1032_2301_125403

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: point_and_row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24005/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[12,x]*F[4,x]
F[4,x] = F[1,x]+F[103,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[1,x]+F[41,x]+F[7,x]+F[75,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[101,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]+F[13,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[12,x]*F[6,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[18,x,k[0]]+F[92,x]+F[99,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[4,x]
F[19,x,k[0]] = 2*F[20,x]+F[21,x,k[0]]+F[23,x,k[0]]
F[20,x] = 0
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[12,x]*F[19,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[57,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[25,x]+F[38,x,k[0]]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[1,x]+F[31,x]
F[34,x] = F[20,x]+F[35,x]+F[37,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[28,x]+F[34,x]
F[37,x] = F[12,x]*F[30,x]
F[39,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[38,x,k[0]]+F[41,x]+F[7,x]
F[39,x,k[0]] = F[40,x,k[0]]+F[6,x]
F[40,x,k[0]] = F[19,x,k[0]]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[6,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[20,x]+F[45,x,k[0]]+F[63,x,k[0]]+F[65,x,k[0]]+F[81,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[12,x]*F[47,x,k[0]]
F[47,x,k[0]] = -k[0]*(F[48,x,1]-F[48,x,k[0]])/(-1+k[0])
F[48,x,k[0]] = F[20,x]+F[49,x,k[0]]+F[51,x,k[0]]+F[52,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[12,x]*F[48,x,k[0]]
F[51,x,k[0]] = F[12,x]*F[44,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]*F[57,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[58,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[54,x,k[0]]*F[57,x,k[0]]
F[57,x,k[0]] = k[0]*x
F[58,x,k[0]] = F[31,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[20,x]+F[60,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[12,x]*F[61,x,k[0]]
F[61,x,k[0]] = F[55,x,k[0]]+F[59,x,k[0]]
F[62,x,k[0]] = F[57,x,k[0]]*F[58,x,k[0]]
F[63,x,k[0]] = F[12,x]*F[64,x,k[0]]
F[64,x,k[0]] = -k[0]*(F[44,x,1]-F[44,x,k[0]])/(-1+k[0])
F[65,x,k[0]] = F[12,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[20,x]+F[67,x,k[0]]+F[68,x,k[0]]+F[70,x,k[0]]+F[72,x,k[0]]
F[67,x,k[0]] = F[12,x]*F[66,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[12,x]*F[44,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[12,x]*F[48,x,k[0]]
F[72,x,k[0]] = F[57,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = F[66,x,k[0]]+F[74,x]
F[74,x] = 1/F[12,x]*F[75,x]
F[75,x] = -F[1,x]-F[76,x]+F[4,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[1,x]+F[78,x]+F[79,x]+F[80,x]
F[78,x] = F[12,x]*F[42,x]
F[79,x] = F[12,x]*F[8,x]
F[80,x] = F[12,x]*F[77,x]
F[81,x,k[0]] = F[57,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[53,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[58,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[85,x]+F[88,x,k[0]]
F[85,x] = F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[31,x]+F[85,x]
F[88,x,k[0]] = 2*F[20,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[12,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[59,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[57,x,k[0]]*F[84,x,k[0]]
F[92,x] = F[93,x,1]
F[93,x,k[0]] = F[12,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]+F[96,x]+F[97,x,k[0]]
F[95,x,k[0]] = F[10,x]+F[48,x,k[0]]
F[96,x] = F[12,x]*F[16,x]
F[97,x,k[0]] = F[12,x]*F[98,x,k[0]]
F[98,x,k[0]] = 1/(-1+k[0])*(F[94,x,k[0]]*k[0]-F[94,x,1])
F[99,x,k[0]] = F[100,x,k[0]]*F[12,x]
F[100,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[101,x] = F[102,x]
F[102,x] = F[48,x,1]
F[103,x] = F[12,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)+F_{7}\! \left(x \right)+F_{75}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{101}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{92}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{19}\! \left(x , y\right) = 2 F_{20}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x \right)+F_{38}\! \left(x , y\right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{28}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = -\frac{y \left(F_{48}\! \left(x , 1\right)-F_{48}\! \left(x , y\right)\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = y x
F_{58}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = -\frac{y \left(F_{44}\! \left(x , 1\right)-F_{44}\! \left(x , y\right)\right)}{-1+y}
F_{65}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)+F_{70}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{75}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{76}\! \left(x \right)+F_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{78}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x \right)+F_{88}\! \left(x , y\right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{31}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x , y\right) = 2 F_{20}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{92}\! \left(x \right) = F_{93}\! \left(x , 1\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)+F_{96}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = -\frac{-y F_{94}\! \left(x , y\right)+F_{94}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{100}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_103(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_41(x) + F_7(x) + F_75(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_101(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x) + F_13(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_12(x)*F_6(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_18(x, k_0) + F_92(x) + F_99(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_4(x))
Eq(F_19(x, k_0), 2*F_20(x) + F_21(x, k_0) + F_23(x, k_0))
Eq(F_20(x), 0)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_12(x)*F_19(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_57(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_23(x, k_0) + F_25(x) + F_38(x, k_0))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_1(x) + F_31(x))
Eq(F_34(x), F_20(x) + F_35(x) + F_37(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_28(x) + F_34(x))
Eq(F_37(x), F_12(x)*F_30(x))
Eq(F_39(x, k_0), F_1(x) + F_23(x, k_0) + F_38(x, k_0) + F_41(x) + F_7(x))
Eq(F_39(x, k_0), F_40(x, k_0) + F_6(x))
Eq(F_40(x, k_0), F_19(x, k_0))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_6(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_20(x) + F_45(x, k_0) + F_63(x, k_0) + F_65(x, k_0) + F_81(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_12(x)*F_47(x, k_0))
Eq(F_47(x, k_0), -F_48(x, 1) + (k_0*F_48(x, k_0) - F_48(x, 1))/(k_0 - 1))
Eq(F_48(x, k_0), F_20(x) + F_49(x, k_0) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_12(x)*F_48(x, k_0))
Eq(F_51(x, k_0), F_12(x)*F_44(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0)*F_57(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_58(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_54(x, k_0)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x)
Eq(F_58(x, k_0), F_31(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_20(x) + F_60(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_12(x)*F_61(x, k_0))
Eq(F_61(x, k_0), F_55(x, k_0) + F_59(x, k_0))
Eq(F_62(x, k_0), F_57(x, k_0)*F_58(x, k_0))
Eq(F_63(x, k_0), F_12(x)*F_64(x, k_0))
Eq(F_64(x, k_0), -F_44(x, 1) + (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_65(x, k_0), F_12(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_20(x) + F_67(x, k_0) + F_68(x, k_0) + F_70(x, k_0) + F_72(x, k_0))
Eq(F_67(x, k_0), F_12(x)*F_66(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_12(x)*F_44(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_12(x)*F_48(x, k_0))
Eq(F_72(x, k_0), F_57(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), F_66(x, k_0) + F_74(x))
Eq(F_74(x), F_75(x)/F_12(x))
Eq(F_75(x), -F_1(x) + F_4(x) - F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_1(x) + F_78(x) + F_79(x) + F_80(x))
Eq(F_78(x), F_12(x)*F_42(x))
Eq(F_79(x), F_12(x)*F_8(x))
Eq(F_80(x), F_12(x)*F_77(x))
Eq(F_81(x, k_0), F_57(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_53(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_58(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x) + F_88(x, k_0))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_31(x) + F_85(x))
