01234_01243_01324_02314_10234_10243_10324_20134_20143
Counting sequence:
1, 1, 2, 6, 24, 111, 551, 2843, 15008, 80361, 434304, 2361950, 12901991, 70699255, 388312757, 2136508955, 11770758443, 64915815245, 358299844294, 1978884580252, 10934955150741, 60449651089421, 334285649087344, 1849109853643808, 10230761832809527, 56615696095844796, 313354444394632191, 1734578689869620411, 9602897120350317093, 53168354573148919743, 294401930251527072657, 1630269520854776383338, 9028282758963555248666, 50000486081037765570716, 276925873271015429205365, 1533806030068455246617612, 8495573431370649712992010, 47057448794399059267613997, 260660860501299921994590306, 1443888334685027282971610009, 7998351594320188527538629939, 44307311864724603578556676133, 245446818781543235657345855981, 1359708129156034907908372261690, 7532507107860922905774590228954, 41729036095432277940750727227261, 231175366964220962661311495571453, 1280703738371419455215230822932607, 7095112626420304066522721144243013, 39307283504312511375865848304134281, 217765741524450315769752531499519844, 1206447930480882787068255016985879566, 6683898469949178341346317790127768225, 37029948836029121246535065429209852275, 205153145786055304536862295403064068573, 1136592713990316818783614066892584983350, 6296990090586334654536567984481575348097, 34886906531734419662353859198611503565401, 193282748704358946359593320310280093033359, 1070840499431014953940358683501799711505786, 5932769041377353566799622226939104330371275, 32869338323827302906037756073520891957987054, 182106422775406075124841685122323054033597702, 1008928225479815109305836502269747855046715160, 5589795499201662310475167029343152792488520176, 30969353962534330130146039125493284968797996337, 171580881899469993342353846790466578176297427324, 950618189454541848053934787395002108474512566785, 5266762979699525224468357462682853418564534678583, 29179766909026464500756967775148802833680393787792, 161666567046863056601946452043682495273661487668041, 895692494876038254149503448185793074171003003890633, 4962470587459538185044720055328472304558406658869190, 27493955225148548733365780673609143943245626333567779, 152326946742457909739157560454804573118060079792969026, 843949522957263547912678250390990139522923294271498075, 4675805161063958062076407349038756497883675341327457293, 25905770934277812111175761554120558211513063866240689050, 143528055452864486500053974723927846377341956547296943146, 795201573981522162615491248188018218817205586074574704213, 4405729181935745331323217709449796645745414457885650969963, 24409477832351807180029475424691507056901205717726818332011, 135238172665052656014581484389731850233202816536899599175738, 749273205717861644713297883855583975505102870907230656570760, 4151272142984412642696043285740485686230866230819800184370650, 22999706503967401869154763634060217683090180225248273690616292, 127427587684471215321918139605885597101774524937200813164642313, 705999999724085409487662427949354277915737373508641723455603410, 3911524057276587350684222164800025363586629731616873347370655753, 21671420062589506810316271630758313808129270436234102523418603403, 120068418281687238942434255276160666129568330257930243969941150790, 665227598590997406736724884459075600952213352046372706038501950430, 3685630332816964971604561637270024060421341422628207583967484614646, 20419886793602487702129962687987664004709741802083691683048686114429, 113134464295289357736215239073201100112738413435804973491179486597344, 626810920606065347294323903915252874051164169341650212999850598613746, 3472787549899807928504686767221727771230621729764936058974859182213703, 19240657399819752524568470205844181734925181625542427833414598864361505, 106601084760984944478993207637410343578826922861747895672667724343390112, 590613494973461639487972760553977875267796277526804249878067311153598041, 3272239857798273107922032495325512240195741151148790205752157926699594878
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25463/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[69,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[50,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,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,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[53,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[68,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[52,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[3,x]
F[17,x,k[0],k[1]] = (F[11,x,k[0]]*k[0]-F[11,x,k[1]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1]] = F[19,x,k[0]]*F[20,x,k[0],k[1]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0],k[1]] = (F[21,x,k[0],1]*k[0]-F[21,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[0]*k[1]]
F[22,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[50,x,k[0]]+F[52,x,k[1],k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[3,x]
F[24,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[42,x,k[0],k[1]]+F[43,x,k[0],k[1]]+F[47,x,k[0]]+F[49,x,k[1],k[0]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]*F[3,x]
F[26,x,k[0],k[1]] = F[27,x,1,k[0],k[1]]
F[27,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2]]*k[0]-F[28,x,1,k[1],k[2]])
