01342_02341_03241_12340_13240
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3511, 21050, 130686, 833434, 5429428, 35984323, 241893577, 1645390651, 11304461046, 78330644003, 546765853000, 3840953605467, 27132970231745, 192613145258863, 1373283135089943, 9829057380443204, 70593268841311640, 508582056166148008, 3674279856437223990, 26612221342498035560, 193190759121684091487, 1405396015867930599308, 10243289326293835540213, 74789153371707076057173, 546932855714965348423437, 4005622524326709985139682, 29376279343643787960228225, 215709611496838573623646148, 1585797475626077555358736130, 11670646559739710107874879853, 85976140819932571943432373261, 633967074783711894841028254606, 4678792228331412976022009478509, 34558436231169629949393984143723, 255449332136685986529016256023898, 1889578067707951798131145840415489, 13986692087791649098260983487683126, 103594707283379716632308061919016830, 767743528049606312208203611912735872, 5692928458552892389768109770487283521, 42235954759457658654980296671497948693, 313503959199054221735177830864139361710, 2328122907676410785055698363834216740445, 17296563740244637980676606707195647100231, 128556632156559838468526147639185500059953, 955873137812752892494054379790143975846163, 7109976829577493535767289688060903677407742, 52904170929300454859890187514601114806161098, 393783605672889870443394363118597564835600994, 2932000489998704623197343200151064316715298602, 21837468859616429872989326768847713175051824905, 162691927826726032401279064919446472155310210208, 1212408993088686170814010441521895703660103465584, 9037453735835426267111934999903010095342303072933, 67383182069043503207340751864889285329474709423699, 502528210923863867762450531902800146461318711373341, 3748592083235510011305933771110699235430898325254842, 27968572413932177543310712816512125443607609580368195, 208719305320803654859607929223265679732120577223346947, 1557905848399663393533409627888178499896356180688222275, 11630605884952132949895361081181738776715716201675723567, 86844535897582408972022242235316933011569202132309081296, 648572242432628137975710020033035942994311798601854781207, 4844475538858478157607091461785364768987474689755361097788, 36191346690208735405751176055341198845244279127326242721357, 270414178085968491535382300827071533628131372520385359378680, 2020776249444027107504518448611115227539153187402862714459586, 15103183848662626388123452976097155723362453884812899307411291, 112895824729728457948416790281481449693270923923588228905428530, 844003107095837437585576837394520359482548760998775504949382920, 6310515221344984674570421901322126692397681758448407448554315021, 47188711741848150891544529048454448079654804287586811414186593890, 352908382586210001447109527631951651485728270223462175454958562980, 2639577956037293654384315165912691987587282666621086353214645584684, 19744851902105061125783513570989839030720790470890485991353504202645, 147712900183740516832655928288248470168425609394432396832420442770019, 1105163396647456606812325335293686928996951239221305339953475571479926, 8269448054463859978606078836379848215394360019652896036692123832906417, 61882382947445185623447635417544371036161127184389532826617741874293124, 463123252608519750616842453231574032426792331803082087458154329998436485, 3466281561150543248141461315131326913207031054794577116799446598166283106, 25945824709317006371841420008028595892692650181683299214858143292350486220, 194225510300163119898395856135948419522477890848549347217203047643659865750, 1454048930091512794969371429881802990866620519373470555174965883296922016022, 10886407580697220086296929358944999198688655241807580665824582757468930507614, 81512063210250083443868719717681845958262426748622705460750857107639638838895, 610365338785831945412098745013350476108074953293145260046810079001876230821542, 4570750530943229938137349618002548131799495363254220591654149638754018402899338, 34230551019742726251096556828854763956189280719012323528938159990232409250805765, 256370503161588231028821880389393661305780504635426176645446881109040304306745422, 1920211779678725434562569122043882879386730359426929042065570876612994294617789534, 14383224574297866965460658373569511965705534421408156126231147583555812349532023421, 107742893516008738956554597172415002281441624540737883425797593259383475827859655666, 807133670429389026723255337500100717473381527309973222368633990804016990779127828944
