
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[24,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[24,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[117,x]*F[12,x]*F[24,x]
F[12,x] = F[13,x,1]
F[14,x,k[0]] = F[13,x,k[0]]*F[25,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[26,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[25,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[22,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[21,x,k[0]]
F[20,x,k[0]] = F[0,x]+F[16,x,k[0]]
F[21,x,k[0]] = F[16,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[13,x,k[0]]*F[24,x]
F[24,x] = x
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[24,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[47,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[12,x]*F[24,x]*F[33,x,k[0]]
F[33,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[25,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x]+F[40,x,k[0]]
F[37,x] = F[38,x,1]
F[38,x,k[0]] = (F[39,x,k[0]]*k[0]-F[39,x,1])/(-1+k[0])
F[39,x,k[0]] = (-1+x^3*F[39,x,k[0]]^2*k[0]^3+6*x^2*F[39,x,k[0]]*k[0]^2+(-11*F[39,x,k[0]]+9)*x*k[0])*(x*F[39,x,k[0]]*k[0]-1)
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[25,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,1,k[0]]
F[43,x,k[0],k[1]] = (F[44,x,k[0],k[1]]*k[0]-F[44,x,1,k[1]])/(-1+k[0])
F[44,x,k[0],k[1]] = F[38,x,k[0]]+F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[25,x,k[1]]*F[43,x,k[0],k[1]]
F[47,x,k[0]] = F[101,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[13,x,k[0]]*F[25,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[34,x,k[0]]+F[52,x]
F[52,x] = (-1+x^3*F[52,x]^2+6*x^2*F[52,x]+(-11*F[52,x]+9)*x)*(x*F[52,x]-1)
F[53,x,k[0]] = F[54,x,k[0],1]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[0]*k[1]]
F[56,x,k[0],k[1]] = F[51,x,k[0]]+F[55,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[57,x,k[0],k[1]]+F[68,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[58,x,k[1]]+F[61,x,k[0],k[1]]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[25,x,k[0]]*F[58,x,k[0]]
F[61,x,k[0],k[1]] = F[62,x,k[0]]+F[63,x,k[0],k[1]]
F[62,x,k[0]] = F[59,x,k[0]]
F[63,x,k[0],k[1]] = F[64,x]+F[65,x,k[0],k[1]]+F[67,x,k[1],k[0]]
F[64,x] = 0
F[65,x,k[0],k[1]] = F[25,x,k[0]]*F[66,x,k[0],k[1]]
F[66,x,k[0],k[1]] = F[59,x,k[1]]+F[63,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[25,x,k[0]]*F[61,x,k[1],k[0]]
F[68,x,k[0],k[1]] = F[69,x,k[0],k[1]]
F[69,x,k[0],k[1]] = F[24,x]*F[57,x,k[0],k[1]]*F[70,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[56,x,k[0],k[1]]+F[71,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[24,x]*F[73,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[74,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,1,k[0],k[1]]
F[75,x,k[0],k[1],k[2]] = (F[76,x,k[0],k[1],k[2]]*k[2]-F[76,x,k[0],k[1],1])/(-1+k[2])
F[76,x,k[0],k[1],k[2]] = F[77,x,k[0],k[2],k[1]]+F[97,x,k[0],k[1],k[2]]
F[77,x,k[0],k[1],k[2]] = F[78,x,k[1]]*F[95,x,k[0],k[2]]
F[78,x,k[0]] = F[79,x,k[0]]+F[82,x,k[0]]
F[79,x,k[0]] = F[58,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[24,x]*F[58,x,k[0]]*F[78,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[24,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[78,x,k[0]]*F[79,x,k[0]]
F[86,x,k[0]] = F[52,x]*F[87,x,k[0]]
F[87,x,k[0]] = (F[88,x,k[0]]-F[88,x,1])/(-1+k[0])
F[78,x,k[0]] = F[88,x,k[0]]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[52,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[24,x]*F[52,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[78,x,1]
F[95,x,k[0],k[1]] = F[52,x]+F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = k[0]*F[34,x,k[1]]
F[97,x,k[0],k[1],k[2]] = k[0]*F[98,x,k[2],k[2]]
F[98,x,k[0],k[1]] = F[51,x,k[0]]*F[99,x,k[0],k[1]]
F[70,x,k[0],k[1]] = F[78,x,k[1]]+F[99,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[55,x,k[0],k[1]]*F[70,x,k[0],k[1]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[25,x,k[0]]*F[51,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]*F[116,x,k[0]]*F[25,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]+F[110,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[108,x,k[0]]
F[107,x,k[0]] = (F[15,x,k[0]]-F[15,x,1])/(-1+k[0])
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[106,x,k[0]]*F[25,x,k[0]]
F[110,x,k[0]] = F[111,x,1,k[0]]
F[111,x,k[0],k[1]] = F[112,x]*F[114,x,k[0],k[1]]
F[112,x] = F[113,x]
F[113,x] = F[12,x]*F[24,x]
F[114,x,k[0],k[1]] = F[1,x]+F[115,x,k[0],k[1]]
F[115,x,k[0],k[1]] = k[0]*F[62,x,k[1]]
F[116,x,k[0]] = F[58,x,k[0]]
F[117,x] = F[118,x]+F[52,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[24,x]
F[120,x] = F[121,x]+F[37,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[24,x]
F[123,x] = F[124,x,1]
F[124,x,k[0]] = (F[125,x,k[0]]*k[0]-F[125,x,1])/(-1+k[0])
F[125,x,k[0]] = F[126,x,k[0]]+F[38,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[127,x,k[0]] = F[124,x,k[0]]*F[24,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_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{14}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = x
F_{25}\! \left(x , y_{0}\right) = y_{0} x
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)+F_{47}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y_{0}\right) = F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right) F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)
