01243_01342_01432_02143
Counting sequence:
1, 1, 2, 6, 24, 116, 635, 3791, 24134, 161486, 1124514, 8091104, 59831778, 452835816, 3496384939, 27468313049, 219105816281, 1771417945615, 14494228174477, 119877376341569, 1001125148352731, 8434399508076265, 71629735527297054, 612785639084923332, 5277633480073484454, 45735721918466627904, 398615284976671440657, 3492635215085658339779, 30753272741729250489375, 272033760834661248194707, 2416665420434595820876059, 21555293977063370388363273, 192986755808221715380209140, 1733960885584804606156318190, 15631475329792938218144925068, 141360394048710167104584031624, 1282175854541184578719863605416, 11662468822747406891062416515556, 106363551326929505157173881362357, 972513898585195639083115853807085, 8913433807487484559962716299828760, 81882300996102102868261310748412440, 753848194274160613932313996299748177, 6954773074512060924282813139420541059, 64290458278818574563737802135203515541, 595438000514437233214937327185020152391, 5524811635365693091461410433849119008719, 51351837507972883715746873826960184601591, 478102299522507688724204858445880594080646, 4458437170954805011732312307986030120953418, 41640298346349660271853677163748041190715519, 389482883474436620502228297523185578108252323, 3648226297129451358009602639829327402412221705, 34219280484018050952538067274842085949325896987, 321391084973242830620283788698440693583496449325, 3022386117983171568877121691311742783067526835919, 28457690543011204085189987992989798014494364754056, 268265229541100087534497230831059073386888487261222, 2531783360022470867280193521189921757917867836645182, 23920452898984382179380736180966701729872987069239154, 226243998834638065977061992267275942057106950268378057, 2142073843004372784334384248824922452922059788661942391, 20301452885779426313220284332038972658450962727712445360, 192593402162886767360713887820978991603483021468085931304, 1828791625990200172346128096767297766044894831030189335392, 17381334057678929524390062398021719108675902452796268139846, 165343125469433059089378676547122392837854930771769529818924, 1574207417030563019628154286873803074459950906963538962914934, 15000290172440365450764636017001405046537680250269047064654293, 143050325410201208047133518099750983859051797654820059884814455, 1365273170253588581962236244551982342712518662469592369266519553, 13040139213422190019408311431937371203562082245269581692460961247, 124642947961728496277736051533457602845977976300593207749976671608, 1192249716242375878787493036886515740851754969678082156379111869832, 11412278143121270257793450841752429648581168186032033447744464693740, 109313797122137588720965604985931800939561183148452172011986632582712, 1047773354671832499224608831790769122219540273760996168537612140100985, 10049442814110920639868504877572635660740253800315949555614572853631297, 96447659190822038131043375344701129695569968059248038890464203122420750, 926210197688701283533042807623953899190531578316220033398040079279597692, 8899977810704171060548214674787787835246274309181897114314088950178777772, 85570362963770384573520539498914815740540914305629075212465954151909382380, 823202590026164599138139824089304512764024258140252542316053692680873813817, 7923791275203734556914303057344643875454608305442065301220192023955770673813, 76312647963489213660204909150554159090910867457157986474375902785624939972556, 735345893294120083637412570615274639430939293322588682861746914232353132727984, 7089459364804814358674921718734295301830016782036277496683305000210862411691840, 68384187631047485932130701540891236290367180793692530361835929533230584777558732, 659955116447210797024752061751624102941741309589668743457547802725191653644008500, 6372126875858159274078420195735921073306127901097419042600507783754628933008433150, 61554678547117177528593269241600960849159773780186353574318089624269316850252292996, 594894351540101421767569855729515998211147533233501220227369516817522502876282605438, 5751966918344871609578795249713618714895573709071203120888832040850059701211123439864, 55639913031830760946204251201407108100034449354555162057387381352224842420712698379160, 538450693159159536265824192624827547551356765878272632459877948002773136485970056903952, 5213038209111550203264540472877426922603284686304090065932268590885278905784400936513570, 50491410586776697316776462739124474900603676497087666624197532390506509312753719739735672, 489240052145933326201484463909620736718727274397981333470945003522032525620210895379654910, 4742428563214426771323102871289122187397555436403017759042110883835138554983874914975060418, 45988620666456772025905526507419375094823295049028443515277949070805019267942457922307594688, 446136099227774002359615280319988515298053530097206024657186214483777344775504326757904691213
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24575/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[35,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[8,x]
F[13,x,k[0],k[1]] = F[14,x,k[1]]+F[52,x,k[0],k[1]]
F[15,x,k[0]] = F[14,x,k[0]]*F[8,x]
F[16,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[45,x,k[0]]