Eq(F_88(x, k_0), 2*F_20(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_12(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_59(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_57(x, k_0)*F_84(x, k_0))
Eq(F_92(x), F_93(x, 1))
Eq(F_93(x, k_0), F_12(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0) + F_96(x) + F_97(x, k_0))
Eq(F_95(x, k_0), F_10(x) + F_48(x, k_0))
Eq(F_96(x), F_12(x)*F_16(x))
Eq(F_97(x, k_0), F_12(x)*F_98(x, k_0))
Eq(F_98(x, k_0), (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_99(x, k_0), F_100(x, k_0)*F_12(x))
Eq(F_100(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_48(x, 1))
Eq(F_103(x), F_12(x)*F_9(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, 2, 5, 4, 0, 3], "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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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, 2, 0, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 0], [3, 0], [3, 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[0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [5, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [5, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [5, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[5, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [5, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [2, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [2, 1], [2, 1], [4, 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], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [4, 1], [4, 1], [5, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 1], [4, 1], [4, 1], [5, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 1], [2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [1, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 1], [1, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[4, 1], [4, 1], [4, 1], [4, 1], [4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[5, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}], "strategy_class": "ObstructionInferralStrategy"}}, "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": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 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, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, {"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, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "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": "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": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24006/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[136,x]
F[10,x] = F[11,x]+F[79,x]
F[11,x] = F[12,x]+F[15,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[1,x]+F[12,x]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]+F[26,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[25,x,k[0]]
F[20,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[24,x,k[0]]
F[23,x,k[0]] = k[0]*x
F[24,x,k[0]] = F[1,x]+F[21,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]*F[24,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[78,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[2,x]*F[21,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]+F[42,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[38,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[37,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[4,x]
F[36,x,k[0]] = F[21,x,k[0]]+F[34,x,k[0]]
F[37,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[38,x,k[0]] = F[39,x,k[0]]+F[41,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[12,x]*F[2,x]*F[21,x,k[0]]
F[41,x,k[0]] = -k[0]*(F[29,x,1]-F[29,x,k[0]])/(-1+k[0])
F[42,x,k[0]] = F[43,x,k[0]]+F[48,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[21,x,k[0]]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[12,x]*F[2,x]
F[47,x] = F[12,x]^2*F[14,x]
F[48,x,k[0]] = F[49,x,k[0]]+F[55,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[12,x]*F[21,x,k[0]]*F[51,x]
F[51,x] = -F[2,x]+F[52,x]
F[52,x] = -F[0,x]+F[53,x]
F[53,x] = 1/F[4,x]*F[54,x]
F[54,x] = F[2,x]
F[55,x,k[0]] = -k[0]*(F[56,x,1]-F[56,x,k[0]])/(-1+k[0])
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[23,x,k[0]]*F[58,x,k[0]]
F[58,x,k[0]] = F[56,x,k[0]]+F[59,x]
F[59,x] = -F[77,x]+F[60,x]
F[60,x] = -F[76,x]+F[61,x]
F[61,x] = -F[75,x]+F[62,x]
F[62,x] = -F[69,x]+F[63,x]
F[63,x] = 1/F[4,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[66,x]
F[66,x] = -F[0,x]+F[67,x]
F[67,x] = 1/F[4,x]*F[68,x]
F[68,x] = F[2,x]
F[69,x] = F[70,x]+F[72,x]
F[70,x] = F[12,x]+F[71,x]
F[71,x] = F[15,x]+F[2,x]
F[72,x] = F[46,x]+F[73,x]
F[73,x] = F[65,x]+F[74,x]
F[74,x] = F[29,x,1]
F[75,x] = F[45,x]
F[76,x] = F[12,x]*F[51,x]
F[77,x] = F[56,x,1]
F[78,x,k[0]] = F[16,x,k[0]]*F[24,x,k[0]]
F[79,x] = -F[130,x]+F[80,x]
F[80,x] = 1/F[4,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[91,x]
F[85,x] = F[86,x]*F[88,x]
F[86,x] = 1/F[4,x]*F[87,x]
F[87,x] = F[2,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[1,x]+F[88,x]
F[91,x] = F[90,x]*F[92,x]
F[92,x] = F[93,x]+F[95,x]
F[93,x] = F[94,x]
F[94,x] = F[88,x]*F[90,x]
F[95,x] = -F[129,x]+F[96,x]
F[97,x,k[0]] = F[4,x]*F[96,x]*F[99,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[102,x]*F[4,x]*F[90,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[23,x,k[0]]
F[101,x,k[0]] = F[1,x]+F[99,x,k[0]]
F[102,x] = F[103,x]+F[82,x]
F[103,x] = -F[107,x]+F[104,x]
F[104,x] = -F[127,x]+F[105,x]
F[105,x] = 1/F[4,x]*F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[107,x]+F[12,x]
F[111,x] = F[112,x]+F[126,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[0,x]*F[12,x]
F[114,x] = F[107,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[125,x]
F[118,x] = F[119,x]+F[121,x]
F[119,x] = -F[2,x]+F[120,x]
F[120,x] = -F[0,x]+F[86,x]
F[121,x] = F[122,x]+F[124,x]
F[122,x] = F[123,x]
F[123,x] = F[88,x]^2
F[124,x] = -F[82,x]+F[95,x]
F[125,x] = F[115,x]
F[126,x] = F[110,x]*F[12,x]
F[127,x] = F[128,x]+F[2,x]
F[128,x] = F[82,x]+F[88,x]
F[129,x] = F[103,x]
F[130,x] = F[12,x]+F[131,x]
F[131,x] = F[132,x]+F[133,x]+F[134,x]
F[132,x] = 0
F[133,x] = F[130,x]*F[4,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[131,x]+F[88,x]
F[136,x] = F[137,x]
F[137,x] = F[138,x,1]
F[139,x,k[0]] = F[138,x,k[0]]+F[141,x,k[0]]
F[140,x,k[0]] = F[139,x,k[0]]*F[4,x]
F[140,x,k[0]] = F[16,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[20,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[21,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]+F[24,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]+F[88,x]
F[145,x,k[0]] = F[132,x]+F[146,x,k[0]]+F[148,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[4,x]
F[147,x,k[0]] = F[145,x,k[0]]+F[21,x,k[0]]
F[148,x,k[0]] = F[144,x,k[0]]*F[23,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{136}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{79}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = y x
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{y \left(F_{29}\! \left(x , 1\right)-F_{29}\! \left(x , y\right)\right)}{-1+y}
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{21}\! \left(x , y\right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{2}\! \left(x \right)
F_{55}\! \left(x , y\right) = -\frac{y \left(F_{56}\! \left(x , 1\right)-F_{56}\! \left(x , y\right)\right)}{-1+y}
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{2}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{72}\! \left(x \right) = F_{46}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{75}\! \left(x \right) = F_{45}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{77}\! \left(x \right) = F_{56}\! \left(x , 1\right)
F_{78}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{79}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right) F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{2}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{1}\! \left(x \right)+F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{90}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{88}\! \left(x \right) F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{96}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right) F_{90}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{82}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{127}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{126}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{107}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{125}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{86}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{124}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{88} \left(x \right)^{2}
