1032_2301_135204
Counting sequence:
1, 1, 2, 6, 22, 86, 339, 1327, 5150, 19854, 76207, 291779, 1115824, 4265768, 16311631, 62408147, 238953334, 915710678, 3512353576, 13484647856, 51817954180, 199302558244, 767232933822, 2956049094966, 11398657769708, 43988678547980, 169887272986273, 656600806194661, 2539515844733796, 9828746938209132, 38065568786413783, 147517363220479915, 572032590569193638, 2219503498227297638, 8616668223964686324, 33470549573238727596, 130082268367374971332, 505821598625885167876, 1967855596726121709722, 7659467618390172506914, 29826800934795476277188, 116201312263238480476516, 452903287026819046237742, 1765973099190564814331254, 6888762458183982317122160, 26882610263438038482199264, 104946891311649846095957030, 409855409527853384357955022, 1601216123953765776698518460, 6257817079905895496743292668, 24464988859841405630775390368, 95678030636685491494425695920, 374300533626986323198063887080, 1464757748881493693649533492392, 5733826909158786386577316812764, 22451904707976730366427697800140, 87940351637974042070207490578072, 344545268113741627626364999935448, 1350281380277557676235904100505317, 5293209661182967445982655514716873, 20755241269985071963262857383643340, 81404328743159346762760862956158580, 319356301596499925503279666534662311, 1253167461677515054969630295501816347, 4918648683156963216460450746034028294, 19310037024617537975461030970974613638, 75826085631094290923052183724772952476, 297817419600931105903915514733999019252, 1169971448726859255466012359608398249604, 4597185115455809311859172891463555753348, 18067505927854219981254637958601569692226, 71021836539650726585393063969029276096042, 279235819740083254353410377232946100058324, 1098080084424061308017116341547507345962868, 4318955612274211541310407005591523696258546, 16990397651381667292078598273119185580379082, 66850816646440384310633933418775014144089344, 263079257752022105934515857437344547271583888, 1035479758387251934518036235646453837022369666, 4076337937012456828231309622256341555074741882, 16049843509807372488488385508354439040973656404, 63203629208359459982936855809453613632375827348, 248932961172952266356312557300995167717522328976, 980597070990555988758439025791886430930112777472, 3863360535752769511907972935242557058445500783224, 15223168332234318420767998048503094654803550223928, 59994130331818470523862669493133901671606267249956, 236469510098552630665579579390186723333021252894132, 932186967767488520394277427833782957984423874665064, 3675286767554615814046947267551650445583207175333928, 14492344113774260955107079739256582762571915105246506, 57153673847772356705027565860120483065984215788425362, 225427403849681667117809990045063147972862017226807624, 889252865090800531833869527225618925836055383637265048, 3508317051404196219950954521776215621072179548644132886, 13842878617909455114825411885349723279175893192240630302, 54626961726971071413986968863916952919789975629782270044, 215595558431558067723981351191829998520668716484788433628, 850988699345872282950187886100877049315859304051440316776, 3359372110562576845922563105872173365413824029878419445912, 13263004170949752202457670768179675120201353599630473119464
Generating function in Maple syntax:
-1/2*(3*(1-4*x)^(1/2)*x^2+2*x^3-4*(1-4*x)^(1/2)*x-9*x^2+(1-4*x)^(1/2)+6*x-1)*(3*x-1)^2*(x-1)/x^6/(2*x-1)
Generating function in latex syntax:
-\frac{\left(3 \sqrt{1-4 x}\, x^{2}+2 x^{3}-4 \sqrt{1-4 x}\, x -9 x^{2}+\sqrt{1-4 x}+6 x -1\right) \left(3 x -1\right)^{2} \left(x -1\right)}{2 x^{6} \left(2 x -1\right)}
Generating function in sympy syntax:
(x - 1)*(3*x - 1)**2*(-x**3 - 3*x**2*sqrt(1 - 4*x)/2 + 9*x**2/2 + 2*x*sqrt(1 - 4*x) - 3*x - sqrt(1 - 4*x)/2 + 1/2)/(x**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x^6*(2*x-1)^2*F(x)^2+(x-1)*(x^2-4*x+1)*(3*x-1)^2*(2*x-1)^2*F(x)+(x-1)^2*(3*x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
x^{6} \left(2 x -1\right)^{2} F \! \left(x \right)^{2}+\left(x -1\right) \left(x^{2}-4 x +1\right) \left(3 x -1\right)^{2} \left(2 x -1\right)^{2} F \! \left(x \right)+\left(x -1\right)^{2} \left(3 x -1\right)^{4} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -12*(3+2*n)/(10+n)*a(n)+2*(94+25*n)/(10+n)*a(n+1)-7*(29+5*n)/(10+n)*a(n+2)+(79+10*n)/(10+n)*a(n+3), n >= 4
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(n +4\right) = -\frac{12 \left(3+2 n \right) a \! \left(n \right)}{10+n}+\frac{2 \left(94+25 n \right) a \! \left(n +1\right)}{10+n}-\frac{7 \left(29+5 n \right) a \! \left(n +2\right)}{10+n}+\frac{\left(79+10 n \right) a \! \left(n +3\right)}{10+n}, \quad n \geq 4
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24010/
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[5,x]
F[3,x] = F[1,x]+F[114,x]+F[4,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[1,x]+F[112,x]+F[7,x]+F[87,x]
F[7,x] = F[5,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x]+F[52,x,k[0]]
F[10,x] = F[11,x]+F[3,x]
F[11,x] = F[12,x]*F[5,x]
F[12,x] = F[13,x]+F[47,x]+F[50,x]
F[13,x] = F[14,x,1]
F[15,x,k[0]] = F[14,x,k[0]]*F[5,x]
F[16,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[49,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[32,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]+F[22,x,k[0]]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[5,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]*F[26,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[1,x]+F[23,x,k[0]]
F[27,x,k[0]] = F[28,x]+F[29,x,k[0]]+F[31,x,k[0]]
F[28,x] = 0
F[29,x,k[0]] = F[25,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = F[20,x]+F[27,x,k[0]]
F[31,x,k[0]] = F[22,x,k[0]]*F[5,x]
F[32,x,k[0]] = F[33,x,k[0]]*F[5,x]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[35,x,k[0]]+F[41,x,k[0]]
F[34,x,k[0]] = F[25,x,k[0]]*F[33,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[5,x]
F[36,x,k[0]] = F[14,x,k[0]]+F[37,x]
F[37,x] = -F[38,x]+F[6,x]
F[38,x] = F[1,x]+F[39,x]+F[40,x]
F[39,x] = F[10,x]*F[5,x]
F[40,x] = F[5,x]*F[6,x]
F[41,x,k[0]] = F[42,x,k[0]]*F[5,x]
F[42,x,k[0]] = F[33,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]*F[5,x]
F[44,x,k[0]] = (F[45,x,k[0]]*k[0]-F[45,x,1])/(-1+k[0])
F[45,x,k[0]] = F[14,x,k[0]]+F[46,x,k[0]]+F[47,x]
F[46,x,k[0]] = F[44,x,k[0]]*F[5,x]
F[47,x] = F[48,x]*F[5,x]
F[48,x] = 1/F[5,x]*F[37,x]
F[49,x,k[0]] = F[16,x,k[0]]*F[25,x,k[0]]
F[50,x] = F[5,x]*F[51,x]