F[16,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[40,x,k[0]]+F[44,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[37,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[8,x]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[20,x,k[1]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[36,x,k[0],k[1]]
F[25,x] = 0
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[8,x]
F[27,x,k[0],k[1]] = -k[0]*(F[24,x,1,k[1]]-F[24,x,k[0],k[1]])/(-1+k[0])
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[35,x,k[0]]
F[29,x,k[0],k[1]] = F[23,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = k[0]*(F[32,x,k[0],1]-F[32,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[32,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[34,x,k[0],k[1]] = F[33,x,k[0],k[1]]+F[5,x,k[0]]
F[11,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[35,x,k[1]]
F[37,x,k[0]] = F[38,x,k[0],1]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[0]*k[1]]
F[39,x,k[0],k[1]] = F[20,x,k[1]]*F[35,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[8,x]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[43,x,k[0],k[1]] = F[35,x,k[0]]*F[42,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[24,x,k[0],k[1]]
F[44,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[45,x,k[0]] = F[35,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0],1]
F[47,x,k[0],k[1]] = F[48,x,k[0],k[0]*k[1]]
F[48,x,k[0],k[1]] = F[20,x,k[1]]+F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = k[0]*F[50,x,k[1]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[19,x,k[0]]*F[8,x]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*k[1]*(F[54,x,k[0],k[1]]-F[54,x,1/k[1],k[1]])/(k[0]*k[1]-1)
F[11,x,k[0],k[1]] = F[16,x,k[1]]+F[54,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[56,x,k[0],k[1]] = F[35,x,k[1]]*F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[59,x,k[0],k[1],1]
F[59,x,k[0],k[1],k[2]] = F[23,x,k[0]*k[1],k[1]*k[2]]
F[60,x,k[0],k[1]] = k[1]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]*F[8,x]
F[64,x,k[0],k[1]] = F[35,x,k[1]]*F[63,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[65,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[33,x,k[0]*k[1],k[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_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{16}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , 1, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{24}\! \left(x , 1, y_{1}\right)-F_{24}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} \left(F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{5}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = y_{0} x
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}, 1\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}, 1\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{50}\! \left(x , y_{1}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{8}\! \left(x \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) = \frac{y_{0} y_{1} \left(F_{54}\! \left(x , y_{0}, y_{1}\right)-F_{54}\! \left(x , \frac{1}{y_{1}}, y_{1}\right)\right)}{y_{0} y_{1}-1}
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}\right)+F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{59}\! \left(x , y_{0}, y_{1}, 1\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = y_{1} F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{65}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0} y_{1}, y_{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_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_35(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_8(x))
Eq(F_13(x, k_0, k_1), F_14(x, k_1) + F_52(x, k_0, k_1))
Eq(F_15(x, k_0), F_14(x, k_0)*F_8(x))
Eq(F_16(x, k_0), F_1(x) + F_15(x, k_0) + F_45(x, k_0))
Eq(F_16(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_40(x, k_0) + F_44(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_37(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_8(x))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_20(x, k_1) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_36(x, k_0, k_1))
Eq(F_25(x), 0)
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_8(x))
Eq(F_27(x, k_0, k_1), -F_24(x, 1, k_1) + (k_0*F_24(x, k_0, k_1) - F_24(x, 1, k_1))/(k_0 - 1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_35(x, k_0))
Eq(F_29(x, k_0, k_1), F_23(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), -F_32(x, k_0, k_1/k_0) + (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_34(x, k_0, k_1), F_33(x, k_0, k_1) + F_5(x, k_0))
Eq(F_11(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0, k_1), F_24(x, k_0, k_1)*F_35(x, k_1))
Eq(F_37(x, k_0), F_38(x, k_0, 1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_0*k_1))
Eq(F_39(x, k_0, k_1), F_20(x, k_1)*F_35(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_8(x))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_43(x, k_0, k_1), F_35(x, k_0)*F_42(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_24(x, k_0, k_1))
Eq(F_44(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_45(x, k_0), F_35(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0, 1))
Eq(F_47(x, k_0, k_1), F_48(x, k_0, k_0*k_1))