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24939/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[58,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[56,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,k[0]]+F[35,x,k[0],k[1]]
F[14,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]
F[15,x,k[0]] = F[10,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[17,x,k[0]] = F[10,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]+F[21,x,k[0]]+F[25,x,k[0]]
F[19,x,k[0]] = F[10,x]*F[20,x,k[0]]
F[20,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[21,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = (F[13,x,k[0],k[1]]*k[0]*k[1]-F[13,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[10,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0],1]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[28,x,k[0],k[1]]*k[0]-F[28,x,1,k[1]])
F[31,x,k[0],k[1]] = F[24,x,k[0]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[10,x]*F[27,x,k[0],k[1]]
F[35,x,k[0],k[1]] = 2*F[36,x]+F[37,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[52,x,k[0],k[1]]
F[36,x] = 0
F[37,x,k[0],k[1]] = F[10,x]*F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[39,x,1,k[0],k[1]]
F[39,x,k[0],k[1],k[2]] = 2*F[36,x]+F[40,x,k[0],k[1],k[2]]+F[42,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[40,x,k[0],k[1],k[2]] = F[10,x]*F[41,x,k[0],k[1],k[2]]
F[41,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[39,x,k[0],k[1],k[2]]*k[0]-F[39,x,1,k[1],k[2]])
F[42,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[43,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = -k[2]*(F[44,x,k[0],k[1]]-F[44,x,k[0],k[1]*k[2]])/(k[2]-1)
F[44,x,k[0],k[1]] = k[1]*(F[35,x,k[0],1]-F[35,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[45,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[46,x,k[0],k[1],k[2]]
F[46,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1],k[2]]+F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[48,x,k[0],k[1],k[2]] = F[49,x,k[0],k[1],k[2]]
F[49,x,k[0],k[1],k[2]] = F[10,x]*F[50,x,k[0],k[1],k[2]]
F[50,x,k[0],k[1],k[2]] = k[1]*k[2]*(F[39,x,k[0],k[1],k[2]]-F[39,x,k[0],k[1],1/k[1]])/(k[1]*k[2]-1)
F[51,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[24,x,k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[10,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1],1]
F[55,x,k[0],k[1],k[2]] = k[0]*k[1]*(F[35,x,k[0],k[1]]-F[35,x,k[0],k[2]/k[0]])/(k[0]*k[1]-k[2])
F[56,x,k[0]] = F[10,x]*F[57,x,k[0]]
F[57,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[58,x] = F[10,x]*F[59,x]
F[59,x] = F[14,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{58}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{56}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)+F_{17}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = -\frac{-F_{18}\! \left(x , y_{0}\right) y_{0}+F_{18}\! \left(x , 1\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}, 1\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{13}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}, 1\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, 1\right) y_{0}-F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = 2 F_{36}\! \left(x \right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , 1, y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 2 F_{36}\! \left(x \right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{39}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} \left(F_{44}\! \left(x , y_{0}, y_{1}\right)-F_{44}\! \left(x , y_{0}, y_{1} y_{2}\right)\right)}{y_{2}-1}
F_{44}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{35}\! \left(x , y_{0}, 1\right)-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}\right)-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} y_{2} \left(F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{39}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}\right)\right)}{y_{1} y_{2}-1}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}, 1\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} \left(F_{35}\! \left(x , y_{0}, y_{1}\right)-F_{35}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)\right)}{y_{0} y_{1}-y_{2}}