F[51,x] = F[44,x,1]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[25,x,k[0]]*F[54,x,k[0]]*F[66,x]
F[54,x,k[0]] = F[55,x,k[0]]+F[58,x,k[0]]
F[55,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[25,x,k[0]]*F[55,x,k[0]]
F[58,x,k[0]] = F[59,x]+F[62,x,k[0]]
F[59,x] = F[60,x]
F[60,x] = F[5,x]*F[61,x]
F[61,x] = F[1,x]+F[59,x]
F[62,x,k[0]] = F[28,x]+F[63,x,k[0]]+F[65,x,k[0]]
F[63,x,k[0]] = F[5,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[56,x,k[0]]+F[62,x,k[0]]
F[65,x,k[0]] = F[25,x,k[0]]*F[58,x,k[0]]
F[66,x] = F[1,x]+F[67,x]+F[74,x]
F[67,x] = F[5,x]*F[68,x]
F[68,x] = F[61,x]+F[69,x]
F[69,x] = F[20,x]+F[70,x]
F[70,x] = F[28,x]+F[71,x]+F[73,x]
F[71,x] = F[5,x]*F[72,x]
F[72,x] = F[59,x]+F[70,x]
F[73,x] = F[5,x]*F[69,x]
F[74,x] = F[5,x]*F[75,x]
F[75,x] = F[1,x]+F[76,x]+F[77,x]+F[82,x]
F[76,x] = F[5,x]*F[75,x]
F[77,x] = F[5,x]*F[78,x]
F[78,x] = F[11,x]+F[79,x]
F[79,x] = 1/F[5,x]*F[80,x]
F[80,x] = -F[1,x]-F[81,x]+F[66,x]
F[81,x] = F[5,x]*F[66,x]
F[82,x] = F[5,x]*F[83,x]
F[83,x] = 1/F[5,x]*F[84,x]
F[84,x] = -F[1,x]-F[85,x]-F[86,x]+F[6,x]
F[85,x] = -F[1,x]-F[74,x]+F[38,x]
F[86,x] = F[5,x]*F[78,x]
F[87,x] = F[5,x]*F[88,x]
F[88,x] = F[89,x,1]
F[89,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[90,x,k[0]]+F[92,x,k[0]]+F[94,x,k[0]]
F[90,x,k[0]] = F[5,x]*F[91,x,k[0]]
F[91,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[92,x,k[0]] = F[5,x]*F[93,x,k[0]]
F[93,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[95,x,k[0]] = F[1,x]+F[101,x,k[0]]+F[94,x,k[0]]+F[99,x,k[0]]
F[95,x,k[0]] = F[1,x]+F[96,x,k[0]]+F[97,x,k[0]]+F[98,x,k[0]]
F[96,x,k[0]] = F[5,x]*F[89,x,k[0]]
F[97,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[98,x,k[0]] = F[25,x,k[0]]*F[95,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[5,x]
F[100,x,k[0]] = 1/(-1+k[0])*(F[95,x,k[0]]*k[0]-F[95,x,1])
F[101,x,k[0]] = F[102,x,k[0]]*F[25,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[54,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[58,x,k[0]]
F[104,x,k[0]] = F[105,x]+F[108,x,k[0]]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[5,x]
F[107,x] = F[105,x]+F[59,x]
F[108,x,k[0]] = 2*F[28,x]+F[109,x,k[0]]+F[111,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[5,x]
F[110,x,k[0]] = F[108,x,k[0]]+F[62,x,k[0]]
F[111,x,k[0]] = F[104,x,k[0]]*F[25,x,k[0]]
F[112,x] = F[113,x]*F[5,x]
F[113,x] = F[33,x,1]
F[114,x] = F[10,x]*F[5,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{114}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{7}\! \left(x \right)+F_{87}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{3}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right) F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = F_{5}\! \left(x \right) F_{6}\! \left(x \right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{44}\! \left(x , y\right) = -\frac{-y F_{45}\! \left(x , y\right)+F_{45}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{47}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{49}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{5}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{54}\! \left(x , y\right) F_{66}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{5}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{67}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{61}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{28}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{5}\! \left(x \right) F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{5}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)+F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{76}\! \left(x \right) = F_{5}\! \left(x \right) F_{75}\! \left(x \right)
F_{77}\! \left(x \right) = F_{5}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{80}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{81}\! \left(x \right)+F_{66}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right) F_{66}\! \left(x \right)
F_{82}\! \left(x \right) = F_{5}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{84}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{85}\! \left(x \right)-F_{86}\! \left(x \right)+F_{6}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{74}\! \left(x \right)+F_{38}\! \left(x \right)
F_{86}\! \left(x \right) = F_{5}\! \left(x \right) F_{78}\! \left(x \right)
F_{87}\! \left(x \right) = F_{5}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x , 1\right)
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{92}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{94}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{100}\! \left(x , y\right) = -\frac{-y F_{95}\! \left(x , y\right)+F_{95}\! \left(x , 1\right)}{-1+y}
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x \right)+F_{108}\! \left(x , y\right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{5}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{59}\! \left(x \right)
F_{108}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{5}\! \left(x \right)
F_{113}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{114}\! \left(x \right) = F_{10}\! \left(x \right) F_{5}\! \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)*F_5(x))
Eq(F_3(x), F_1(x) + F_114(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_6(x))
Eq(F_5(x), x)
Eq(F_6(x), F_1(x) + F_112(x) + F_7(x) + F_87(x))
Eq(F_7(x), F_5(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x) + F_52(x, k_0))
Eq(F_10(x), F_11(x) + F_3(x))
Eq(F_11(x), F_12(x)*F_5(x))
Eq(F_12(x), F_13(x) + F_47(x) + F_50(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_15(x, k_0), F_14(x, k_0)*F_5(x))
Eq(F_16(x, k_0), F_1(x) + F_15(x, k_0) + F_49(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_32(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) + F_22(x, k_0))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_5(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_27(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0)*F_26(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_1(x) + F_23(x, k_0))
Eq(F_27(x, k_0), F_28(x) + F_29(x, k_0) + F_31(x, k_0))
Eq(F_28(x), 0)
Eq(F_29(x, k_0), F_25(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), F_20(x) + F_27(x, k_0))
Eq(F_31(x, k_0), F_22(x, k_0)*F_5(x))
Eq(F_32(x, k_0), F_33(x, k_0)*F_5(x))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0) + F_35(x, k_0) + F_41(x, k_0))
Eq(F_34(x, k_0), F_25(x, k_0)*F_33(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_5(x))