Eq(F_48(x, k_0, k_1), F_20(x, k_1) + F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), k_0*F_50(x, k_1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_19(x, k_0)*F_8(x))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), -F_54(x, 1/k_1, k_1) + (k_0*k_1*F_54(x, k_0, k_1) - F_54(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_11(x, k_0, k_1), F_16(x, k_1) + F_54(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_56(x, k_0, k_1), F_35(x, k_1)*F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_59(x, k_0, k_1, 1))
Eq(F_59(x, k_0, k_1, k_2), F_23(x, k_0*k_1, k_1*k_2))
Eq(F_60(x, k_0, k_1), k_1*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1)*F_8(x))
Eq(F_64(x, k_0, k_1), F_35(x, k_1)*F_63(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_65(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_33(x, k_0*k_1, k_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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 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, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 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], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 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, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 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], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"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, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}, "children": [{"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": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24726/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[35,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[8,x]
F[13,x,k[0],k[1]] = F[14,x,k[1]]+F[52,x,k[0],k[1]]
F[15,x,k[0]] = F[14,x,k[0]]*F[8,x]
F[16,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[45,x,k[0]]
F[16,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[40,x,k[0]]+F[44,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[37,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[8,x]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[20,x,k[1]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[36,x,k[0],k[1]]
F[25,x] = 0
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[8,x]
F[27,x,k[0],k[1]] = -k[0]*(F[24,x,1,k[1]]-F[24,x,k[0],k[1]])/(-1+k[0])
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[35,x,k[0]]
F[29,x,k[0],k[1]] = F[23,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = k[0]*(F[32,x,k[0],1]-F[32,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[32,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[34,x,k[0],k[1]] = F[33,x,k[0],k[1]]+F[5,x,k[0]]
F[11,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[35,x,k[1]]
F[37,x,k[0]] = F[38,x,k[0],1]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[0]*k[1]]
F[39,x,k[0],k[1]] = F[20,x,k[1]]*F[35,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[8,x]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[43,x,k[0],k[1]] = F[35,x,k[0]]*F[42,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[24,x,k[0],k[1]]
F[44,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[45,x,k[0]] = F[35,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0],1]
F[47,x,k[0],k[1]] = F[48,x,k[0],k[0]*k[1]]
F[48,x,k[0],k[1]] = F[20,x,k[1]]+F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = k[0]*F[50,x,k[1]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[19,x,k[0]]*F[8,x]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*k[1]*(F[54,x,k[0],k[1]]-F[54,x,1/k[1],k[1]])/(k[0]*k[1]-1)
F[11,x,k[0],k[1]] = F[16,x,k[1]]+F[54,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[56,x,k[0],k[1]] = F[35,x,k[1]]*F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[59,x,k[0],k[1],1]
F[59,x,k[0],k[1],k[2]] = F[23,x,k[0]*k[1],k[1]*k[2]]
F[60,x,k[0],k[1]] = k[1]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]*F[8,x]
F[64,x,k[0],k[1]] = F[35,x,k[1]]*F[63,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[65,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[33,x,k[0]*k[1],k[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_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{16}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , 1, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{24}\! \left(x , 1, y_{1}\right)-F_{24}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} \left(F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{5}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = y_{0} x
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}, 1\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}, 1\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{50}\! \left(x , y_{1}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{8}\! \left(x \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) = \frac{y_{0} y_{1} \left(F_{54}\! \left(x , y_{0}, y_{1}\right)-F_{54}\! \left(x , \frac{1}{y_{1}}, y_{1}\right)\right)}{y_{0} y_{1}-1}
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}\right)+F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{59}\! \left(x , y_{0}, y_{1}, 1\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = y_{1} F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{65}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0} y_{1}, y_{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_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_35(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_8(x))