F_{124}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{95}\! \left(x \right)
F_{125}\! \left(x \right) = F_{115}\! \left(x \right)
F_{126}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{2}\! \left(x \right)
F_{128}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{129}\! \left(x \right) = F_{103}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{132}\! \left(x \right) = 0
F_{133}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{131}\! \left(x \right)+F_{88}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x , 1\right)
F_{139}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{88}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{132}\! \left(x \right)+F_{146}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{23}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_136(x))
Eq(F_10(x), F_11(x) + F_79(x))
Eq(F_11(x), F_12(x) + F_15(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_1(x) + F_12(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0) + F_26(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_25(x, k_0))
Eq(F_20(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_24(x, k_0))
Eq(F_23(x, k_0), k_0*x)
Eq(F_24(x, k_0), F_1(x) + F_21(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_24(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_78(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_2(x)*F_21(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0) + F_42(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_38(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_37(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_4(x))
Eq(F_36(x, k_0), F_21(x, k_0) + F_34(x, k_0))
Eq(F_37(x, k_0), -F_16(x, 1) + (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_39(x, k_0) + F_41(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_12(x)*F_2(x)*F_21(x, k_0))
Eq(F_41(x, k_0), -F_29(x, 1) + (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_42(x, k_0), F_43(x, k_0) + F_48(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_21(x, k_0)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_12(x)*F_2(x))
Eq(F_47(x), F_12(x)**2*F_14(x))
Eq(F_48(x, k_0), F_49(x, k_0) + F_55(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_12(x)*F_21(x, k_0)*F_51(x))
Eq(F_51(x), -F_2(x) + F_52(x))
Eq(F_52(x), -F_0(x) + F_53(x))
Eq(F_53(x), F_54(x)/F_4(x))
Eq(F_54(x), F_2(x))
Eq(F_55(x, k_0), -F_56(x, 1) + (k_0*F_56(x, k_0) - F_56(x, 1))/(k_0 - 1))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_23(x, k_0)*F_58(x, k_0))
Eq(F_58(x, k_0), F_56(x, k_0) + F_59(x))
Eq(F_59(x), F_60(x) - F_77(x))
Eq(F_60(x), F_61(x) - F_76(x))
Eq(F_61(x), F_62(x) - F_75(x))
Eq(F_62(x), F_63(x) - F_69(x))
Eq(F_63(x), F_64(x)/F_4(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_66(x))
Eq(F_66(x), -F_0(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_4(x))
Eq(F_68(x), F_2(x))
Eq(F_69(x), F_70(x) + F_72(x))
Eq(F_70(x), F_12(x) + F_71(x))
Eq(F_71(x), F_15(x) + F_2(x))
Eq(F_72(x), F_46(x) + F_73(x))
Eq(F_73(x), F_65(x) + F_74(x))
Eq(F_74(x), F_29(x, 1))
Eq(F_75(x), F_45(x))
Eq(F_76(x), F_12(x)*F_51(x))
Eq(F_77(x), F_56(x, 1))
Eq(F_78(x, k_0), F_16(x, k_0)*F_24(x, k_0))
Eq(F_79(x), -F_130(x) + F_80(x))
Eq(F_80(x), F_81(x)/F_4(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_91(x))
Eq(F_85(x), F_86(x)*F_88(x))
Eq(F_86(x), F_87(x)/F_4(x))
Eq(F_87(x), F_2(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_1(x) + F_88(x))
Eq(F_91(x), F_90(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_95(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_88(x)*F_90(x))
Eq(F_95(x), -F_129(x) + F_96(x))
Eq(F_97(x, k_0), F_4(x)*F_96(x)*F_99(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_102(x)*F_4(x)*F_90(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_23(x, k_0))
Eq(F_101(x, k_0), F_1(x) + F_99(x, k_0))
Eq(F_102(x), F_103(x) + F_82(x))
Eq(F_103(x), F_104(x) - F_107(x))
Eq(F_104(x), F_105(x) - F_127(x))
Eq(F_105(x), F_106(x)/F_4(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_107(x) + F_12(x))
Eq(F_111(x), F_112(x) + F_126(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_0(x)*F_12(x))
Eq(F_114(x), F_107(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_125(x))
Eq(F_118(x), F_119(x) + F_121(x))
Eq(F_119(x), F_120(x) - F_2(x))
Eq(F_120(x), -F_0(x) + F_86(x))
Eq(F_121(x), F_122(x) + F_124(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_88(x)**2)
Eq(F_124(x), -F_82(x) + F_95(x))
Eq(F_125(x), F_115(x))
Eq(F_126(x), F_110(x)*F_12(x))
Eq(F_127(x), F_128(x) + F_2(x))
Eq(F_128(x), F_82(x) + F_88(x))
Eq(F_129(x), F_103(x))
Eq(F_130(x), F_12(x) + F_131(x))
Eq(F_131(x), F_132(x) + F_133(x) + F_134(x))
Eq(F_132(x), 0)
Eq(F_133(x), F_130(x)*F_4(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_131(x) + F_88(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x, 1))
Eq(F_139(x, k_0), F_138(x, k_0) + F_141(x, k_0))
Eq(F_140(x, k_0), F_139(x, k_0)*F_4(x))
Eq(F_140(x, k_0), F_16(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_20(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_21(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0) + F_24(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_88(x))
Eq(F_145(x, k_0), F_132(x) + F_146(x, k_0) + F_148(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_4(x))
Eq(F_147(x, k_0), F_145(x, k_0) + F_21(x, k_0))
Eq(F_148(x, k_0), F_144(x, k_0)*F_23(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion_req_corrob_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, 2, 5, 4, 0, 3], "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], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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": [[1, 2]]}, {"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], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 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": [[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], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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], 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"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": [{"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", "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": [[1, 2]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "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", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 3
Strategy pack name: insertion_row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24007/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[25,x]+F[9,x]
F[9,x] = F[10,x]+F[15,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]*F[17,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]+F[22,x]+F[23,x]
F[21,x] = 0
F[22,x] = F[14,x]*F[16,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[12,x]+F[20,x]
F[25,x] = F[123,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[0,x]*F[17,x]
F[28,x] = F[121,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[17,x]+F[29,x]
F[33,x] = F[120,x]+F[34,x]
F[34,x] = -F[38,x]+F[35,x]
F[35,x] = -F[5,x]+F[36,x]
F[36,x] = 1/F[14,x]*F[37,x]
F[37,x] = F[6,x]
F[38,x] = F[39,x]+F[46,x]
F[39,x] = F[40,x]
F[40,x] = F[14,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[17,x]+F[39,x]
F[43,x] = F[38,x]+F[44,x]
F[44,x] = F[17,x]*F[45,x]
F[45,x] = F[0,x]+F[42,x]
F[46,x] = F[21,x]+F[47,x]+F[53,x]
F[47,x] = F[14,x]*F[48,x]
F[48,x] = F[46,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[14,x]*F[51,x]
F[51,x] = F[35,x]+F[52,x]
F[52,x] = F[2,x]+F[49,x]
F[53,x] = F[14,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[17,x]*F[19,x]
F[57,x] = F[105,x]+F[58,x]
F[58,x] = -F[39,x]+F[59,x]
F[59,x] = -F[104,x]+F[60,x]
F[60,x] = -F[87,x]+F[61,x]
F[61,x] = 1/F[14,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[14,x]*F[65,x]
F[65,x] = F[66,x]+F[72,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[12,x]+F[68,x]
F[68,x] = F[11,x]*F[12,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[12,x]*F[2,x]
F[71,x] = F[11,x]*F[63,x]
F[72,x] = F[63,x]+F[73,x]
F[73,x] = F[74,x,1]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[14,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[93,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[79,x]*F[89,x,k[0]]
F[79,x] = -F[86,x]+F[80,x]
F[80,x] = 1/F[14,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = -F[2,x]+F[83,x]
F[83,x] = -F[0,x]+F[84,x]
F[84,x] = 1/F[14,x]*F[85,x]
F[85,x] = F[2,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[2,x]+F[63,x]