Eq(F_36(x, k_0), F_14(x, k_0) + F_37(x))
Eq(F_37(x), -F_38(x) + F_6(x))
Eq(F_38(x), F_1(x) + F_39(x) + F_40(x))
Eq(F_39(x), F_10(x)*F_5(x))
Eq(F_40(x), F_5(x)*F_6(x))
Eq(F_41(x, k_0), F_42(x, k_0)*F_5(x))
Eq(F_42(x, k_0), F_33(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0)*F_5(x))
Eq(F_44(x, k_0), (-k_0*F_45(x, k_0) + F_45(x, 1))/(1 - k_0))
Eq(F_45(x, k_0), F_14(x, k_0) + F_46(x, k_0) + F_47(x))
Eq(F_46(x, k_0), F_44(x, k_0)*F_5(x))
Eq(F_47(x), F_48(x)*F_5(x))
Eq(F_48(x), F_37(x)/F_5(x))
Eq(F_49(x, k_0), F_16(x, k_0)*F_25(x, k_0))
Eq(F_50(x), F_5(x)*F_51(x))
Eq(F_51(x), F_44(x, 1))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_25(x, k_0)*F_54(x, k_0)*F_66(x))
Eq(F_54(x, k_0), F_55(x, k_0) + F_58(x, k_0))
Eq(F_55(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_25(x, k_0)*F_55(x, k_0))
Eq(F_58(x, k_0), F_59(x) + F_62(x, k_0))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_5(x)*F_61(x))
Eq(F_61(x), F_1(x) + F_59(x))
Eq(F_62(x, k_0), F_28(x) + F_63(x, k_0) + F_65(x, k_0))
Eq(F_63(x, k_0), F_5(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_56(x, k_0) + F_62(x, k_0))
Eq(F_65(x, k_0), F_25(x, k_0)*F_58(x, k_0))
Eq(F_66(x), F_1(x) + F_67(x) + F_74(x))
Eq(F_67(x), F_5(x)*F_68(x))
Eq(F_68(x), F_61(x) + F_69(x))
Eq(F_69(x), F_20(x) + F_70(x))
Eq(F_70(x), F_28(x) + F_71(x) + F_73(x))
Eq(F_71(x), F_5(x)*F_72(x))
Eq(F_72(x), F_59(x) + F_70(x))
Eq(F_73(x), F_5(x)*F_69(x))
Eq(F_74(x), F_5(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_76(x) + F_77(x) + F_82(x))
Eq(F_76(x), F_5(x)*F_75(x))
Eq(F_77(x), F_5(x)*F_78(x))
Eq(F_78(x), F_11(x) + F_79(x))
Eq(F_79(x), F_80(x)/F_5(x))
Eq(F_80(x), -F_1(x) + F_66(x) - F_81(x))
Eq(F_81(x), F_5(x)*F_66(x))
Eq(F_82(x), F_5(x)*F_83(x))
Eq(F_83(x), F_84(x)/F_5(x))
Eq(F_84(x), -F_1(x) + F_6(x) - F_85(x) - F_86(x))
Eq(F_85(x), -F_1(x) + F_38(x) - F_74(x))
Eq(F_86(x), F_5(x)*F_78(x))
Eq(F_87(x), F_5(x)*F_88(x))
Eq(F_88(x), F_89(x, 1))
Eq(F_89(x, k_0), F_1(x) + F_101(x, k_0) + F_90(x, k_0) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_90(x, k_0), F_5(x)*F_91(x, k_0))
Eq(F_91(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_92(x, k_0), F_5(x)*F_93(x, k_0))
Eq(F_93(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_95(x, k_0), F_1(x) + F_101(x, k_0) + F_94(x, k_0) + F_99(x, k_0))
Eq(F_95(x, k_0), F_1(x) + F_96(x, k_0) + F_97(x, k_0) + F_98(x, k_0))
Eq(F_96(x, k_0), F_5(x)*F_89(x, k_0))
Eq(F_97(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_98(x, k_0), F_25(x, k_0)*F_95(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_5(x))
Eq(F_100(x, k_0), (k_0*F_95(x, k_0) - F_95(x, 1))/(k_0 - 1))
Eq(F_101(x, k_0), F_102(x, k_0)*F_25(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_54(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_58(x, k_0))
Eq(F_104(x, k_0), F_105(x) + F_108(x, k_0))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_5(x))
Eq(F_107(x), F_105(x) + F_59(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_111(x, k_0) + 2*F_28(x))
Eq(F_109(x, k_0), F_110(x, k_0)*F_5(x))
Eq(F_110(x, k_0), F_108(x, k_0) + F_62(x, k_0))
Eq(F_111(x, k_0), F_104(x, k_0)*F_25(x, k_0))
Eq(F_112(x), F_113(x)*F_5(x))
Eq(F_113(x), F_33(x, 1))
Eq(F_114(x), F_10(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"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, 3], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 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[0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 0], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 0], [2, 2]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24011/
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[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[118,x]+F[9,x]
F[9,x] = F[10,x]+F[88,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[13,x]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[27,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[26,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[25,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[26,x,k[0]] = F[22,x,k[0]]*F[25,x,k[0]]
F[27,x,k[0]] = F[117,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[2,x]*F[22,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[13,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[110,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[39,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[38,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[13,x]*F[37,x,k[0]]
F[37,x,k[0]] = F[22,x,k[0]]+F[35,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[22,x,k[0]]*F[41,x]
F[41,x] = F[109,x]+F[42,x]+F[43,x]
F[42,x] = 0
F[43,x] = F[13,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[11,x]+F[41,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]^2
F[49,x] = -F[41,x]+F[50,x]
F[50,x] = 1/F[13,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[101,x]-2*F[42,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[13,x]*F[14,x]*F[55,x]
F[55,x] = F[41,x]+F[56,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[13,x]*F[60,x]
F[60,x] = F[1,x]+F[58,x]
F[61,x] = -F[66,x]+F[62,x]
F[62,x] = -F[57,x]+F[63,x]
F[63,x] = -F[100,x]+F[64,x]
F[64,x] = 1/F[13,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[13,x]*F[68,x]
F[68,x] = F[69,x]+F[98,x]
F[69,x] = -F[90,x]+F[70,x]
F[70,x] = 1/F[13,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[13,x]*F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[11,x]+F[16,x]
F[77,x] = F[2,x]+F[41,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[11,x]*F[2,x]
F[81,x] = F[30,x,1]
F[82,x] = F[72,x]+F[83,x]
F[83,x] = -F[88,x]+F[84,x]
F[84,x] = -F[87,x]+F[85,x]
F[85,x] = 1/F[13,x]*F[86,x]
F[86,x] = F[6,x]
F[87,x] = F[10,x]+F[41,x]
F[88,x] = F[80,x]+F[89,x]
F[89,x] = F[6,x]+F[81,x]
F[90,x] = -F[93,x]+F[91,x]
F[91,x] = 1/F[13,x]*F[92,x]
F[92,x] = F[16,x]
F[93,x] = F[58,x]+F[94,x]
F[94,x] = F[42,x]+F[95,x]+F[97,x]
F[95,x] = F[13,x]*F[96,x]
F[96,x] = F[11,x]+F[94,x]
F[97,x] = F[13,x]*F[93,x]
F[98,x] = F[58,x]*F[99,x]
F[99,x] = F[14,x]+F[93,x]
F[100,x] = F[11,x]+F[77,x]
F[101,x] = F[102,x]*F[13,x]
F[102,x] = -F[105,x]+F[103,x]
F[103,x] = 1/F[13,x]*F[104,x]
F[104,x] = F[53,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[11,x]
F[107,x] = 1/F[13,x]*F[108,x]
F[108,x] = F[41,x]
F[109,x] = F[13,x]*F[77,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[115,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[114,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[11,x]*F[2,x]*F[22,x,k[0]]