Eq(F_13(x, k_0, k_1), F_14(x, k_1) + F_52(x, k_0, k_1))
Eq(F_15(x, k_0), F_14(x, k_0)*F_8(x))
Eq(F_16(x, k_0), F_1(x) + F_15(x, k_0) + F_45(x, k_0))
Eq(F_16(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_40(x, k_0) + F_44(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_37(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_8(x))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_20(x, k_1) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_36(x, k_0, k_1))
Eq(F_25(x), 0)
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_8(x))
Eq(F_27(x, k_0, k_1), -F_24(x, 1, k_1) + (k_0*F_24(x, k_0, k_1) - F_24(x, 1, k_1))/(k_0 - 1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_35(x, k_0))
Eq(F_29(x, k_0, k_1), F_23(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), -F_32(x, k_0, k_1/k_0) + (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_34(x, k_0, k_1), F_33(x, k_0, k_1) + F_5(x, k_0))
Eq(F_11(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0, k_1), F_24(x, k_0, k_1)*F_35(x, k_1))
Eq(F_37(x, k_0), F_38(x, k_0, 1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_0*k_1))
Eq(F_39(x, k_0, k_1), F_20(x, k_1)*F_35(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_8(x))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_43(x, k_0, k_1), F_35(x, k_0)*F_42(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_24(x, k_0, k_1))
Eq(F_44(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_45(x, k_0), F_35(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0, 1))
Eq(F_47(x, k_0, k_1), F_48(x, k_0, k_0*k_1))
Eq(F_48(x, k_0, k_1), F_20(x, k_1) + F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), k_0*F_50(x, k_1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_19(x, k_0)*F_8(x))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), -F_54(x, 1/k_1, k_1) + (k_0*k_1*F_54(x, k_0, k_1) - F_54(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_11(x, k_0, k_1), F_16(x, k_1) + F_54(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_56(x, k_0, k_1), F_35(x, k_1)*F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_59(x, k_0, k_1, 1))
Eq(F_59(x, k_0, k_1, k_2), F_23(x, k_0*k_1, k_1*k_2))
Eq(F_60(x, k_0, k_1), k_1*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1)*F_8(x))
Eq(F_64(x, k_0, k_1), F_35(x, k_1)*F_63(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_65(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_33(x, k_0*k_1, k_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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": 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1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"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, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], 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"assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}, "children": [{"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": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"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, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25839/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[35,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[8,x]
F[13,x,k[0],k[1]] = F[14,x,k[1]]+F[52,x,k[0],k[1]]
F[15,x,k[0]] = F[14,x,k[0]]*F[8,x]
F[16,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[45,x,k[0]]
F[16,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[40,x,k[0]]+F[44,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[37,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[8,x]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[20,x,k[1]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[36,x,k[0],k[1]]
F[25,x] = 0
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[8,x]
F[27,x,k[0],k[1]] = -k[0]*(F[24,x,1,k[1]]-F[24,x,k[0],k[1]])/(-1+k[0])
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[35,x,k[0]]
F[29,x,k[0],k[1]] = F[23,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = k[0]*(F[32,x,k[0],1]-F[32,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[32,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[34,x,k[0],k[1]] = F[33,x,k[0],k[1]]+F[5,x,k[0]]
F[11,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[35,x,k[1]]
F[37,x,k[0]] = F[38,x,k[0],1]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[0]*k[1]]
F[39,x,k[0],k[1]] = F[20,x,k[1]]*F[35,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[8,x]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[43,x,k[0],k[1]] = F[35,x,k[0]]*F[42,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[24,x,k[0],k[1]]
F[44,x,k[0]] = F[19,x,k[0]]*F[35,x,k[0]]
F[45,x,k[0]] = F[35,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0],1]
F[47,x,k[0],k[1]] = F[48,x,k[0],k[0]*k[1]]
F[48,x,k[0],k[1]] = F[20,x,k[1]]+F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = k[0]*F[50,x,k[1]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[19,x,k[0]]*F[8,x]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*k[1]*(F[54,x,k[0],k[1]]-F[54,x,1/k[1],k[1]])/(k[0]*k[1]-1)