F[88,x] = F[73,x]+F[82,x]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]*F[92,x,k[0]]
F[91,x,k[0]] = k[0]*x
F[92,x,k[0]] = F[1,x]+F[89,x,k[0]]
F[93,x,k[0]] = -k[0]*(F[94,x,1]-F[94,x,k[0]])/(-1+k[0])
F[94,x,k[0]] = F[74,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[14,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[94,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[101,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[89,x,k[0]]
F[100,x,k[0]] = F[89,x,k[0]]*F[92,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]
F[102,x,k[0]] = F[2,x]*F[89,x,k[0]]
F[103,x,k[0]] = F[92,x,k[0]]*F[95,x,k[0]]
F[104,x] = F[11,x]*F[17,x]
F[105,x] = -F[112,x]+F[106,x]
F[106,x] = -F[110,x]+F[107,x]
F[107,x] = -F[88,x]+F[108,x]
F[108,x] = 1/F[14,x]*F[109,x]
F[109,x] = F[73,x]
F[110,x] = F[111,x]
F[111,x] = F[17,x]^2*F[11,x]
F[112,x] = -F[39,x]+F[113,x]
F[113,x] = -F[118,x]+F[114,x]
F[114,x] = 1/F[14,x]*F[115,x]
F[115,x] = -F[116,x]-F[21,x]+F[39,x]
F[116,x] = F[117,x]*F[14,x]
F[117,x] = F[2,x]+F[39,x]
F[118,x] = F[119,x]
F[119,x] = F[17,x]*F[19,x]
F[120,x] = F[17,x]*F[32,x]
F[121,x] = F[122,x]
F[122,x] = F[17,x]^3
F[123,x] = F[124,x]+F[144,x]
F[124,x] = -F[133,x]+F[125,x]
F[125,x] = -F[131,x]+F[126,x]
F[126,x] = -F[129,x]+F[127,x]
F[127,x] = 1/F[14,x]*F[128,x]
F[128,x] = F[39,x]
F[129,x] = F[130,x]*F[17,x]
F[130,x] = F[19,x]+F[24,x]
F[131,x] = F[132,x]*F[17,x]
F[132,x] = F[0,x]+F[119,x]
F[133,x] = F[134,x]*F[17,x]
F[134,x] = F[135,x]+F[141,x]+F[21,x]
F[135,x] = F[136,x]*F[14,x]
F[136,x] = F[135,x]+F[137,x]+F[21,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[14,x]*F[19,x]
F[139,x] = F[137,x]+F[140,x]+F[19,x]
F[140,x] = F[139,x]*F[14,x]
F[141,x] = F[142,x]
F[142,x] = F[14,x]*F[143,x]*F[19,x]
F[143,x] = F[140,x]+F[141,x]+F[21,x]
F[144,x] = F[145,x]+F[164,x]
F[145,x] = F[146,x]+F[162,x]+F[21,x]
F[146,x] = F[14,x]*F[147,x]
F[147,x] = F[148,x]+F[155,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[150,x]+F[2,x]
F[150,x] = F[12,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[14,x]*F[153,x]
F[153,x] = F[154,x]+F[79,x]
F[154,x] = F[11,x]*F[150,x]
F[155,x] = F[145,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[12,x]*F[158,x]
F[158,x] = -F[29,x]+F[159,x]
F[159,x] = -F[149,x]+F[160,x]
F[160,x] = 1/F[14,x]*F[161,x]
F[161,x] = F[29,x]
F[162,x] = F[14,x]*F[163,x]
F[163,x] = F[145,x]+F[29,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[17,x]
F[166,x] = F[167,x]+F[172,x]+F[21,x]
F[167,x] = F[14,x]*F[168,x]
F[168,x] = F[135,x]+F[169,x]+F[21,x]
F[169,x] = F[170,x]
F[170,x] = F[14,x]*F[171,x]*F[19,x]
F[171,x] = F[140,x]+F[169,x]+F[21,x]
F[172,x] = F[173,x]
F[173,x] = F[14,x]*F[174,x]
F[174,x] = F[175,x]+F[177,x]
F[175,x] = F[172,x]+F[176,x]+F[21,x]
F[176,x] = F[14,x]*F[171,x]
F[177,x] = F[14,x]*F[143,x]*F[19,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{25}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{123}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right)
F_{28}\! \left(x \right) = F_{121}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{120}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{0}\! \left(x \right)+F_{42}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{35}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{57}\! \left(x \right) = F_{105}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{72}\! \left(x \right) = F_{63}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x , 1\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{79}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{2}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{2}\! \left(x \right)+F_{63}\! \left(x \right)
F_{88}\! \left(x \right) = F_{73}\! \left(x \right)+F_{82}\! \left(x \right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = y x
F_{92}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = -\frac{y \left(F_{94}\! \left(x , 1\right)-F_{94}\! \left(x , y\right)\right)}{-1+y}
F_{94}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{89}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{92}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{104}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{109}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{73}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{118}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{115}\! \left(x \right) = -F_{116}\! \left(x \right)-F_{21}\! \left(x \right)+F_{39}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{117}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{120}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{17} \left(x \right)^{3}
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{144}\! \left(x \right)
F_{124}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = -F_{131}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{39}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{17}\! \left(x \right)
F_{130}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{17}\! \left(x \right)
F_{132}\! \left(x \right) = F_{0}\! \left(x \right)+F_{119}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{17}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{141}\! \left(x \right)+F_{21}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{135}\! \left(x \right)+F_{137}\! \left(x \right)+F_{21}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{139}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)+F_{19}\! \left(x \right)
F_{140}\! \left(x \right) = F_{139}\! \left(x \right) F_{14}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{14}\! \left(x \right) F_{143}\! \left(x \right) F_{19}\! \left(x \right)
F_{143}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)+F_{21}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{164}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{162}\! \left(x \right)+F_{21}\! \left(x \right)
F_{146}\! \left(x \right) = F_{14}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{155}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{2}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{14}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{79}\! \left(x \right)
F_{154}\! \left(x \right) = F_{11}\! \left(x \right) F_{150}\! \left(x \right)
F_{155}\! \left(x \right) = F_{145}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{12}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{29}\! \left(x \right)
F_{162}\! \left(x \right) = F_{14}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{145}\! \left(x \right)+F_{29}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{17}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{172}\! \left(x \right)+F_{21}\! \left(x \right)
F_{167}\! \left(x \right) = F_{14}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{135}\! \left(x \right)+F_{169}\! \left(x \right)+F_{21}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{14}\! \left(x \right) F_{171}\! \left(x \right) F_{19}\! \left(x \right)
F_{171}\! \left(x \right) = F_{140}\! \left(x \right)+F_{169}\! \left(x \right)+F_{21}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{14}\! \left(x \right) F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{177}\! \left(x \right)
F_{175}\! \left(x \right) = F_{172}\! \left(x \right)+F_{176}\! \left(x \right)+F_{21}\! \left(x \right)
F_{176}\! \left(x \right) = F_{14}\! \left(x \right) F_{171}\! \left(x \right)
F_{177}\! \left(x \right) = F_{14}\! \left(x \right) F_{143}\! \left(x \right) F_{19}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_25(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_15(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x)*F_17(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_23(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_14(x)*F_16(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_12(x) + F_20(x))
Eq(F_25(x), F_123(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_0(x)*F_17(x))
Eq(F_28(x), F_121(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_17(x) + F_29(x))
Eq(F_33(x), F_120(x) + F_34(x))
Eq(F_34(x), F_35(x) - F_38(x))
Eq(F_35(x), F_36(x) - F_5(x))
Eq(F_36(x), F_37(x)/F_14(x))
Eq(F_37(x), F_6(x))
Eq(F_38(x), F_39(x) + F_46(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_14(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_17(x) + F_39(x))
Eq(F_43(x), F_38(x) + F_44(x))
Eq(F_44(x), F_17(x)*F_45(x))
Eq(F_45(x), F_0(x) + F_42(x))
Eq(F_46(x), F_21(x) + F_47(x) + F_53(x))
Eq(F_47(x), F_14(x)*F_48(x))
Eq(F_48(x), F_46(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_14(x)*F_51(x))
Eq(F_51(x), F_35(x) + F_52(x))