F[114,x,k[0]] = -k[0]*(F[30,x,1]-F[30,x,k[0]])/(-1+k[0])
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[22,x,k[0]]*F[83,x]
F[117,x,k[0]] = F[17,x,k[0]]*F[25,x,k[0]]
F[118,x] = F[119,x]+F[122,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[80,x]
F[121,x] = F[11,x]^2*F[14,x]
F[122,x] = F[123,x]+F[128,x]
F[123,x] = F[11,x]*F[124,x]
F[124,x] = -F[2,x]+F[125,x]
F[125,x] = -F[0,x]+F[126,x]
F[126,x] = 1/F[13,x]*F[127,x]
F[127,x] = F[2,x]
F[128,x] = F[129,x]+F[53,x]
F[129,x] = F[130,x,1]
F[130,x,k[0]] = 2*F[42,x]+F[131,x,k[0]]+F[133,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]
F[132,x,k[0]] = F[13,x]*F[22,x,k[0]]*F[50,x]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[102,x]*F[13,x]*F[22,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{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_{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_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{118}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{88}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{y \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y\right)\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{109}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = 0
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11} \left(x \right)^{2}
F_{49}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{101}\! \left(x \right)-2 F_{42}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{41}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{13}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{1}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{98}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{13}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{81}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{82}\! \left(x \right) = F_{72}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{6}\! \left(x \right)
F_{87}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{88}\! \left(x \right) = F_{80}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{6}\! \left(x \right)+F_{81}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{16}\! \left(x \right)
F_{93}\! \left(x \right) = F_{58}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{42}\! \left(x \right)+F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right)+F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{58}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{14}\! \left(x \right)+F_{93}\! \left(x \right)
F_{100}\! \left(x \right) = F_{11}\! \left(x \right)+F_{77}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{13}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{53}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{41}\! \left(x \right)
F_{109}\! \left(x \right) = F_{13}\! \left(x \right) F_{77}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = -\frac{y \left(F_{30}\! \left(x , 1\right)-F_{30}\! \left(x , y\right)\right)}{-1+y}
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{83}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{122}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{80}\! \left(x \right)
F_{121}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{128}\! \left(x \right)
F_{123}\! \left(x \right) = F_{11}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{127}\! \left(x \right) = F_{2}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{53}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x , 1\right)
F_{130}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{22}\! \left(x , y\right) F_{50}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{13}\! \left(x \right) F_{22}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(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_13(x)*F_8(x))
Eq(F_8(x), F_118(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_88(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_13(x)*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_27(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_26(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_25(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_26(x, k_0), F_22(x, k_0)*F_25(x, k_0))
Eq(F_27(x, k_0), F_117(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_2(x)*F_22(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_13(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_110(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_39(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_38(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_13(x)*F_37(x, k_0))
Eq(F_37(x, k_0), F_22(x, k_0) + F_35(x, k_0))
Eq(F_38(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_22(x, k_0)*F_41(x))
Eq(F_41(x), F_109(x) + F_42(x) + F_43(x))
Eq(F_42(x), 0)
Eq(F_43(x), F_13(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_11(x) + F_41(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)**2)
Eq(F_49(x), -F_41(x) + F_50(x))
Eq(F_50(x), F_51(x)/F_13(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_101(x) - 2*F_42(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_13(x)*F_14(x)*F_55(x))
Eq(F_55(x), F_41(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_13(x)*F_60(x))
Eq(F_60(x), F_1(x) + F_58(x))
Eq(F_61(x), F_62(x) - F_66(x))
Eq(F_62(x), -F_57(x) + F_63(x))
Eq(F_63(x), -F_100(x) + F_64(x))
Eq(F_64(x), F_65(x)/F_13(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_13(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_98(x))
Eq(F_69(x), F_70(x) - F_90(x))
Eq(F_70(x), F_71(x)/F_13(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_13(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_11(x) + F_16(x))
Eq(F_77(x), F_2(x) + F_41(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_11(x)*F_2(x))
Eq(F_81(x), F_30(x, 1))
Eq(F_82(x), F_72(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_88(x))
Eq(F_84(x), F_85(x) - F_87(x))
Eq(F_85(x), F_86(x)/F_13(x))
Eq(F_86(x), F_6(x))
Eq(F_87(x), F_10(x) + F_41(x))
Eq(F_88(x), F_80(x) + F_89(x))
Eq(F_89(x), F_6(x) + F_81(x))
Eq(F_90(x), F_91(x) - F_93(x))
Eq(F_91(x), F_92(x)/F_13(x))
Eq(F_92(x), F_16(x))
Eq(F_93(x), F_58(x) + F_94(x))
Eq(F_94(x), F_42(x) + F_95(x) + F_97(x))
Eq(F_95(x), F_13(x)*F_96(x))
Eq(F_96(x), F_11(x) + F_94(x))
Eq(F_97(x), F_13(x)*F_93(x))
Eq(F_98(x), F_58(x)*F_99(x))