F[28,x,k[0],k[1],k[2]] = F[1,x]+F[29,x,k[0],k[1],k[2]]+F[31,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]+F[37,x,k[1],k[0]]+F[40,x,k[2],k[0],k[1]]
F[29,x,k[0],k[1],k[2]] = F[3,x]*F[30,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2]]*k[0]-F[28,x,1,k[1],k[2]])
F[31,x,k[0],k[1],k[2]] = F[3,x]*F[32,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = (F[17,x,k[0],k[2]]*k[0]-F[17,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1],k[2]] = F[19,x,k[0]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0],1,k[2]]*k[0]-F[35,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1],k[2]] = F[36,x,k[0],k[0]*k[1],k[2]]
F[36,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[37,x,k[0],k[1]] = F[19,x,k[0]]*F[38,x,k[1],k[0]]
F[38,x,k[0],k[1]] = (-F[39,x,1,k[1]]*k[1]+F[39,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[39,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[40,x,k[0],k[1],k[2]] = F[19,x,k[0]]*F[41,x,k[1],k[2]]
F[41,x,k[0],k[1]] = (F[7,x,k[0]]*k[0]-F[7,x,k[1]]*k[1])/(-k[1]+k[0])
F[42,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[43,x,k[0],k[1]] = F[3,x]*F[44,x,k[0],k[1]]
F[44,x,k[0],k[1]] = 1/(-1+k[0])*(F[45,x,k[0],k[1]]*k[0]-F[45,x,1,k[1]])
F[45,x,k[0],k[1]] = (F[46,x,k[0]]*k[0]-F[46,x,k[1]]*k[1])/(-k[1]+k[0])
F[46,x,k[0]] = F[22,x,1,k[0]]
F[47,x,k[0]] = F[19,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[38,x,1,k[0]]
F[49,x,k[0],k[1]] = F[19,x,k[0]]*F[9,x,k[1]]
F[50,x,k[0]] = F[19,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[39,x,1,k[0]]
F[52,x,k[0],k[1]] = F[19,x,k[0]]*F[7,x,k[1]]
F[53,x,k[0],k[1]] = F[3,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[55,x,k[0],k[1]] = F[19,x,k[0]]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = (F[57,x,k[0],1]*k[0]-F[57,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[57,x,k[0],k[1]] = F[1,x]+F[58,x,k[0],k[1]]+F[62,x,k[0]]+F[65,x,k[0]]+F[67,x,k[1],k[0]]
F[58,x,k[0],k[1]] = F[3,x]*F[59,x,k[0],k[1]]
F[59,x,k[0],k[1]] = F[60,x,1,k[0],k[1]]
F[60,x,k[0],k[1],k[2]] = (-F[61,x,1,k[1],k[2]]*k[1]+F[61,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[61,x,k[0],k[1],k[2]] = F[22,x,k[0]*k[1],k[1]*k[2]]
F[62,x,k[0]] = F[3,x]*F[63,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[64,x,k[0]] = F[1,x]+F[62,x,k[0]]+F[65,x,k[0]]+F[8,x,k[0]]
F[65,x,k[0]] = F[19,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[57,x,k[0],1]
F[67,x,k[0],k[1]] = F[68,x,k[0]*k[1],k[1]]
F[68,x,k[0],k[1]] = F[19,x,k[0]]*F[64,x,k[1]]
F[69,x] = F[3,x]*F[70,x]
F[70,x] = F[64,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{69}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \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_{10}\! \left(x , y_{0}\right)+F_{50}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \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 , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}\right) y_{0}-F_{11}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}\right) = y_{0} x
F_{20}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{21}\! \left(x , y_{0}, 1\right) y_{0}-F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{1}, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{47}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{1}, y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , 1, y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{37}\! \left(x , y_{1}, y_{0}\right)+F_{40}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{17}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{17}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{1}, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{39}\! \left(x , 1, y_{1}\right) y_{1}-F_{39}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{7}\! \left(x , y_{0}\right) y_{0}-F_{7}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{45}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{45}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{46}\! \left(x , y_{0}\right) y_{0}-F_{46}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{46}\! \left(x , y_{0}\right) = F_{22}\! \left(x , 1, y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{38}\! \left(x , 1, y_{0}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{1}\right)
F_{50}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{57}\! \left(x , y_{0}, 1\right) y_{0}-F_{57}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{58}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{1}, y_{0}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{59}\! \left(x , y_{0}, y_{1}\right)
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{60}\! \left(x , 1, y_{0}, y_{1}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{61}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-y_{0} F_{61}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{62}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{64}\! \left(x , y_{0}\right)+F_{64}\! \left(x , 1\right)}{-1+y_{0}}
F_{64}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{57}\! \left(x , y_{0}, 1\right)
F_{67}\! \left(x , y_{0}, y_{1}\right) = F_{68}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{68}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{1}\right)