F_{37}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{38}\! \left(x , y_{0}\right) = -\frac{-F_{39}\! \left(x , y_{0}\right) y_{0}+F_{39}\! \left(x , 1\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}\right) = y_{0}^{4} x^{4} F_{39}\! \left(x , y_{0}\right)^{3}+5 x^{3} F_{39}\! \left(x , y_{0}\right)^{2} y_{0}^{3}-11 y_{0}^{2} x^{2} F_{39}\! \left(x , y_{0}\right)^{2}+3 x^{2} F_{39}\! \left(x , y_{0}\right) y_{0}^{2}+10 x F_{39}\! \left(x , y_{0}\right) y_{0}-9 y_{0} x +1
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = x^{4} F_{52} \left(x \right)^{3}+5 x^{3} F_{52} \left(x \right)^{2}-11 x^{2} F_{52} \left(x \right)^{2}+3 x^{2} F_{52}\! \left(x \right)+10 x F_{52}\! \left(x \right)-9 x +1
F_{53}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}, 1\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{1}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{62}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}, y_{1}\right) = F_{64}\! \left(x \right)+F_{65}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}, y_{0}\right)
F_{64}\! \left(x \right) = 0
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}, y_{1}\right)
F_{66}\! \left(x , y_{0}, y_{1}\right) = F_{59}\! \left(x , y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{67}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}\right) F_{61}\! \left(x , y_{1}, y_{0}\right)
F_{68}\! \left(x , y_{0}, y_{1}\right) = F_{69}\! \left(x , y_{0}, y_{1}\right)
F_{69}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x \right) F_{57}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = F_{72}\! \left(x , y_{0}, y_{1}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , 1, y_{0}, y_{1}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{76}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{77}\! \left(x , y_{0}, y_{2}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{78}\! \left(x , y_{1}\right) F_{95}\! \left(x , y_{0}, y_{2}\right)
F_{78}\! \left(x , y_{0}\right) = F_{79}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{81}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{58}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{83}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{85}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{78}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{52}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = -\frac{-F_{88}\! \left(x , y_{0}\right)+F_{88}\! \left(x , 1\right)}{-1+y_{0}}
F_{78}\! \left(x , y_{0}\right) = F_{88}\! \left(x , y_{0}\right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{52}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{24}\! \left(x \right) F_{52}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{52}\! \left(x \right)+F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{34}\! \left(x , y_{1}\right)
F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{98}\! \left(x , y_{2}, y_{2}\right)
F_{98}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}\right) F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{78}\! \left(x , y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right) F_{116}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)+F_{110}\! \left(x , y_{0}\right)
F_{106}\! \left(x , y_{0}\right) = F_{107}\! \left(x , y_{0}\right)+F_{108}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}\right) = -\frac{-F_{15}\! \left(x , y_{0}\right)+F_{15}\! \left(x , 1\right)}{-1+y_{0}}
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , y_{0}\right)
F_{109}\! \left(x , y_{0}\right) = F_{106}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , 1, y_{0}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x \right) F_{114}\! \left(x , y_{0}, y_{1}\right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{115}\! \left(x , y_{0}, y_{1}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{62}\! \left(x , y_{1}\right)
F_{116}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{52}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{24}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{37}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{24}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x , 1\right)
F_{124}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{125}\! \left(x , y_{0}\right)+F_{125}\! \left(x , 1\right)}{-1+y_{0}}
F_{125}\! \left(x , y_{0}\right) = F_{126}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)
F_{127}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right) F_{24}\! \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_24(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_24(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_117(x)*F_12(x)*F_24(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_14(x, k_0), F_13(x, k_0)*F_25(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_26(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_25(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_22(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_21(x, k_0))
Eq(F_20(x, k_0), F_0(x) + F_16(x, k_0))
Eq(F_21(x, k_0), F_16(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_13(x, k_0)*F_24(x))
Eq(F_24(x), x)
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_24(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_47(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_12(x)*F_24(x)*F_33(x, k_0))
Eq(F_33(x, k_0), -F_34(x, 1) + (-k_0*F_34(x, k_0) + F_34(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_25(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x) + F_40(x, k_0))