Eq(F_99(x), F_14(x) + F_93(x))
Eq(F_100(x), F_11(x) + F_77(x))
Eq(F_101(x), F_102(x)*F_13(x))
Eq(F_102(x), F_103(x) - F_105(x))
Eq(F_103(x), F_104(x)/F_13(x))
Eq(F_104(x), F_53(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_11(x))
Eq(F_107(x), F_108(x)/F_13(x))
Eq(F_108(x), F_41(x))
Eq(F_109(x), F_13(x)*F_77(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_115(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_114(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_11(x)*F_2(x)*F_22(x, k_0))
Eq(F_114(x, k_0), -F_30(x, 1) + (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_22(x, k_0)*F_83(x))
Eq(F_117(x, k_0), F_17(x, k_0)*F_25(x, k_0))
Eq(F_118(x), F_119(x) + F_122(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_80(x))
Eq(F_121(x), F_11(x)**2*F_14(x))
Eq(F_122(x), F_123(x) + F_128(x))
Eq(F_123(x), F_11(x)*F_124(x))
Eq(F_124(x), F_125(x) - F_2(x))
Eq(F_125(x), -F_0(x) + F_126(x))
Eq(F_126(x), F_127(x)/F_13(x))
Eq(F_127(x), F_2(x))
Eq(F_128(x), F_129(x) + F_53(x))
Eq(F_129(x), F_130(x, 1))
Eq(F_130(x, k_0), F_131(x, k_0) + F_133(x, k_0) + 2*F_42(x))
Eq(F_131(x, k_0), F_132(x, k_0))
Eq(F_132(x, k_0), F_13(x)*F_22(x, k_0)*F_50(x))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_102(x)*F_13(x)*F_22(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_row_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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], [0, 1], [0, 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": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], 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{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24012/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[6,x]
F[4,x] = F[1,x]+F[118,x]+F[5,x]
F[5,x] = F[6,x]*F[7,x]
F[6,x] = x
F[7,x] = F[1,x]+F[116,x]+F[8,x]+F[91,x]
F[8,x] = F[6,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x]+F[55,x,k[0]]
F[11,x] = F[12,x]+F[4,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[6,x]
F[14,x] = F[15,x]+F[50,x]+F[53,x]
F[15,x] = F[16,x,1]
F[17,x,k[0]] = F[16,x,k[0]]*F[6,x]
F[18,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[52,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[34,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[20,x,k[0]] = F[21,x]+F[24,x,k[0]]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[6,x]
F[24,x,k[0]] = F[25,x,k[0]]+F[29,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[28,x,k[0]]
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[31,x,k[0]]+F[33,x,k[0]]
F[30,x] = 0
F[31,x,k[0]] = F[27,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[22,x]+F[29,x,k[0]]
F[33,x,k[0]] = F[24,x,k[0]]*F[6,x]
F[34,x,k[0]] = F[35,x,k[0]]*F[6,x]
F[35,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[37,x,k[0]]+F[44,x,k[0]]
F[36,x,k[0]] = F[27,x,k[0]]*F[35,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[6,x]
F[38,x,k[0]] = F[16,x,k[0]]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[41,x]+F[7,x]
F[41,x] = F[1,x]+F[42,x]+F[43,x]
F[42,x] = F[11,x]*F[6,x]
F[43,x] = F[6,x]*F[7,x]
F[44,x,k[0]] = F[45,x,k[0]]*F[6,x]
F[45,x,k[0]] = F[35,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[6,x]
F[47,x,k[0]] = (F[48,x,k[0]]*k[0]-F[48,x,1])/(-1+k[0])
F[48,x,k[0]] = F[16,x,k[0]]+F[49,x,k[0]]+F[50,x]
F[49,x,k[0]] = F[47,x,k[0]]*F[6,x]
F[50,x] = F[51,x]*F[6,x]
F[51,x] = 1/F[6,x]*F[39,x]
F[52,x,k[0]] = F[18,x,k[0]]*F[27,x,k[0]]
F[53,x] = F[54,x]*F[6,x]
F[54,x] = F[47,x,1]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[27,x,k[0]]*F[57,x,k[0]]*F[69,x]
F[57,x,k[0]] = F[58,x,k[0]]+F[61,x,k[0]]
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[27,x,k[0]]*F[58,x,k[0]]
F[61,x,k[0]] = F[62,x]+F[65,x,k[0]]
F[62,x] = F[63,x]
F[63,x] = F[6,x]*F[64,x]
F[64,x] = F[1,x]+F[62,x]
F[65,x,k[0]] = F[30,x]+F[66,x,k[0]]+F[68,x,k[0]]
F[66,x,k[0]] = F[6,x]*F[67,x,k[0]]
F[67,x,k[0]] = F[59,x,k[0]]+F[65,x,k[0]]
F[68,x,k[0]] = F[27,x,k[0]]*F[61,x,k[0]]
F[69,x] = F[1,x]+F[70,x]+F[77,x]
F[70,x] = F[6,x]*F[71,x]
F[71,x] = F[64,x]+F[72,x]
F[72,x] = F[22,x]+F[73,x]
F[73,x] = F[30,x]+F[74,x]+F[76,x]
F[74,x] = F[6,x]*F[75,x]
F[75,x] = F[62,x]+F[73,x]
F[76,x] = F[6,x]*F[72,x]
F[77,x] = F[6,x]*F[78,x]
F[78,x] = F[1,x]+F[79,x]+F[80,x]+F[86,x]
F[79,x] = F[6,x]*F[78,x]
F[80,x] = F[6,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = 1/F[6,x]*F[83,x]
F[83,x] = -F[1,x]-F[84,x]+F[69,x]
F[84,x] = F[6,x]*F[69,x]
F[85,x] = F[12,x]
F[86,x] = F[6,x]*F[87,x]
F[87,x] = 1/F[6,x]*F[88,x]
F[88,x] = -F[1,x]-F[89,x]-F[90,x]+F[7,x]
F[89,x] = -F[1,x]-F[77,x]+F[41,x]
F[90,x] = F[6,x]*F[81,x]
F[91,x] = F[6,x]*F[92,x]
F[92,x] = F[93,x,1]
F[93,x,k[0]] = F[1,x]+F[105,x,k[0]]+F[94,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[94,x,k[0]] = F[6,x]*F[95,x,k[0]]
F[95,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[96,x,k[0]] = F[6,x]*F[97,x,k[0]]
F[97,x,k[0]] = 1/(-1+k[0])*(F[93,x,k[0]]*k[0]-F[93,x,1])
F[99,x,k[0]] = F[1,x]+F[103,x,k[0]]+F[105,x,k[0]]+F[98,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[101,x,k[0]]+F[102,x,k[0]]
F[100,x,k[0]] = F[6,x]*F[93,x,k[0]]
F[101,x,k[0]] = F[10,x,k[0]]*F[6,x]
F[102,x,k[0]] = F[27,x,k[0]]*F[99,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[6,x]
F[104,x,k[0]] = 1/(-1+k[0])*(F[99,x,k[0]]*k[0]-F[99,x,1])
F[105,x,k[0]] = F[106,x,k[0]]*F[27,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[57,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[61,x,k[0]]
F[108,x,k[0]] = F[109,x]+F[112,x,k[0]]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[6,x]
F[111,x] = F[109,x]+F[62,x]
F[112,x,k[0]] = 2*F[30,x]+F[113,x,k[0]]+F[115,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[6,x]
F[114,x,k[0]] = F[112,x,k[0]]+F[65,x,k[0]]
F[115,x,k[0]] = F[108,x,k[0]]*F[27,x,k[0]]
F[116,x] = F[117,x]*F[6,x]
F[117,x] = F[35,x,1]
F[118,x] = F[11,x]*F[6,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{116}\! \left(x \right)+F_{8}\! \left(x \right)+F_{91}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{6}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{45}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{47}\! \left(x , y\right) = -\frac{-y F_{48}\! \left(x , y\right)+F_{48}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{49}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{6}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{6}\! \left(x \right)}