Eq(F_52(x), F_2(x) + F_49(x))
Eq(F_53(x), F_14(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_17(x)*F_19(x))
Eq(F_57(x), F_105(x) + F_58(x))
Eq(F_58(x), -F_39(x) + F_59(x))
Eq(F_59(x), -F_104(x) + F_60(x))
Eq(F_60(x), F_61(x) - F_87(x))
Eq(F_61(x), F_62(x)/F_14(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_14(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_72(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_12(x) + F_68(x))
Eq(F_68(x), F_11(x)*F_12(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_12(x)*F_2(x))
Eq(F_71(x), F_11(x)*F_63(x))
Eq(F_72(x), F_63(x) + F_73(x))
Eq(F_73(x), F_74(x, 1))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_14(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_93(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x)*F_89(x, k_0))
Eq(F_79(x), F_80(x) - F_86(x))
Eq(F_80(x), F_81(x)/F_14(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), -F_2(x) + F_83(x))
Eq(F_83(x), -F_0(x) + F_84(x))
Eq(F_84(x), F_85(x)/F_14(x))
Eq(F_85(x), F_2(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_2(x) + F_63(x))
Eq(F_88(x), F_73(x) + F_82(x))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0)*F_92(x, k_0))
Eq(F_91(x, k_0), k_0*x)
Eq(F_92(x, k_0), F_1(x) + F_89(x, k_0))
Eq(F_93(x, k_0), -F_94(x, 1) + (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_94(x, k_0), F_74(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_14(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_94(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_101(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_89(x, k_0))
Eq(F_100(x, k_0), F_89(x, k_0)*F_92(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0))
Eq(F_102(x, k_0), F_2(x)*F_89(x, k_0))
Eq(F_103(x, k_0), F_92(x, k_0)*F_95(x, k_0))
Eq(F_104(x), F_11(x)*F_17(x))
Eq(F_105(x), F_106(x) - F_112(x))
Eq(F_106(x), F_107(x) - F_110(x))
Eq(F_107(x), F_108(x) - F_88(x))
Eq(F_108(x), F_109(x)/F_14(x))
Eq(F_109(x), F_73(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_11(x)*F_17(x)**2)
Eq(F_112(x), F_113(x) - F_39(x))
Eq(F_113(x), F_114(x) - F_118(x))
Eq(F_114(x), F_115(x)/F_14(x))
Eq(F_115(x), -F_116(x) - F_21(x) + F_39(x))
Eq(F_116(x), F_117(x)*F_14(x))
Eq(F_117(x), F_2(x) + F_39(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_17(x)*F_19(x))
Eq(F_120(x), F_17(x)*F_32(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_17(x)**3)
Eq(F_123(x), F_124(x) + F_144(x))
Eq(F_124(x), F_125(x) - F_133(x))
Eq(F_125(x), F_126(x) - F_131(x))
Eq(F_126(x), F_127(x) - F_129(x))
Eq(F_127(x), F_128(x)/F_14(x))
Eq(F_128(x), F_39(x))
Eq(F_129(x), F_130(x)*F_17(x))
Eq(F_130(x), F_19(x) + F_24(x))
Eq(F_131(x), F_132(x)*F_17(x))
Eq(F_132(x), F_0(x) + F_119(x))
Eq(F_133(x), F_134(x)*F_17(x))
Eq(F_134(x), F_135(x) + F_141(x) + F_21(x))
Eq(F_135(x), F_136(x)*F_14(x))
Eq(F_136(x), F_135(x) + F_137(x) + F_21(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_14(x)*F_19(x))
Eq(F_139(x), F_137(x) + F_140(x) + F_19(x))
Eq(F_140(x), F_139(x)*F_14(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_14(x)*F_143(x)*F_19(x))
Eq(F_143(x), F_140(x) + F_141(x) + F_21(x))
Eq(F_144(x), F_145(x) + F_164(x))
Eq(F_145(x), F_146(x) + F_162(x) + F_21(x))
Eq(F_146(x), F_14(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_155(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_2(x))
Eq(F_150(x), F_12(x) + F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_14(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_79(x))
Eq(F_154(x), F_11(x)*F_150(x))
Eq(F_155(x), F_145(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_12(x)*F_158(x))
Eq(F_158(x), F_159(x) - F_29(x))
Eq(F_159(x), -F_149(x) + F_160(x))
Eq(F_160(x), F_161(x)/F_14(x))
Eq(F_161(x), F_29(x))
Eq(F_162(x), F_14(x)*F_163(x))
Eq(F_163(x), F_145(x) + F_29(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_17(x))
Eq(F_166(x), F_167(x) + F_172(x) + F_21(x))
Eq(F_167(x), F_14(x)*F_168(x))
Eq(F_168(x), F_135(x) + F_169(x) + F_21(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_14(x)*F_171(x)*F_19(x))
Eq(F_171(x), F_140(x) + F_169(x) + F_21(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_14(x)*F_174(x))
Eq(F_174(x), F_175(x) + F_177(x))
Eq(F_175(x), F_172(x) + F_176(x) + F_21(x))
Eq(F_176(x), F_14(x)*F_171(x))
Eq(F_177(x), F_14(x)*F_143(x)*F_19(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.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_row_and_col_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, 2, 5, 4, 0, 3], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"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, 2], [1, 2], [1, 2], [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": [1, 4, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, "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, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "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, 2, 5, 4, 0, 3], "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": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": 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"Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 3]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 4
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24008/
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[136,x]+F[4,x]
F[4,x] = F[5,x]*F[6,x]
F[5,x] = x
F[6,x] = F[1,x]+F[134,x]+F[7,x]+F[95,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[57,x]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[25,x,k[0]]*F[54,x,k[0]]
F[57,x] = 1/F[5,x]*F[58,x]
F[58,x] = -F[0,x]+F[59,x]
F[59,x] = F[1,x]+F[60,x]+F[70,x]
F[60,x] = F[5,x]*F[61,x]
F[61,x] = F[19,x]+F[62,x]
F[62,x] = F[63,x]+F[66,x]
F[63,x] = F[64,x]
F[64,x] = F[5,x]*F[65,x]
F[65,x] = F[1,x]+F[63,x]
F[66,x] = F[28,x]+F[67,x]+F[69,x]
F[67,x] = F[5,x]*F[68,x]
F[68,x] = F[20,x]+F[66,x]
F[69,x] = F[5,x]*F[62,x]
F[70,x] = -F[1,x]-F[75,x]+F[71,x]
F[71,x] = F[0,x]+F[72,x]
F[72,x] = F[5,x]*F[73,x]
F[73,x] = F[38,x]+F[47,x]+F[74,x]
F[74,x] = F[12,x]*F[5,x]
F[75,x] = F[5,x]*F[76,x]
F[76,x] = F[71,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[5,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]+F[84,x]
F[80,x] = 1/F[5,x]*F[81,x]
F[81,x] = -F[0,x]+F[82,x]
F[82,x] = F[1,x]+F[60,x]+F[75,x]
F[83,x] = F[5,x]*F[79,x]
F[84,x] = F[85,x]
F[85,x] = F[5,x]*F[86,x]
F[86,x] = 1/F[5,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = -F[80,x]-F[89,x]+F[12,x]
F[89,x] = -F[82,x]-F[90,x]+F[73,x]
F[90,x] = F[91,x]
F[91,x] = F[5,x]*F[92,x]
F[92,x] = 1/F[5,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = -F[82,x]+F[76,x]
F[95,x] = F[5,x]*F[96,x]
F[96,x] = F[97,x,1]
F[97,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[109,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[5,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[5,x]
F[101,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
F[103,x,k[0]] = F[1,x]+F[102,x,k[0]]+F[107,x,k[0]]+F[109,x,k[0]]
F[103,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[105,x,k[0]]+F[106,x,k[0]]
F[104,x,k[0]] = F[5,x]*F[97,x,k[0]]
F[105,x,k[0]] = F[5,x]*F[9,x,k[0]]
F[106,x,k[0]] = F[103,x,k[0]]*F[25,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[5,x]
F[108,x,k[0]] = 1/(-1+k[0])*(F[103,x,k[0]]*k[0]-F[103,x,1])
F[109,x,k[0]] = F[110,x,k[0]]*F[25,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[120,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[54,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[63,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[119,x,k[0]]+F[28,x]
F[114,x,k[0]] = F[115,x,k[0]]*F[5,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[55,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[25,x,k[0]]
F[118,x,k[0]] = F[116,x,k[0]]+F[63,x]
F[119,x,k[0]] = F[112,x,k[0]]*F[25,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[126,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[63,x]
F[122,x,k[0]] = F[123,x,k[0]]+F[125,x,k[0]]+F[28,x]
F[123,x,k[0]] = F[124,x,k[0]]*F[5,x]
F[124,x,k[0]] = F[122,x,k[0]]+F[55,x,k[0]]
F[125,x,k[0]] = F[121,x,k[0]]*F[25,x,k[0]]
F[126,x,k[0]] = F[127,x]+F[130,x,k[0]]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[5,x]
F[129,x] = F[127,x]+F[63,x]
F[130,x,k[0]] = 2*F[28,x]+F[131,x,k[0]]+F[133,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[5,x]
F[132,x,k[0]] = F[113,x,k[0]]+F[130,x,k[0]]
F[133,x,k[0]] = F[126,x,k[0]]*F[25,x,k[0]]
F[134,x] = F[135,x]*F[5,x]
F[135,x] = F[33,x,1]