F_{69}\! \left(x \right) = F_{3}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{64}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_69(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_50(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(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, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_53(x, k_0, k_1) + F_55(x, k_0, k_1) + F_68(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1) + F_52(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_3(x))
Eq(F_17(x, k_0, k_1), (-k_0*F_11(x, k_0) + k_1*F_11(x, k_1))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0)*F_20(x, k_0, k_1))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, 1) + k_1*F_21(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_0*k_1))
Eq(F_22(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_23(x, k_0, k_1) + F_50(x, k_0) + F_52(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_3(x))
Eq(F_24(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_42(x, k_0, k_1) + F_43(x, k_0, k_1) + F_47(x, k_0) + F_49(x, k_1, k_0))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1)*F_3(x))
Eq(F_26(x, k_0, k_1), F_27(x, 1, k_0, k_1))
Eq(F_27(x, k_0, k_1, k_2), (-k_0*F_28(x, k_0, k_1, k_2) + F_28(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_28(x, k_0, k_1, k_2), F_1(x) + F_29(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2) + F_37(x, k_1, k_0) + F_40(x, k_2, k_0, k_1))
Eq(F_29(x, k_0, k_1, k_2), F_3(x)*F_30(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1, k_2), (k_0*F_28(x, k_0, k_1, k_2) - F_28(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_31(x, k_0, k_1, k_2), F_3(x)*F_32(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), (-k_0*F_17(x, k_0, k_2) + k_1*F_17(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1, k_2), F_19(x, k_0)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*F_35(x, k_0, 1, k_2) + k_1*F_35(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1, k_2), F_36(x, k_0, k_0*k_1, k_2))
Eq(F_36(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_37(x, k_0, k_1), F_19(x, k_0)*F_38(x, k_1, k_0))
Eq(F_38(x, k_0, k_1), (-k_0*F_39(x, k_0/k_1, k_1) + k_1*F_39(x, 1, k_1))/(-k_0 + k_1))
Eq(F_39(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_40(x, k_0, k_1, k_2), F_19(x, k_0)*F_41(x, k_1, k_2))
Eq(F_41(x, k_0, k_1), (-k_0*F_7(x, k_0) + k_1*F_7(x, k_1))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_3(x)*F_44(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), (k_0*F_45(x, k_0, k_1) - F_45(x, 1, k_1))/(k_0 - 1))
Eq(F_45(x, k_0, k_1), (-k_0*F_46(x, k_0) + k_1*F_46(x, k_1))/(-k_0 + k_1))
Eq(F_46(x, k_0), F_22(x, 1, k_0))
Eq(F_47(x, k_0), F_19(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_38(x, 1, k_0))
Eq(F_49(x, k_0, k_1), F_19(x, k_0)*F_9(x, k_1))
Eq(F_50(x, k_0), F_19(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_39(x, 1, k_0))
Eq(F_52(x, k_0, k_1), F_19(x, k_0)*F_7(x, k_1))
Eq(F_53(x, k_0, k_1), F_3(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_55(x, k_0, k_1), F_19(x, k_0)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (-k_0*F_57(x, k_0, 1) + k_1*F_57(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_57(x, k_0, k_1), F_1(x) + F_58(x, k_0, k_1) + F_62(x, k_0) + F_65(x, k_0) + F_67(x, k_1, k_0))
Eq(F_58(x, k_0, k_1), F_3(x)*F_59(x, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_60(x, 1, k_0, k_1))
Eq(F_60(x, k_0, k_1, k_2), (-k_0*F_61(x, k_0/k_1, k_1, k_2) + k_1*F_61(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_61(x, k_0, k_1, k_2), F_22(x, k_0*k_1, k_1*k_2))
Eq(F_62(x, k_0), F_3(x)*F_63(x, k_0))
Eq(F_63(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_1(x) + F_62(x, k_0) + F_65(x, k_0) + F_8(x, k_0))
Eq(F_65(x, k_0), F_19(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_57(x, k_0, 1))
Eq(F_67(x, k_0, k_1), F_68(x, k_0*k_1, k_1))
Eq(F_68(x, k_0, k_1), F_19(x, k_0)*F_64(x, k_1))
Eq(F_69(x), F_3(x)*F_70(x))
Eq(F_70(x), F_64(x, 1))
Pack JSON:
{"name": "col_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "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], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 3, 4], "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], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 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2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 4]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 4]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 4]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 4]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 4]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25744/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[6,x]+F[62,x]
F[6,x] = F[4,x]*F[7,x]
F[7,x] = F[5,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[59,x,k[0]]
F[10,x] = 0
F[11,x,k[0]] = F[12,x,k[0]]*F[4,x]
F[12,x,k[0]] = -k[0]*(F[9,x,1]-F[9,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]*F[4,x]