F_{52}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{6}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{57}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x \right)+F_{65}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{6}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{70}\! \left(x \right) = F_{6}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{30}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{6}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{62}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{6}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)+F_{86}\! \left(x \right)
F_{79}\! \left(x \right) = F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{80}\! \left(x \right) = F_{6}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{6}\! \left(x \right)}
F_{83}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{84}\! \left(x \right)+F_{69}\! \left(x \right)
F_{84}\! \left(x \right) = F_{6}\! \left(x \right) F_{69}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right)
F_{86}\! \left(x \right) = F_{6}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{6}\! \left(x \right)}
F_{88}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{89}\! \left(x \right)-F_{90}\! \left(x \right)+F_{7}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{77}\! \left(x \right)+F_{41}\! \left(x \right)
F_{90}\! \left(x \right) = F_{6}\! \left(x \right) F_{81}\! \left(x \right)
F_{91}\! \left(x \right) = F_{6}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x , 1\right)
F_{93}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{94}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{96}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = -\frac{-y F_{93}\! \left(x , y\right)+F_{93}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{104}\! \left(x , y\right) = -\frac{-y F_{99}\! \left(x , y\right)+F_{99}\! \left(x , 1\right)}{-1+y}
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x \right)+F_{112}\! \left(x , y\right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{6}\! \left(x \right)
F_{111}\! \left(x \right) = F_{109}\! \left(x \right)+F_{62}\! \left(x \right)
F_{112}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{6}\! \left(x \right)
F_{117}\! \left(x \right) = F_{35}\! \left(x , 1\right)
F_{118}\! \left(x \right) = F_{11}\! \left(x \right) F_{6}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_6(x))
Eq(F_4(x), F_1(x) + F_118(x) + F_5(x))
Eq(F_5(x), F_6(x)*F_7(x))
Eq(F_6(x), x)
Eq(F_7(x), F_1(x) + F_116(x) + F_8(x) + F_91(x))
Eq(F_8(x), F_6(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x) + F_55(x, k_0))
Eq(F_11(x), F_12(x) + F_4(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_6(x))
Eq(F_14(x), F_15(x) + F_50(x) + F_53(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_17(x, k_0), F_16(x, k_0)*F_6(x))
Eq(F_18(x, k_0), F_1(x) + F_17(x, k_0) + F_52(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_34(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_20(x, k_0), F_21(x) + F_24(x, k_0))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_6(x))
Eq(F_24(x, k_0), F_25(x, k_0) + F_29(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_28(x, k_0))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_30(x), 0)
Eq(F_31(x, k_0), F_27(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_22(x) + F_29(x, k_0))
Eq(F_33(x, k_0), F_24(x, k_0)*F_6(x))
Eq(F_34(x, k_0), F_35(x, k_0)*F_6(x))
Eq(F_35(x, k_0), F_1(x) + F_36(x, k_0) + F_37(x, k_0) + F_44(x, k_0))
Eq(F_36(x, k_0), F_27(x, k_0)*F_35(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_6(x))
Eq(F_38(x, k_0), F_16(x, k_0) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_41(x) + F_7(x))
Eq(F_41(x), F_1(x) + F_42(x) + F_43(x))
Eq(F_42(x), F_11(x)*F_6(x))
Eq(F_43(x), F_6(x)*F_7(x))
Eq(F_44(x, k_0), F_45(x, k_0)*F_6(x))
Eq(F_45(x, k_0), F_35(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_6(x))
Eq(F_47(x, k_0), (-k_0*F_48(x, k_0) + F_48(x, 1))/(1 - k_0))
Eq(F_48(x, k_0), F_16(x, k_0) + F_49(x, k_0) + F_50(x))
Eq(F_49(x, k_0), F_47(x, k_0)*F_6(x))
Eq(F_50(x), F_51(x)*F_6(x))
Eq(F_51(x), F_39(x)/F_6(x))
Eq(F_52(x, k_0), F_18(x, k_0)*F_27(x, k_0))
Eq(F_53(x), F_54(x)*F_6(x))
Eq(F_54(x), F_47(x, 1))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_27(x, k_0)*F_57(x, k_0)*F_69(x))
Eq(F_57(x, k_0), F_58(x, k_0) + F_61(x, k_0))
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_27(x, k_0)*F_58(x, k_0))
Eq(F_61(x, k_0), F_62(x) + F_65(x, k_0))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_6(x)*F_64(x))
Eq(F_64(x), F_1(x) + F_62(x))
Eq(F_65(x, k_0), F_30(x) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_66(x, k_0), F_6(x)*F_67(x, k_0))
Eq(F_67(x, k_0), F_59(x, k_0) + F_65(x, k_0))
Eq(F_68(x, k_0), F_27(x, k_0)*F_61(x, k_0))
Eq(F_69(x), F_1(x) + F_70(x) + F_77(x))
Eq(F_70(x), F_6(x)*F_71(x))
Eq(F_71(x), F_64(x) + F_72(x))
Eq(F_72(x), F_22(x) + F_73(x))
Eq(F_73(x), F_30(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_6(x)*F_75(x))
Eq(F_75(x), F_62(x) + F_73(x))
Eq(F_76(x), F_6(x)*F_72(x))
Eq(F_77(x), F_6(x)*F_78(x))
Eq(F_78(x), F_1(x) + F_79(x) + F_80(x) + F_86(x))
Eq(F_79(x), F_6(x)*F_78(x))
Eq(F_80(x), F_6(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_83(x)/F_6(x))
Eq(F_83(x), -F_1(x) + F_69(x) - F_84(x))
Eq(F_84(x), F_6(x)*F_69(x))
Eq(F_85(x), F_12(x))
Eq(F_86(x), F_6(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_6(x))
Eq(F_88(x), -F_1(x) + F_7(x) - F_89(x) - F_90(x))
Eq(F_89(x), -F_1(x) + F_41(x) - F_77(x))
Eq(F_90(x), F_6(x)*F_81(x))
Eq(F_91(x), F_6(x)*F_92(x))
Eq(F_92(x), F_93(x, 1))
Eq(F_93(x, k_0), F_1(x) + F_105(x, k_0) + F_94(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_94(x, k_0), F_6(x)*F_95(x, k_0))
Eq(F_95(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_96(x, k_0), F_6(x)*F_97(x, k_0))
Eq(F_97(x, k_0), (k_0*F_93(x, k_0) - F_93(x, 1))/(k_0 - 1))
Eq(F_99(x, k_0), F_1(x) + F_103(x, k_0) + F_105(x, k_0) + F_98(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_100(x, k_0) + F_101(x, k_0) + F_102(x, k_0))
Eq(F_100(x, k_0), F_6(x)*F_93(x, k_0))
Eq(F_101(x, k_0), F_10(x, k_0)*F_6(x))
Eq(F_102(x, k_0), F_27(x, k_0)*F_99(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_6(x))
Eq(F_104(x, k_0), (k_0*F_99(x, k_0) - F_99(x, 1))/(k_0 - 1))
Eq(F_105(x, k_0), F_106(x, k_0)*F_27(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_57(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_61(x, k_0))