F_{56}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{57}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_58(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_56(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0) + F_35(x, k_0, k_1))
Eq(F_14(x, k_0), F_1(x) + F_11(x, k_0) + F_15(x, k_0) + F_17(x, k_0))
Eq(F_15(x, k_0), F_10(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_10(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0) + F_21(x, k_0) + F_25(x, k_0))
Eq(F_19(x, k_0), F_10(x)*F_20(x, k_0))
Eq(F_20(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), (-k_0*k_1*F_13(x, k_0, k_1) + F_13(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_10(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0, 1))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_28(x, k_0, k_1) - F_28(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_24(x, k_0)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_10(x)*F_27(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), 2*F_36(x) + F_37(x, k_0, k_1) + F_51(x, k_0, k_1) + F_52(x, k_0, k_1))
Eq(F_36(x), 0)
Eq(F_37(x, k_0, k_1), F_10(x)*F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_39(x, 1, k_0, k_1))
Eq(F_39(x, k_0, k_1, k_2), 2*F_36(x) + F_40(x, k_0, k_1, k_2) + F_42(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_40(x, k_0, k_1, k_2), F_10(x)*F_41(x, k_0, k_1, k_2))
Eq(F_41(x, k_0, k_1, k_2), (k_0*F_39(x, k_0, k_1, k_2) - F_39(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_42(x, k_0, k_1, k_2), F_24(x, k_0)*F_43(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), -F_44(x, k_0, k_1) + (k_1*k_2*F_44(x, k_0, k_1*k_2) - k_1*F_44(x, k_0, k_1))/(k_1*k_2 - k_1))
Eq(F_44(x, k_0, k_1), -F_35(x, k_0, 1) + (-k_0*F_35(x, k_0, 1) + k_1*F_35(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1, k_2), F_24(x, k_2)*F_46(x, k_0, k_1, k_2))
Eq(F_46(x, k_0, k_1, k_2), F_39(x, k_0, k_1, k_2) + F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_48(x, k_0, k_1, k_2), F_49(x, k_0, k_1, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_10(x)*F_50(x, k_0, k_1, k_2))
Eq(F_50(x, k_0, k_1, k_2), -F_39(x, k_0, k_1, 1/k_1) + (-k_1*k_2*F_39(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, 1/k_1))/(-k_1*k_2 + 1))
Eq(F_51(x, k_0, k_1), F_13(x, k_0, k_1)*F_24(x, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_10(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1, 1))
Eq(F_55(x, k_0, k_1, k_2), -F_35(x, k_0, k_2/k_0) + (-k_0*k_1*F_35(x, k_0, k_1) + k_2*F_35(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_56(x, k_0), F_10(x)*F_57(x, k_0))
Eq(F_57(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_58(x), F_10(x)*F_59(x))
Eq(F_59(x), F_14(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 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"pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [6, 1], [6, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [6, 1], [6, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [6, 1], [6, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [6, 1], [6, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [1, 1], [6, 1], [6, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [6, 1], [6, 1]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[5, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0, 1], "pos": [[2, 1], [4, 1]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25178/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[58,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[56,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,k[0]]+F[35,x,k[0],k[1]]
F[14,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]
F[15,x,k[0]] = F[10,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[17,x,k[0]] = F[10,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]+F[21,x,k[0]]+F[25,x,k[0]]
F[19,x,k[0]] = F[10,x]*F[20,x,k[0]]
F[20,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[21,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = (F[13,x,k[0],k[1]]*k[0]*k[1]-F[13,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[10,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0],1]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[28,x,k[0],k[1]]*k[0]-F[28,x,1,k[1]])
F[31,x,k[0],k[1]] = F[24,x,k[0]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[10,x]*F[27,x,k[0],k[1]]
F[35,x,k[0],k[1]] = 2*F[36,x]+F[37,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[52,x,k[0],k[1]]
F[36,x] = 0