F[136,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_{136}\! \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_{134}\! \left(x \right)+F_{7}\! \left(x \right)+F_{95}\! \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_{57}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)+F_{70}\! \left(x \right)
F_{60}\! \left(x \right) = F_{5}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{5}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{28}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{5}\! \left(x \right) F_{62}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{75}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{0}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{5}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{38}\! \left(x \right)+F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{75}\! \left(x \right) = F_{5}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{5}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{81}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)+F_{75}\! \left(x \right)
F_{83}\! \left(x \right) = F_{5}\! \left(x \right) F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{5}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{80}\! \left(x \right)-F_{89}\! \left(x \right)+F_{12}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{82}\! \left(x \right)-F_{90}\! \left(x \right)+F_{73}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{5}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = \frac{F_{93}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{76}\! \left(x \right)
F_{95}\! \left(x \right) = F_{5}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x , 1\right)
F_{97}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{101}\! \left(x , y\right) = -\frac{-y F_{97}\! \left(x , y\right)+F_{97}\! \left(x , 1\right)}{-1+y}
F_{103}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{108}\! \left(x , y\right) = -\frac{-y F_{103}\! \left(x , y\right)+F_{103}\! \left(x , 1\right)}{-1+y}
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x \right)+F_{130}\! \left(x , y\right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{5}\! \left(x \right)
F_{129}\! \left(x \right) = F_{127}\! \left(x \right)+F_{63}\! \left(x \right)
F_{130}\! \left(x , y\right) = 2 F_{28}\! \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_{5}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{5}\! \left(x \right)
F_{135}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{136}\! \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_136(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_134(x) + F_7(x) + F_95(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_57(x))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_25(x, k_0)*F_54(x, k_0))
Eq(F_57(x), F_58(x)/F_5(x))
Eq(F_58(x), -F_0(x) + F_59(x))
Eq(F_59(x), F_1(x) + F_60(x) + F_70(x))
Eq(F_60(x), F_5(x)*F_61(x))
Eq(F_61(x), F_19(x) + F_62(x))
Eq(F_62(x), F_63(x) + F_66(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_5(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_63(x))
Eq(F_66(x), F_28(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_5(x)*F_68(x))
Eq(F_68(x), F_20(x) + F_66(x))
Eq(F_69(x), F_5(x)*F_62(x))
Eq(F_70(x), -F_1(x) + F_71(x) - F_75(x))
Eq(F_71(x), F_0(x) + F_72(x))
Eq(F_72(x), F_5(x)*F_73(x))
Eq(F_73(x), F_38(x) + F_47(x) + F_74(x))
Eq(F_74(x), F_12(x)*F_5(x))
Eq(F_75(x), F_5(x)*F_76(x))
Eq(F_76(x), F_71(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_5(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x) + F_84(x))
Eq(F_80(x), F_81(x)/F_5(x))
Eq(F_81(x), -F_0(x) + F_82(x))
Eq(F_82(x), F_1(x) + F_60(x) + F_75(x))
Eq(F_83(x), F_5(x)*F_79(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_5(x)*F_86(x))
Eq(F_86(x), F_87(x)/F_5(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x) - F_80(x) - F_89(x))
Eq(F_89(x), F_73(x) - F_82(x) - F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_5(x)*F_92(x))
Eq(F_92(x), F_93(x)/F_5(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_76(x) - F_82(x))
Eq(F_95(x), F_5(x)*F_96(x))
Eq(F_96(x), F_97(x, 1))
Eq(F_97(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_109(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_5(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_5(x))
Eq(F_101(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_103(x, k_0), F_1(x) + F_102(x, k_0) + F_107(x, k_0) + F_109(x, k_0))
Eq(F_103(x, k_0), F_1(x) + F_104(x, k_0) + F_105(x, k_0) + F_106(x, k_0))
Eq(F_104(x, k_0), F_5(x)*F_97(x, k_0))
Eq(F_105(x, k_0), F_5(x)*F_9(x, k_0))
Eq(F_106(x, k_0), F_103(x, k_0)*F_25(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_5(x))
Eq(F_108(x, k_0), (k_0*F_103(x, k_0) - F_103(x, 1))/(k_0 - 1))
Eq(F_109(x, k_0), F_110(x, k_0)*F_25(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_120(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_54(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_63(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_119(x, k_0) + F_28(x))
Eq(F_114(x, k_0), F_115(x, k_0)*F_5(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_55(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_25(x, k_0))
Eq(F_118(x, k_0), F_116(x, k_0) + F_63(x))
Eq(F_119(x, k_0), F_112(x, k_0)*F_25(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_126(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_63(x))
Eq(F_122(x, k_0), F_123(x, k_0) + F_125(x, k_0) + F_28(x))
Eq(F_123(x, k_0), F_124(x, k_0)*F_5(x))
Eq(F_124(x, k_0), F_122(x, k_0) + F_55(x, k_0))
Eq(F_125(x, k_0), F_121(x, k_0)*F_25(x, k_0))
Eq(F_126(x, k_0), F_127(x) + F_130(x, k_0))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_5(x))
Eq(F_129(x), F_127(x) + F_63(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_133(x, k_0) + 2*F_28(x))
Eq(F_131(x, k_0), F_132(x, k_0)*F_5(x))
Eq(F_132(x, k_0), F_113(x, k_0) + F_130(x, k_0))
Eq(F_133(x, k_0), F_126(x, k_0)*F_25(x, k_0))
Eq(F_134(x), F_135(x)*F_5(x))
Eq(F_135(x), F_33(x, 1))
Eq(F_136(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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_and_col_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, 2, 5, 4, 0, 3], "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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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, 2, 0, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "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": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 0], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 2], [2, 1], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 2], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"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, 3, 0, 1], "pos": [[2, 1], [2, 2], [2, 0], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 2], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 1], [2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[2, 1], [2, 2], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 1], [2, 1], [2, 2], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[0, 2], [2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[2, 1], [2, 1], [2, 2], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 5, 4, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}], 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[{"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": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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 5
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24009/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[1,x]+F[169,x]+F[5,x]
F[5,x] = F[18,x]*F[6,x]
F[6,x] = F[1,x]+F[35,x]+F[69,x]+F[7,x]
F[7,x] = F[18,x]*F[8,x]
F[8,x] = F[167,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]+F[120,x]+F[86,x]
F[10,x] = F[11,x]*F[18,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]+F[6,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = 2*F[15,x]+F[16,x,k[0]]+F[19,x,k[0]]
F[15,x] = 0
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[14,x,k[0]]*F[18,x]
F[18,x] = x
F[19,x,k[0]] = F[20,x,k[0]]*F[51,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[21,x]+F[34,x,k[0]]
F[21,x] = F[18,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[18,x]*F[23,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[28,x]
F[28,x] = F[18,x]*F[29,x]
F[29,x] = F[1,x]+F[27,x]
F[30,x] = F[15,x]+F[31,x]+F[33,x]
F[31,x] = F[18,x]*F[32,x]
F[32,x] = F[24,x]+F[30,x]
F[33,x] = F[18,x]*F[26,x]
F[12,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[34,x,k[0]]+F[35,x]+F[7,x]