Eq(F_108(x, k_0), F_109(x) + F_112(x, k_0))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_6(x))
Eq(F_111(x), F_109(x) + F_62(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0) + 2*F_30(x))
Eq(F_113(x, k_0), F_114(x, k_0)*F_6(x))
Eq(F_114(x, k_0), F_112(x, k_0) + F_65(x, k_0))
Eq(F_115(x, k_0), F_108(x, k_0)*F_27(x, k_0))
Eq(F_116(x), F_117(x)*F_6(x))
Eq(F_117(x), F_35(x, 1))
Eq(F_118(x), F_11(x)*F_6(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"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, 3], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": 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[1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"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]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24013/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[1,x]+F[125,x]+F[5,x]
F[5,x] = F[14,x]*F[6,x]
F[6,x] = F[1,x]+F[117,x]+F[119,x]+F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[9,x,1]
F[10,x,k[0]] = F[14,x]*F[9,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[116,x,k[0]]+F[31,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[30,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[15,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x]
F[14,x] = x
F[15,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[17,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x]+F[25,x,k[0]]
F[22,x] = F[23,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x,k[0]] = F[26,x]+F[27,x,k[0]]+F[29,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[14,x]*F[28,x,k[0]]
F[28,x,k[0]] = F[18,x,k[0]]+F[25,x,k[0]]
F[29,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[30,x,k[0]] = F[115,x,k[0]]+F[26,x]+F[31,x,k[0]]+F[51,x,k[0]]
F[31,x,k[0]] = F[14,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[35,x,k[0]]+F[37,x,k[0]]+F[40,x,k[0]]
F[33,x,k[0]] = F[14,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[35,x,k[0]] = F[14,x]*F[36,x,k[0]]
F[36,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[11,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[14,x]*F[39,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[40,x,k[0]] = F[20,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[16,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[21,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x]+F[47,x,k[0]]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[22,x]+F[44,x]
F[47,x,k[0]] = 2*F[26,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[14,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[25,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[20,x,k[0]]*F[43,x,k[0]]
F[51,x,k[0]] = F[52,x]
F[52,x] = F[14,x]*F[53,x]
F[53,x] = -F[107,x]+F[54,x]
F[54,x] = F[1,x]+F[106,x]+F[55,x]+F[81,x]
F[55,x] = F[14,x]*F[56,x]
F[56,x] = F[57,x,1]
F[57,x,k[0]] = F[58,x,k[0]]+F[6,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[26,x]+F[60,x,k[0]]+F[62,x,k[0]]+F[68,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[14,x]*F[59,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[64,x,k[0]] = F[26,x]+F[63,x,k[0]]+F[68,x,k[0]]
F[64,x,k[0]] = F[26,x]+F[65,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[14,x]*F[59,x,k[0]]
F[66,x,k[0]] = F[20,x,k[0]]*F[67,x,k[0]]
F[67,x,k[0]] = F[0,x]+F[64,x,k[0]]
F[68,x,k[0]] = F[20,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[73,x,k[0]]
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[20,x,k[0]]*F[70,x,k[0]]
F[73,x,k[0]] = F[74,x]+F[77,x,k[0]]
F[74,x] = F[75,x]
F[75,x] = F[14,x]*F[76,x]
F[76,x] = F[1,x]+F[74,x]
F[77,x,k[0]] = F[26,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[14,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[71,x,k[0]]+F[77,x,k[0]]
F[80,x,k[0]] = F[20,x,k[0]]*F[73,x,k[0]]
F[81,x] = F[14,x]*F[82,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[1,x]+F[84,x,k[0]]+F[86,x,k[0]]+F[88,x,k[0]]+F[95,x,k[0]]
F[84,x,k[0]] = F[14,x]*F[85,x,k[0]]
F[85,x,k[0]] = 1/(-1+k[0])*(F[57,x,k[0]]*k[0]-F[57,x,1])
F[86,x,k[0]] = F[14,x]*F[87,x,k[0]]
F[87,x,k[0]] = 1/(-1+k[0])*(F[83,x,k[0]]*k[0]-F[83,x,1])
F[89,x,k[0]] = F[1,x]+F[88,x,k[0]]+F[93,x,k[0]]+F[95,x,k[0]]
F[89,x,k[0]] = F[1,x]+F[90,x,k[0]]+F[91,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[14,x]*F[83,x,k[0]]
F[91,x,k[0]] = F[14,x]*F[57,x,k[0]]
F[92,x,k[0]] = F[20,x,k[0]]*F[89,x,k[0]]
F[93,x,k[0]] = F[14,x]*F[94,x,k[0]]
F[94,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[95,x,k[0]] = F[20,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[69,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[73,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[102,x,k[0]]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[14,x]
F[101,x] = F[74,x]+F[99,x]
F[102,x,k[0]] = 2*F[26,x]+F[103,x,k[0]]+F[105,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[14,x]
F[104,x,k[0]] = F[102,x,k[0]]+F[77,x,k[0]]
F[105,x,k[0]] = F[20,x,k[0]]*F[98,x,k[0]]
F[106,x] = -F[1,x]-F[110,x]+F[107,x]
F[107,x] = F[1,x]+F[108,x]+F[109,x]
F[108,x] = F[14,x]*F[54,x]
F[109,x] = F[14,x]*F[6,x]
F[110,x] = F[111,x]*F[14,x]
F[111,x] = F[1,x]+F[112,x]+F[113,x]+F[114,x]
F[112,x] = F[14,x]*F[82,x]
F[113,x] = F[14,x]*F[56,x]
F[114,x] = F[111,x]*F[14,x]
F[115,x,k[0]] = F[20,x,k[0]]*F[30,x,k[0]]
F[116,x,k[0]] = F[11,x,k[0]]*F[20,x,k[0]]
F[117,x] = F[118,x]*F[14,x]
F[118,x] = F[32,x,1]
F[119,x] = -F[1,x]-F[120,x]+F[4,x]
F[120,x] = F[121,x]*F[14,x]
F[121,x] = F[1,x]+F[122,x]+F[123,x]+F[124,x]
F[122,x] = F[118,x]*F[14,x]
F[123,x] = F[14,x]*F[8,x]
F[124,x] = F[121,x]*F[14,x]
F[125,x] = F[14,x]*F[54,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{125}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)+F_{119}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \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_{17}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{32}\! \left(x , y\right)+F_{32}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{55}\! \left(x \right)+F_{81}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{1}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{-y F_{57}\! \left(x , y\right)+F_{57}\! \left(x , 1\right)}{-1+y}
F_{86}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = -\frac{-y F_{83}\! \left(x , y\right)+F_{83}\! \left(x , 1\right)}{-1+y}
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{-y F_{89}\! \left(x , y\right)+F_{89}\! \left(x , 1\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right)