F[14,x,k[0]] = k[0]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[10,x]+F[11,x,k[0]]+F[18,x,k[0]]+F[20,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[19,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[17,x,k[0]]+F[5,x]
F[24,x,k[0]] = k[0]*F[25,x,k[0]]
F[25,x,k[0]] = 3*F[10,x]+F[26,x,k[0]]+F[58,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[4,x]
F[27,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[30,x,k[0]] = F[31,x,k[0]]+F[32,x,k[0]]+F[48,x]
F[31,x,k[0]] = F[5,x]+F[9,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[4,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[36,x]
F[35,x,k[0]] = 1/(-1+k[0])*(F[30,x,k[0]]*k[0]-F[30,x,1])
F[36,x] = 2*F[10,x]+F[37,x]+F[46,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x,1]
F[40,x,k[0]] = F[41,x,k[0]]
F[42,x,k[0]] = F[34,x,k[0]]+F[41,x,k[0]]
F[43,x,k[0]] = F[21,x,k[0]]*F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[45,x,k[0]] = F[44,x,k[0]]+F[7,x]
F[45,x,k[0]] = 1/(-1+k[0])*(F[31,x,k[0]]*k[0]-F[31,x,1])
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[30,x,1]
F[48,x] = -F[5,x]-F[54,x]+F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = 1/F[4,x]*F[53,x]
F[53,x] = F[2,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = 1/F[4,x]*F[57,x]
F[57,x] = F[8,x]
F[58,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[59,x,k[0]] = F[21,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[31,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = k[0]*F[28,x,k[0]]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[16,x]+F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{62}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{10}\! \left(x \right) = 0
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{14}\! \left(x , y\right) = y F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{y \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y\right)\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = y F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = 3 F_{10}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{36}\! \left(x \right)
F_{35}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x \right) = 2 F_{10}\! \left(x \right)+F_{37}\! \left(x \right)+F_{46}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{48}\! \left(x \right) = -F_{5}\! \left(x \right)-F_{54}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{8}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = y F_{28}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{16}\! \left(x \right)+F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_6(x) + F_62(x))
Eq(F_6(x), F_4(x)*F_7(x))
Eq(F_7(x), F_5(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x) + F_11(x, k_0) + F_13(x, k_0) + F_59(x, k_0))
Eq(F_10(x), 0)
Eq(F_11(x, k_0), F_12(x, k_0)*F_4(x))
Eq(F_12(x, k_0), -F_9(x, 1) + (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0)*F_4(x))
Eq(F_14(x, k_0), k_0*F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_10(x) + F_11(x, k_0) + F_18(x, k_0) + F_20(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_19(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_17(x, k_0) + F_5(x))
Eq(F_24(x, k_0), k_0*F_25(x, k_0))
Eq(F_25(x, k_0), 3*F_10(x) + F_26(x, k_0) + F_58(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_4(x))
Eq(F_27(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_30(x, k_0), F_31(x, k_0) + F_32(x, k_0) + F_48(x))
Eq(F_31(x, k_0), F_5(x) + F_9(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_4(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_36(x))
Eq(F_35(x, k_0), (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_36(x), 2*F_10(x) + F_37(x) + F_46(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x, 1))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_42(x, k_0), F_34(x, k_0) + F_41(x, k_0))
Eq(F_43(x, k_0), F_21(x, k_0)*F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_45(x, k_0), F_44(x, k_0) + F_7(x))
Eq(F_45(x, k_0), (k_0*F_31(x, k_0) - F_31(x, 1))/(k_0 - 1))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_30(x, 1))
Eq(F_48(x), F_49(x) - F_5(x) - F_54(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_53(x)/F_4(x))
Eq(F_53(x), F_2(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x)/F_4(x))
Eq(F_57(x), F_8(x))
Eq(F_58(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_59(x, k_0), F_21(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_31(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), k_0*F_28(x, k_0))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_16(x) + F_5(x))
Pack JSON:
{"name": "point_and_col_placements_tracked_fusion_tracked_component_fusion_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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": 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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"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": false, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [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], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": 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0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], 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