F[35,x] = F[18,x]*F[36,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[38,x,1]
F[38,x,k[0]] = F[15,x]+F[39,x,k[0]]+F[57,x,k[0]]+F[59,x,k[0]]+F[75,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[18,x]*F[41,x,k[0]]
F[41,x,k[0]] = -k[0]*(F[42,x,1]-F[42,x,k[0]])/(-1+k[0])
F[42,x,k[0]] = F[15,x]+F[43,x,k[0]]+F[45,x,k[0]]+F[46,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[18,x]*F[42,x,k[0]]
F[45,x,k[0]] = F[18,x]*F[38,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[51,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[52,x,k[0]]
F[48,x,k[0]] = F[1,x]+F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[48,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = k[0]*x
F[52,x,k[0]] = F[27,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[15,x]+F[54,x,k[0]]+F[56,x,k[0]]
F[54,x,k[0]] = F[18,x]*F[55,x,k[0]]
F[55,x,k[0]] = F[49,x,k[0]]+F[53,x,k[0]]
F[56,x,k[0]] = F[51,x,k[0]]*F[52,x,k[0]]
F[57,x,k[0]] = F[18,x]*F[58,x,k[0]]
F[58,x,k[0]] = -k[0]*(F[38,x,1]-F[38,x,k[0]])/(-1+k[0])
F[59,x,k[0]] = F[18,x]*F[60,x,k[0]]
F[60,x,k[0]] = F[15,x]+F[61,x,k[0]]+F[62,x,k[0]]+F[64,x,k[0]]+F[66,x,k[0]]
F[61,x,k[0]] = F[18,x]*F[60,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[18,x]*F[38,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[18,x]*F[42,x,k[0]]
F[66,x,k[0]] = F[51,x,k[0]]*F[67,x,k[0]]
F[67,x,k[0]] = F[60,x,k[0]]+F[68,x]
F[68,x] = 1/F[18,x]*F[69,x]
F[69,x] = -F[1,x]-F[70,x]+F[4,x]
F[70,x] = F[18,x]*F[71,x]
F[71,x] = F[1,x]+F[72,x]+F[73,x]+F[74,x]
F[72,x] = F[18,x]*F[36,x]
F[73,x] = F[18,x]*F[8,x]
F[74,x] = F[18,x]*F[71,x]
F[75,x,k[0]] = F[51,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[47,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[52,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[79,x]+F[82,x,k[0]]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[27,x]+F[79,x]
F[82,x,k[0]] = 2*F[15,x]+F[83,x,k[0]]+F[85,x,k[0]]
F[83,x,k[0]] = F[18,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[53,x,k[0]]+F[82,x,k[0]]
F[85,x,k[0]] = F[51,x,k[0]]*F[78,x,k[0]]
F[86,x] = F[18,x]*F[87,x]
F[87,x] = F[88,x,1]
F[88,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[89,x,k[0]]+F[91,x,k[0]]+F[93,x,k[0]]
F[89,x,k[0]] = F[18,x]*F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[91,x,k[0]] = F[18,x]*F[92,x,k[0]]
F[92,x,k[0]] = 1/(-1+k[0])*(F[88,x,k[0]]*k[0]-F[88,x,1])
F[94,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[93,x,k[0]]+F[98,x,k[0]]
F[94,x,k[0]] = F[1,x]+F[95,x,k[0]]+F[96,x,k[0]]+F[97,x,k[0]]
F[95,x,k[0]] = F[18,x]*F[88,x,k[0]]
F[96,x,k[0]] = F[12,x,k[0]]*F[18,x]
F[97,x,k[0]] = F[51,x,k[0]]*F[94,x,k[0]]
F[98,x,k[0]] = F[18,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[94,x,k[0]]*k[0]-F[94,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[51,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[111,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]
F[103,x,k[0]] = F[1,x]+F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[103,x,k[0]]*F[51,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]+F[24,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[110,x,k[0]]+F[15,x]
F[108,x,k[0]] = F[109,x,k[0]]*F[18,x]
F[109,x,k[0]] = F[104,x,k[0]]+F[107,x,k[0]]
F[110,x,k[0]] = F[106,x,k[0]]*F[51,x,k[0]]
F[111,x,k[0]] = F[106,x,k[0]]+F[112,x,k[0]]
F[112,x,k[0]] = F[113,x]+F[116,x,k[0]]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[18,x]
F[115,x] = F[113,x]+F[24,x]
F[116,x,k[0]] = 2*F[15,x]+F[117,x,k[0]]+F[119,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[18,x]
F[118,x,k[0]] = F[107,x,k[0]]+F[116,x,k[0]]
F[119,x,k[0]] = F[112,x,k[0]]*F[51,x,k[0]]
F[120,x] = F[121,x]*F[18,x]
F[121,x] = F[122,x,1]
F[122,x,k[0]] = F[1,x]+F[123,x,k[0]]+F[139,x,k[0]]+F[165,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[51,x,k[0]]
F[124,x,k[0]] = F[125,x]+F[127,x,k[0]]
F[125,x] = F[126,x]+F[29,x]
F[126,x] = F[27,x]+F[79,x]
F[127,x,k[0]] = F[128,x,k[0]]+F[133,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[49,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]+F[132,x,k[0]]+F[15,x]
F[130,x,k[0]] = F[131,x,k[0]]*F[51,x,k[0]]
F[131,x,k[0]] = F[129,x,k[0]]+F[27,x]
F[132,x,k[0]] = F[128,x,k[0]]*F[18,x]
F[133,x,k[0]] = F[129,x,k[0]]+F[134,x,k[0]]
F[134,x,k[0]] = 2*F[15,x]+F[135,x,k[0]]+F[137,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[51,x,k[0]]
F[136,x,k[0]] = F[134,x,k[0]]+F[79,x]
F[137,x,k[0]] = F[138,x,k[0]]*F[18,x]
F[138,x,k[0]] = F[129,x,k[0]]+F[134,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[18,x]
F[140,x,k[0]] = F[141,x]+F[145,x,k[0]]
F[141,x] = F[1,x]+F[142,x]+F[143,x]+F[144,x]
F[142,x] = F[18,x]*F[87,x]
F[143,x] = F[11,x]*F[18,x]
F[144,x] = F[141,x]*F[18,x]
F[145,x,k[0]] = F[146,x,k[0]]+F[147,x,k[0]]+F[15,x]+F[162,x,k[0]]+F[164,x,k[0]]
F[146,x,k[0]] = F[140,x,k[0]]*F[51,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[18,x]
F[149,x,k[0]] = F[15,x]+F[150,x,k[0]]+F[152,x,k[0]]+F[160,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]*F[51,x,k[0]]
F[151,x,k[0]] = F[128,x,k[0]]+F[29,x]
F[152,x,k[0]] = F[153,x,k[0]]*F[18,x]
F[153,x,k[0]] = F[123,x,k[0]]+F[15,x]+F[154,x,k[0]]+F[155,x,k[0]]+F[157,x,k[0]]
F[154,x,k[0]] = F[145,x,k[0]]*F[18,x]
F[155,x,k[0]] = F[156,x,k[0]]*F[18,x]
F[156,x,k[0]] = -k[0]*(F[153,x,1]-F[153,x,k[0]])/(-1+k[0])
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[18,x]
F[159,x,k[0]] = -k[0]*(F[149,x,1]-F[149,x,k[0]])/(-1+k[0])
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[149,x,k[0]]*F[18,x]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[153,x,k[0]]*F[18,x]
F[164,x,k[0]] = F[145,x,k[0]]*F[18,x]
F[165,x,k[0]] = F[166,x,k[0]]*F[18,x]
F[166,x,k[0]] = (F[122,x,k[0]]*k[0]-F[122,x,1])/(-1+k[0])
F[167,x] = F[168,x]
F[168,x] = F[42,x,1]
F[169,x] = F[18,x]*F[9,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_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{169}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{18}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{69}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{167}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{120}\! \left(x \right)+F_{86}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{26}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = -\frac{y \left(F_{42}\! \left(x , 1\right)-F_{42}\! \left(x , y\right)\right)}{-1+y}
F_{42}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = y x
F_{52}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = -\frac{y \left(F_{38}\! \left(x , 1\right)-F_{38}\! \left(x , y\right)\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{70}\! \left(x \right)+F_{4}\! \left(x \right)
F_{70}\! \left(x \right) = F_{18}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{72}\! \left(x \right)+F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{18}\! \left(x \right) F_{71}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{27}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{86}\! \left(x \right) = F_{18}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x , 1\right)
F_{88}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-y F_{12}\! \left(x , y\right)+F_{12}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{-y F_{88}\! \left(x , y\right)+F_{88}\! \left(x , 1\right)}{-1+y}
F_{94}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{93}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{94}\! \left(x , y\right)+F_{94}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x \right)+F_{116}\! \left(x , y\right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{18}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{24}\! \left(x \right)
F_{116}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{18}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x , 1\right)
F_{122}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{123}\! \left(x , y\right)+F_{139}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x \right)+F_{127}\! \left(x , y\right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{29}\! \left(x \right)
F_{126}\! \left(x \right) = F_{27}\! \left(x \right)+F_{79}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{132}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{27}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{133}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{79}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x \right)+F_{145}\! \left(x , y\right)
F_{141}\! \left(x \right) = F_{1}\! \left(x \right)+F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{18}\! \left(x \right) F_{87}\! \left(x \right)