F_{101}\! \left(x \right) = F_{74}\! \left(x \right)+F_{99}\! \left(x \right)
F_{102}\! \left(x , y\right) = 2 F_{26}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{98}\! \left(x , y\right)
F_{106}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{110}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{109}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{14}\! \left(x \right) F_{82}\! \left(x \right)
F_{113}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{114}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right)
F_{118}\! \left(x \right) = F_{32}\! \left(x , 1\right)
F_{119}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{120}\! \left(x \right)+F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{1}\! \left(x \right)+F_{122}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right)
F_{123}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{125}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_125(x) + F_5(x))
Eq(F_5(x), F_14(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_117(x) + F_119(x) + F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_10(x, k_0), F_14(x)*F_9(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_10(x, k_0) + F_116(x, k_0) + F_31(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_30(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_15(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x, k_0), F_16(x, k_0)*F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_21(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_17(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x) + F_25(x, k_0))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x, k_0), F_26(x) + F_27(x, k_0) + F_29(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_14(x)*F_28(x, k_0))
Eq(F_28(x, k_0), F_18(x, k_0) + F_25(x, k_0))
Eq(F_29(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_30(x, k_0), F_115(x, k_0) + F_26(x) + F_31(x, k_0) + F_51(x, k_0))
Eq(F_31(x, k_0), F_14(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_35(x, k_0) + F_37(x, k_0) + F_40(x, k_0))
Eq(F_33(x, k_0), F_14(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_14(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_1(x) + F_37(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_14(x)*F_39(x, k_0))
Eq(F_39(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_20(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_16(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_21(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x) + F_47(x, k_0))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_22(x) + F_44(x))
Eq(F_47(x, k_0), 2*F_26(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_14(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_25(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_20(x, k_0)*F_43(x, k_0))
Eq(F_51(x, k_0), F_52(x))
Eq(F_52(x), F_14(x)*F_53(x))
Eq(F_53(x), -F_107(x) + F_54(x))
Eq(F_54(x), F_1(x) + F_106(x) + F_55(x) + F_81(x))
Eq(F_55(x), F_14(x)*F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_57(x, k_0), F_58(x, k_0) + F_6(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_26(x) + F_60(x, k_0) + F_62(x, k_0) + F_68(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_14(x)*F_59(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_64(x, k_0), F_26(x) + F_63(x, k_0) + F_68(x, k_0))
Eq(F_64(x, k_0), F_26(x) + F_65(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_14(x)*F_59(x, k_0))
Eq(F_66(x, k_0), F_20(x, k_0)*F_67(x, k_0))
Eq(F_67(x, k_0), F_0(x) + F_64(x, k_0))
Eq(F_68(x, k_0), F_20(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_73(x, k_0))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_20(x, k_0)*F_70(x, k_0))
Eq(F_73(x, k_0), F_74(x) + F_77(x, k_0))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_14(x)*F_76(x))
Eq(F_76(x), F_1(x) + F_74(x))
Eq(F_77(x, k_0), F_26(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_14(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_71(x, k_0) + F_77(x, k_0))
Eq(F_80(x, k_0), F_20(x, k_0)*F_73(x, k_0))
Eq(F_81(x), F_14(x)*F_82(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_1(x) + F_84(x, k_0) + F_86(x, k_0) + F_88(x, k_0) + F_95(x, k_0))
Eq(F_84(x, k_0), F_14(x)*F_85(x, k_0))
Eq(F_85(x, k_0), (k_0*F_57(x, k_0) - F_57(x, 1))/(k_0 - 1))
Eq(F_86(x, k_0), F_14(x)*F_87(x, k_0))
Eq(F_87(x, k_0), (k_0*F_83(x, k_0) - F_83(x, 1))/(k_0 - 1))
Eq(F_89(x, k_0), F_1(x) + F_88(x, k_0) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_89(x, k_0), F_1(x) + F_90(x, k_0) + F_91(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_14(x)*F_83(x, k_0))
Eq(F_91(x, k_0), F_14(x)*F_57(x, k_0))
Eq(F_92(x, k_0), F_20(x, k_0)*F_89(x, k_0))
Eq(F_93(x, k_0), F_14(x)*F_94(x, k_0))
Eq(F_94(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_95(x, k_0), F_20(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_69(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_73(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_102(x, k_0) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_14(x))
Eq(F_101(x), F_74(x) + F_99(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_105(x, k_0) + 2*F_26(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_14(x))
Eq(F_104(x, k_0), F_102(x, k_0) + F_77(x, k_0))
Eq(F_105(x, k_0), F_20(x, k_0)*F_98(x, k_0))
Eq(F_106(x), -F_1(x) + F_107(x) - F_110(x))
Eq(F_107(x), F_1(x) + F_108(x) + F_109(x))
Eq(F_108(x), F_14(x)*F_54(x))
Eq(F_109(x), F_14(x)*F_6(x))
Eq(F_110(x), F_111(x)*F_14(x))
Eq(F_111(x), F_1(x) + F_112(x) + F_113(x) + F_114(x))
Eq(F_112(x), F_14(x)*F_82(x))
Eq(F_113(x), F_14(x)*F_56(x))
Eq(F_114(x), F_111(x)*F_14(x))
Eq(F_115(x, k_0), F_20(x, k_0)*F_30(x, k_0))
Eq(F_116(x, k_0), F_11(x, k_0)*F_20(x, k_0))
Eq(F_117(x), F_118(x)*F_14(x))
Eq(F_118(x), F_32(x, 1))
Eq(F_119(x), -F_1(x) - F_120(x) + F_4(x))
Eq(F_120(x), F_121(x)*F_14(x))
Eq(F_121(x), F_1(x) + F_122(x) + F_123(x) + F_124(x))
Eq(F_122(x), F_118(x)*F_14(x))
Eq(F_123(x), F_14(x)*F_8(x))
Eq(F_124(x), F_121(x)*F_14(x))
Eq(F_125(x), F_14(x)*F_54(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"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], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 5, 2, 0, 4], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], 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