Eq(F_37(x), F_38(x, 1))
Eq(F_38(x, k_0), (-k_0*F_39(x, k_0) + F_39(x, 1))/(1 - k_0))
Eq(F_39(x, k_0), k_0**4*x**4*F_39(x, k_0)**3 + k_0**2*x**2*(5*k_0*x - 11)*F_39(x, k_0)**2 - 9*k_0*x + (3*k_0**2*x**2 + 10*k_0*x)*F_39(x, k_0) + 1)
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_25(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, 1, k_0))
Eq(F_43(x, k_0, k_1), (-k_0*F_44(x, k_0, k_1) + F_44(x, 1, k_1))/(1 - k_0))
Eq(F_44(x, k_0, k_1), F_38(x, k_0) + F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_25(x, k_1)*F_43(x, k_0, k_1))
Eq(F_47(x, k_0), F_101(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_13(x, k_0)*F_25(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_34(x, k_0) + F_52(x))
Eq(F_52(x), x**4*F_52(x)**3 + x**2*(5*x - 11)*F_52(x)**2 - 9*x + (3*x**2 + 10*x)*F_52(x) + 1)
Eq(F_53(x, k_0), F_54(x, k_0, 1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_0*k_1))
Eq(F_56(x, k_0, k_1), F_51(x, k_0) + F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0, k_1) + F_68(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_1) + F_61(x, k_0, k_1))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_25(x, k_0)*F_58(x, k_0))
Eq(F_61(x, k_0, k_1), F_62(x, k_0) + F_63(x, k_0, k_1))
Eq(F_62(x, k_0), F_59(x, k_0))
Eq(F_63(x, k_0, k_1), F_64(x) + F_65(x, k_0, k_1) + F_67(x, k_1, k_0))
Eq(F_64(x), 0)
Eq(F_65(x, k_0, k_1), F_25(x, k_0)*F_66(x, k_0, k_1))
Eq(F_66(x, k_0, k_1), F_59(x, k_1) + F_63(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_25(x, k_0)*F_61(x, k_1, k_0))
Eq(F_68(x, k_0, k_1), F_69(x, k_0, k_1))
Eq(F_69(x, k_0, k_1), F_24(x)*F_57(x, k_0, k_1)*F_70(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_56(x, k_0, k_1) + F_71(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_24(x)*F_73(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_100(x, k_0, k_1) + F_74(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, 1, k_0, k_1))
Eq(F_75(x, k_0, k_1, k_2), (-k_2*F_76(x, k_0, k_1, k_2) + F_76(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_76(x, k_0, k_1, k_2), F_77(x, k_0, k_2, k_1) + F_97(x, k_0, k_1, k_2))
Eq(F_77(x, k_0, k_1, k_2), F_78(x, k_1)*F_95(x, k_0, k_2))
Eq(F_78(x, k_0), F_79(x, k_0) + F_82(x, k_0))
Eq(F_79(x, k_0), F_58(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_24(x)*F_58(x, k_0)*F_78(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_24(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_78(x, k_0)*F_79(x, k_0))
Eq(F_86(x, k_0), F_52(x)*F_87(x, k_0))
Eq(F_87(x, k_0), -F_88(x, k_0) + (-k_0*F_88(x, k_0) + F_88(x, 1))/(1 - k_0))
Eq(F_78(x, k_0), F_88(x, k_0) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_52(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_24(x)*F_52(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_78(x, 1))
Eq(F_95(x, k_0, k_1), F_52(x) + F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), k_0*F_34(x, k_1))
Eq(F_97(x, k_0, k_1, k_2), k_0*F_98(x, k_2, k_2))
Eq(F_98(x, k_0, k_1), F_51(x, k_0)*F_99(x, k_0, k_1))
Eq(F_70(x, k_0, k_1), F_78(x, k_1) + F_99(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_55(x, k_0, k_1)*F_70(x, k_0, k_1))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_25(x, k_0)*F_51(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0)*F_116(x, k_0)*F_25(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0) + F_110(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_108(x, k_0))
Eq(F_107(x, k_0), -F_15(x, k_0) + (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_106(x, k_0)*F_25(x, k_0))
Eq(F_110(x, k_0), F_111(x, 1, k_0))
Eq(F_111(x, k_0, k_1), F_112(x)*F_114(x, k_0, k_1))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_12(x)*F_24(x))
Eq(F_114(x, k_0, k_1), F_1(x) + F_115(x, k_0, k_1))
Eq(F_115(x, k_0, k_1), k_0*F_62(x, k_1))
Eq(F_116(x, k_0), F_58(x, k_0))
Eq(F_117(x), F_118(x) + F_52(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_24(x))
Eq(F_120(x), F_121(x) + F_37(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_24(x))
Eq(F_123(x), F_124(x, 1))
Eq(F_124(x, k_0), (-k_0*F_125(x, k_0) + F_125(x, 1))/(1 - k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_38(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_127(x, k_0), F_124(x, k_0)*F_24(x))
Pack JSON:
{"name": "point_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, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 3], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 0], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 0], [2, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [2, 3], [2, 4]]}, {"patt": [1, 0, 2], "pos": [[2, 3], [2, 3], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 4], [2, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 4], [0, 4], [2, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 0], [0, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 0], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [2, 3], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 4], [2, 3], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 0], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 0], [2, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [0, 4], [2, 3], [2, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [2, 4], [2, 3], [2, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 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