F_{143}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{144}\! \left(x \right) = F_{141}\! \left(x \right) F_{18}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{147}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{162}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{150}\! \left(x , y\right)+F_{152}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{154}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{156}\! \left(x , y\right) = -\frac{y \left(F_{153}\! \left(x , 1\right)-F_{153}\! \left(x , y\right)\right)}{-1+y}
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{159}\! \left(x , y\right) = -\frac{y \left(F_{149}\! \left(x , 1\right)-F_{149}\! \left(x , y\right)\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{18}\! \left(x \right)
F_{166}\! \left(x , y\right) = -\frac{-y F_{122}\! \left(x , y\right)+F_{122}\! \left(x , 1\right)}{-1+y}
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{169}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \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_18(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_169(x) + F_5(x))
Eq(F_5(x), F_18(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_35(x) + F_69(x) + F_7(x))
Eq(F_7(x), F_18(x)*F_8(x))
Eq(F_8(x), F_167(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x) + F_120(x) + F_86(x))
Eq(F_10(x), F_11(x)*F_18(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0) + F_6(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), 2*F_15(x) + F_16(x, k_0) + F_19(x, k_0))
Eq(F_15(x), 0)
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0)*F_18(x))
Eq(F_18(x), x)
Eq(F_19(x, k_0), F_20(x, k_0)*F_51(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_19(x, k_0) + F_21(x) + F_34(x, k_0))
Eq(F_21(x), F_18(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_18(x)*F_23(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_18(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_27(x))
Eq(F_30(x), F_15(x) + F_31(x) + F_33(x))
Eq(F_31(x), F_18(x)*F_32(x))
Eq(F_32(x), F_24(x) + F_30(x))
Eq(F_33(x), F_18(x)*F_26(x))
Eq(F_12(x, k_0), F_1(x) + F_19(x, k_0) + F_34(x, k_0) + F_35(x) + F_7(x))
Eq(F_35(x), F_18(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_38(x, 1))
Eq(F_38(x, k_0), F_15(x) + F_39(x, k_0) + F_57(x, k_0) + F_59(x, k_0) + F_75(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_18(x)*F_41(x, k_0))
Eq(F_41(x, k_0), -F_42(x, 1) + (k_0*F_42(x, k_0) - F_42(x, 1))/(k_0 - 1))
Eq(F_42(x, k_0), F_15(x) + F_43(x, k_0) + F_45(x, k_0) + F_46(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_18(x)*F_42(x, k_0))
Eq(F_45(x, k_0), F_18(x)*F_38(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_51(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_52(x, k_0))
Eq(F_48(x, k_0), F_1(x) + F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_48(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), k_0*x)
Eq(F_52(x, k_0), F_27(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_15(x) + F_54(x, k_0) + F_56(x, k_0))
Eq(F_54(x, k_0), F_18(x)*F_55(x, k_0))
Eq(F_55(x, k_0), F_49(x, k_0) + F_53(x, k_0))
Eq(F_56(x, k_0), F_51(x, k_0)*F_52(x, k_0))
Eq(F_57(x, k_0), F_18(x)*F_58(x, k_0))
Eq(F_58(x, k_0), -F_38(x, 1) + (k_0*F_38(x, k_0) - F_38(x, 1))/(k_0 - 1))
Eq(F_59(x, k_0), F_18(x)*F_60(x, k_0))
Eq(F_60(x, k_0), F_15(x) + F_61(x, k_0) + F_62(x, k_0) + F_64(x, k_0) + F_66(x, k_0))
Eq(F_61(x, k_0), F_18(x)*F_60(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_18(x)*F_38(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_18(x)*F_42(x, k_0))
Eq(F_66(x, k_0), F_51(x, k_0)*F_67(x, k_0))
Eq(F_67(x, k_0), F_60(x, k_0) + F_68(x))
Eq(F_68(x), F_69(x)/F_18(x))
Eq(F_69(x), -F_1(x) + F_4(x) - F_70(x))
Eq(F_70(x), F_18(x)*F_71(x))
Eq(F_71(x), F_1(x) + F_72(x) + F_73(x) + F_74(x))
Eq(F_72(x), F_18(x)*F_36(x))
Eq(F_73(x), F_18(x)*F_8(x))
Eq(F_74(x), F_18(x)*F_71(x))
Eq(F_75(x, k_0), F_51(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_47(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_52(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x) + F_82(x, k_0))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_27(x) + F_79(x))
Eq(F_82(x, k_0), 2*F_15(x) + F_83(x, k_0) + F_85(x, k_0))
Eq(F_83(x, k_0), F_18(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_53(x, k_0) + F_82(x, k_0))
Eq(F_85(x, k_0), F_51(x, k_0)*F_78(x, k_0))
Eq(F_86(x), F_18(x)*F_87(x))
Eq(F_87(x), F_88(x, 1))
Eq(F_88(x, k_0), F_1(x) + F_100(x, k_0) + F_89(x, k_0) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_89(x, k_0), F_18(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_18(x)*F_92(x, k_0))
Eq(F_92(x, k_0), (k_0*F_88(x, k_0) - F_88(x, 1))/(k_0 - 1))
Eq(F_94(x, k_0), F_1(x) + F_100(x, k_0) + F_93(x, k_0) + F_98(x, k_0))
Eq(F_94(x, k_0), F_1(x) + F_95(x, k_0) + F_96(x, k_0) + F_97(x, k_0))
Eq(F_95(x, k_0), F_18(x)*F_88(x, k_0))
Eq(F_96(x, k_0), F_12(x, k_0)*F_18(x))
Eq(F_97(x, k_0), F_51(x, k_0)*F_94(x, k_0))
Eq(F_98(x, k_0), F_18(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_94(x, k_0) - F_94(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_51(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_111(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_106(x, k_0))
Eq(F_103(x, k_0), F_1(x) + F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_103(x, k_0)*F_51(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_24(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_110(x, k_0) + F_15(x))
Eq(F_108(x, k_0), F_109(x, k_0)*F_18(x))
Eq(F_109(x, k_0), F_104(x, k_0) + F_107(x, k_0))
Eq(F_110(x, k_0), F_106(x, k_0)*F_51(x, k_0))
Eq(F_111(x, k_0), F_106(x, k_0) + F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x) + F_116(x, k_0))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_18(x))
Eq(F_115(x), F_113(x) + F_24(x))
Eq(F_116(x, k_0), F_117(x, k_0) + F_119(x, k_0) + 2*F_15(x))
Eq(F_117(x, k_0), F_118(x, k_0)*F_18(x))
Eq(F_118(x, k_0), F_107(x, k_0) + F_116(x, k_0))
Eq(F_119(x, k_0), F_112(x, k_0)*F_51(x, k_0))
Eq(F_120(x), F_121(x)*F_18(x))
Eq(F_121(x), F_122(x, 1))
Eq(F_122(x, k_0), F_1(x) + F_123(x, k_0) + F_139(x, k_0) + F_165(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0)*F_51(x, k_0))
Eq(F_124(x, k_0), F_125(x) + F_127(x, k_0))
Eq(F_125(x), F_126(x) + F_29(x))
Eq(F_126(x), F_27(x) + F_79(x))
Eq(F_127(x, k_0), F_128(x, k_0) + F_133(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_49(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0) + F_132(x, k_0) + F_15(x))
Eq(F_130(x, k_0), F_131(x, k_0)*F_51(x, k_0))
Eq(F_131(x, k_0), F_129(x, k_0) + F_27(x))
Eq(F_132(x, k_0), F_128(x, k_0)*F_18(x))
Eq(F_133(x, k_0), F_129(x, k_0) + F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0) + F_137(x, k_0) + 2*F_15(x))
Eq(F_135(x, k_0), F_136(x, k_0)*F_51(x, k_0))
Eq(F_136(x, k_0), F_134(x, k_0) + F_79(x))
Eq(F_137(x, k_0), F_138(x, k_0)*F_18(x))
Eq(F_138(x, k_0), F_129(x, k_0) + F_134(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_18(x))
Eq(F_140(x, k_0), F_141(x) + F_145(x, k_0))
Eq(F_141(x), F_1(x) + F_142(x) + F_143(x) + F_144(x))
Eq(F_142(x), F_18(x)*F_87(x))
Eq(F_143(x), F_11(x)*F_18(x))
Eq(F_144(x), F_141(x)*F_18(x))
Eq(F_145(x, k_0), F_146(x, k_0) + F_147(x, k_0) + F_15(x) + F_162(x, k_0) + F_164(x, k_0))
Eq(F_146(x, k_0), F_140(x, k_0)*F_51(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_18(x))
Eq(F_149(x, k_0), F_15(x) + F_150(x, k_0) + F_152(x, k_0) + F_160(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_51(x, k_0))
Eq(F_151(x, k_0), F_128(x, k_0) + F_29(x))
Eq(F_152(x, k_0), F_153(x, k_0)*F_18(x))
Eq(F_153(x, k_0), F_123(x, k_0) + F_15(x) + F_154(x, k_0) + F_155(x, k_0) + F_157(x, k_0))
Eq(F_154(x, k_0), F_145(x, k_0)*F_18(x))
Eq(F_155(x, k_0), F_156(x, k_0)*F_18(x))
Eq(F_156(x, k_0), -F_153(x, 1) + (-k_0*F_153(x, k_0) + F_153(x, 1))/(1 - k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_18(x))
Eq(F_159(x, k_0), -F_149(x, 1) + (-k_0*F_149(x, k_0) + F_149(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_149(x, k_0)*F_18(x))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_153(x, k_0)*F_18(x))
Eq(F_164(x, k_0), F_145(x, k_0)*F_18(x))
Eq(F_165(x, k_0), F_166(x, k_0)*F_18(x))
Eq(F_166(x, k_0), (-k_0*F_122(x, k_0) + F_122(x, 1))/(1 - k_0))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_42(x, 1))
Eq(F_169(x), F_18(x)*F_9(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}], "iterative": false, "name": "point_and_row_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, 2, 5, 4, 0, 3], "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, 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