F[11,x,k[0],k[1]] = F[16,x,k[1]]+F[54,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[56,x,k[0],k[1]] = F[35,x,k[1]]*F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[59,x,k[0],k[1],1]
F[59,x,k[0],k[1],k[2]] = F[23,x,k[0]*k[1],k[1]*k[2]]
F[60,x,k[0],k[1]] = k[1]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[62,x,k[0],k[1]]
F[62,x,k[0],k[1]] = F[63,x,k[0],k[1]]*F[8,x]
F[64,x,k[0],k[1]] = F[35,x,k[1]]*F[63,x,k[0],k[1]]
F[64,x,k[0],k[1]] = F[65,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[33,x,k[0]*k[1],k[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_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{16}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , 1, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{24}\! \left(x , 1, y_{1}\right)-F_{24}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} \left(F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{5}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = y_{0} x
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}, 1\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{41}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , 1, y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}, 1\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{50}\! \left(x , y_{1}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{8}\! \left(x \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) = \frac{y_{0} y_{1} \left(F_{54}\! \left(x , y_{0}, y_{1}\right)-F_{54}\! \left(x , \frac{1}{y_{1}}, y_{1}\right)\right)}{y_{0} y_{1}-1}
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}\right)+F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{59}\! \left(x , y_{0}, y_{1}, 1\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = y_{1} F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{62}\! \left(x , y_{0}, y_{1}\right)
F_{62}\! \left(x , y_{0}, y_{1}\right) = F_{63}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right) F_{63}\! \left(x , y_{0}, y_{1}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{65}\! \left(x , y_{0}, y_{1}\right)
F_{65}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0} y_{1}, y_{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_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_35(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_55(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_8(x))
Eq(F_13(x, k_0, k_1), F_14(x, k_1) + F_52(x, k_0, k_1))
Eq(F_15(x, k_0), F_14(x, k_0)*F_8(x))
Eq(F_16(x, k_0), F_1(x) + F_15(x, k_0) + F_45(x, k_0))
Eq(F_16(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_40(x, k_0) + F_44(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_37(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_8(x))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_20(x, k_1) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_36(x, k_0, k_1))
Eq(F_25(x), 0)
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_8(x))
Eq(F_27(x, k_0, k_1), -F_24(x, 1, k_1) + (k_0*F_24(x, k_0, k_1) - F_24(x, 1, k_1))/(k_0 - 1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_35(x, k_0))
Eq(F_29(x, k_0, k_1), F_23(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), -F_32(x, k_0, k_1/k_0) + (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_34(x, k_0, k_1), F_33(x, k_0, k_1) + F_5(x, k_0))
Eq(F_11(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0, k_1), F_24(x, k_0, k_1)*F_35(x, k_1))
Eq(F_37(x, k_0), F_38(x, k_0, 1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_0*k_1))
Eq(F_39(x, k_0, k_1), F_20(x, k_1)*F_35(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_8(x))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_43(x, k_0, k_1), F_35(x, k_0)*F_42(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_24(x, k_0, k_1))
Eq(F_44(x, k_0), F_19(x, k_0)*F_35(x, k_0))
Eq(F_45(x, k_0), F_35(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0, 1))
Eq(F_47(x, k_0, k_1), F_48(x, k_0, k_0*k_1))
Eq(F_48(x, k_0, k_1), F_20(x, k_1) + F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), k_0*F_50(x, k_1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_19(x, k_0)*F_8(x))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), -F_54(x, 1/k_1, k_1) + (k_0*k_1*F_54(x, k_0, k_1) - F_54(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_11(x, k_0, k_1), F_16(x, k_1) + F_54(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_56(x, k_0, k_1), F_35(x, k_1)*F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_59(x, k_0, k_1, 1))
Eq(F_59(x, k_0, k_1, k_2), F_23(x, k_0*k_1, k_1*k_2))
Eq(F_60(x, k_0, k_1), k_1*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_62(x, k_0, k_1))
Eq(F_62(x, k_0, k_1), F_63(x, k_0, k_1)*F_8(x))
Eq(F_64(x, k_0, k_1), F_35(x, k_1)*F_63(x, k_0, k_1))
Eq(F_64(x, k_0, k_1), F_65(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_33(x, k_0*k_1, k_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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3]]}], "iterative": false}
Specification JSON:
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