F[37,x,k[0],k[1]] = F[10,x]*F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[39,x,1,k[0],k[1]]
F[39,x,k[0],k[1],k[2]] = 2*F[36,x]+F[40,x,k[0],k[1],k[2]]+F[42,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[40,x,k[0],k[1],k[2]] = F[10,x]*F[41,x,k[0],k[1],k[2]]
F[41,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[39,x,k[0],k[1],k[2]]*k[0]-F[39,x,1,k[1],k[2]])
F[42,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[43,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = -k[2]*(F[44,x,k[0],k[1]]-F[44,x,k[0],k[1]*k[2]])/(k[2]-1)
F[44,x,k[0],k[1]] = k[1]*(F[35,x,k[0],1]-F[35,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[45,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[46,x,k[0],k[1],k[2]]
F[46,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1],k[2]]+F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[48,x,k[0],k[1],k[2]] = F[49,x,k[0],k[1],k[2]]
F[49,x,k[0],k[1],k[2]] = F[10,x]*F[50,x,k[0],k[1],k[2]]
F[50,x,k[0],k[1],k[2]] = k[1]*k[2]*(F[39,x,k[0],k[1],k[2]]-F[39,x,k[0],k[1],1/k[1]])/(k[1]*k[2]-1)
F[51,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[24,x,k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[10,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1],1]
F[55,x,k[0],k[1],k[2]] = k[0]*k[1]*(F[35,x,k[0],k[1]]-F[35,x,k[0],k[2]/k[0]])/(k[0]*k[1]-k[2])
F[56,x,k[0]] = F[10,x]*F[57,x,k[0]]
F[57,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[58,x] = F[10,x]*F[59,x]
F[59,x] = F[14,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{58}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{56}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)+F_{17}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = -\frac{-F_{18}\! \left(x , y_{0}\right) y_{0}+F_{18}\! \left(x , 1\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}, 1\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{13}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}, 1\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, 1\right) y_{0}-F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = 2 F_{36}\! \left(x \right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , 1, y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 2 F_{36}\! \left(x \right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{39}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} \left(F_{44}\! \left(x , y_{0}, y_{1}\right)-F_{44}\! \left(x , y_{0}, y_{1} y_{2}\right)\right)}{y_{2}-1}
F_{44}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{35}\! \left(x , y_{0}, 1\right)-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}\right)-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} y_{2} \left(F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{39}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}\right)\right)}{y_{1} y_{2}-1}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}, 1\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} \left(F_{35}\! \left(x , y_{0}, y_{1}\right)-F_{35}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)\right)}{y_{0} y_{1}-y_{2}}
F_{56}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{57}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_58(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_56(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0) + F_35(x, k_0, k_1))
Eq(F_14(x, k_0), F_1(x) + F_11(x, k_0) + F_15(x, k_0) + F_17(x, k_0))
Eq(F_15(x, k_0), F_10(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_10(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0) + F_21(x, k_0) + F_25(x, k_0))
Eq(F_19(x, k_0), F_10(x)*F_20(x, k_0))
Eq(F_20(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), (-k_0*k_1*F_13(x, k_0, k_1) + F_13(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_10(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0, 1))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_28(x, k_0, k_1) - F_28(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_24(x, k_0)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_10(x)*F_27(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), 2*F_36(x) + F_37(x, k_0, k_1) + F_51(x, k_0, k_1) + F_52(x, k_0, k_1))
Eq(F_36(x), 0)
Eq(F_37(x, k_0, k_1), F_10(x)*F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_39(x, 1, k_0, k_1))
Eq(F_39(x, k_0, k_1, k_2), 2*F_36(x) + F_40(x, k_0, k_1, k_2) + F_42(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_40(x, k_0, k_1, k_2), F_10(x)*F_41(x, k_0, k_1, k_2))
Eq(F_41(x, k_0, k_1, k_2), (k_0*F_39(x, k_0, k_1, k_2) - F_39(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_42(x, k_0, k_1, k_2), F_24(x, k_0)*F_43(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), -F_44(x, k_0, k_1) + (k_1*k_2*F_44(x, k_0, k_1*k_2) - k_1*F_44(x, k_0, k_1))/(k_1*k_2 - k_1))
Eq(F_44(x, k_0, k_1), -F_35(x, k_0, 1) + (-k_0*F_35(x, k_0, 1) + k_1*F_35(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1, k_2), F_24(x, k_2)*F_46(x, k_0, k_1, k_2))
Eq(F_46(x, k_0, k_1, k_2), F_39(x, k_0, k_1, k_2) + F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_48(x, k_0, k_1, k_2), F_49(x, k_0, k_1, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_10(x)*F_50(x, k_0, k_1, k_2))
Eq(F_50(x, k_0, k_1, k_2), -F_39(x, k_0, k_1, 1/k_1) + (-k_1*k_2*F_39(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, 1/k_1))/(-k_1*k_2 + 1))
Eq(F_51(x, k_0, k_1), F_13(x, k_0, k_1)*F_24(x, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_10(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1, 1))
Eq(F_55(x, k_0, k_1, k_2), -F_35(x, k_0, k_2/k_0) + (-k_0*k_1*F_35(x, k_0, k_1) + k_2*F_35(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_56(x, k_0), F_10(x)*F_57(x, k_0))
Eq(F_57(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_58(x), F_10(x)*F_59(x))
Eq(F_59(x), F_14(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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[0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25448/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[58,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[56,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,k[0]]+F[35,x,k[0],k[1]]
F[14,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]
F[15,x,k[0]] = F[10,x]*F[16,x,k[0]]
F[16,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[17,x,k[0]] = F[10,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]+F[21,x,k[0]]+F[25,x,k[0]]
F[19,x,k[0]] = F[10,x]*F[20,x,k[0]]
F[20,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[21,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = (F[13,x,k[0],k[1]]*k[0]*k[1]-F[13,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[10,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0],1]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[28,x,k[0],k[1]]*k[0]-F[28,x,1,k[1]])
F[31,x,k[0],k[1]] = F[24,x,k[0]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[10,x]*F[27,x,k[0],k[1]]
F[35,x,k[0],k[1]] = 2*F[36,x]+F[37,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[52,x,k[0],k[1]]
F[36,x] = 0
F[37,x,k[0],k[1]] = F[10,x]*F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[39,x,1,k[0],k[1]]
F[39,x,k[0],k[1],k[2]] = 2*F[36,x]+F[40,x,k[0],k[1],k[2]]+F[42,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[40,x,k[0],k[1],k[2]] = F[10,x]*F[41,x,k[0],k[1],k[2]]
F[41,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[39,x,k[0],k[1],k[2]]*k[0]-F[39,x,1,k[1],k[2]])
F[42,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[43,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = -k[2]*(F[44,x,k[0],k[1]]-F[44,x,k[0],k[1]*k[2]])/(k[2]-1)
F[44,x,k[0],k[1]] = k[1]*(F[35,x,k[0],1]-F[35,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[45,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[46,x,k[0],k[1],k[2]]
F[46,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1],k[2]]+F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[48,x,k[0],k[1],k[2]] = F[49,x,k[0],k[1],k[2]]
F[49,x,k[0],k[1],k[2]] = F[10,x]*F[50,x,k[0],k[1],k[2]]
F[50,x,k[0],k[1],k[2]] = k[1]*k[2]*(F[39,x,k[0],k[1],k[2]]-F[39,x,k[0],k[1],1/k[1]])/(k[1]*k[2]-1)
F[51,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[24,x,k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[10,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[0],k[1],1]
F[55,x,k[0],k[1],k[2]] = k[0]*k[1]*(F[35,x,k[0],k[1]]-F[35,x,k[0],k[2]/k[0]])/(k[0]*k[1]-k[2])
F[56,x,k[0]] = F[10,x]*F[57,x,k[0]]
F[57,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[58,x] = F[10,x]*F[59,x]
F[59,x] = F[14,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{58}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{56}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)+F_{17}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = -\frac{-F_{18}\! \left(x , y_{0}\right) y_{0}+F_{18}\! \left(x , 1\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}, 1\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{13}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}, 1\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{13}\! \left(x , y_{0}, 1\right) y_{0}-F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = 2 F_{36}\! \left(x \right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , 1, y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = 2 F_{36}\! \left(x \right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{39}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} \left(F_{44}\! \left(x , y_{0}, y_{1}\right)-F_{44}\! \left(x , y_{0}, y_{1} y_{2}\right)\right)}{y_{2}-1}
F_{44}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} \left(F_{35}\! \left(x , y_{0}, 1\right)-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}\right)-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} y_{2} \left(F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{39}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}\right)\right)}{y_{1} y_{2}-1}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{55}\! \left(x , y_{0}, y_{1}, 1\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} \left(F_{35}\! \left(x , y_{0}, y_{1}\right)-F_{35}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)\right)}{y_{0} y_{1}-y_{2}}
F_{56}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{57}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_58(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_56(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0) + F_35(x, k_0, k_1))
Eq(F_14(x, k_0), F_1(x) + F_11(x, k_0) + F_15(x, k_0) + F_17(x, k_0))
Eq(F_15(x, k_0), F_10(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_10(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0) + F_21(x, k_0) + F_25(x, k_0))
Eq(F_19(x, k_0), F_10(x)*F_20(x, k_0))
Eq(F_20(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), (-k_0*k_1*F_13(x, k_0, k_1) + F_13(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_10(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0, 1))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1) + F_33(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_28(x, k_0, k_1) - F_28(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_24(x, k_0)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_10(x)*F_27(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), 2*F_36(x) + F_37(x, k_0, k_1) + F_51(x, k_0, k_1) + F_52(x, k_0, k_1))
Eq(F_36(x), 0)
Eq(F_37(x, k_0, k_1), F_10(x)*F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_39(x, 1, k_0, k_1))
Eq(F_39(x, k_0, k_1, k_2), 2*F_36(x) + F_40(x, k_0, k_1, k_2) + F_42(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_40(x, k_0, k_1, k_2), F_10(x)*F_41(x, k_0, k_1, k_2))
Eq(F_41(x, k_0, k_1, k_2), (k_0*F_39(x, k_0, k_1, k_2) - F_39(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_42(x, k_0, k_1, k_2), F_24(x, k_0)*F_43(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), -F_44(x, k_0, k_1) + (k_1*k_2*F_44(x, k_0, k_1*k_2) - k_1*F_44(x, k_0, k_1))/(k_1*k_2 - k_1))
Eq(F_44(x, k_0, k_1), -F_35(x, k_0, 1) + (-k_0*F_35(x, k_0, 1) + k_1*F_35(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1, k_2), F_24(x, k_2)*F_46(x, k_0, k_1, k_2))
Eq(F_46(x, k_0, k_1, k_2), F_39(x, k_0, k_1, k_2) + F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_48(x, k_0, k_1, k_2), F_49(x, k_0, k_1, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_10(x)*F_50(x, k_0, k_1, k_2))
Eq(F_50(x, k_0, k_1, k_2), -F_39(x, k_0, k_1, 1/k_1) + (-k_1*k_2*F_39(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, 1/k_1))/(-k_1*k_2 + 1))
Eq(F_51(x, k_0, k_1), F_13(x, k_0, k_1)*F_24(x, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_10(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_0, k_1, 1))
Eq(F_55(x, k_0, k_1, k_2), -F_35(x, k_0, k_2/k_0) + (-k_0*k_1*F_35(x, k_0, k_1) + k_2*F_35(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_56(x, k_0), F_10(x)*F_57(x, k_0))
Eq(F_57(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_58(x), F_10(x)*F_59(x))
Eq(F_59(x), F_14(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 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]]}]], "assumptions": []}], "strategy": {"class_module": 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