02341_02431_03142_03241_03421_04132_04231_04321_13042_14032

Counting sequence:
1, 1, 2, 6, 24, 110, 540, 2772, 14704, 79974, 443592, 2499596, 14268740, 82339972, 479549860, 2815097792, 16639456452, 98947148126, 591537712636, 3553227623724, 21434384242112, 129796819639908, 788724906697704, 4807951095533744, 29393378297989024, 180173340682095340, 1107113105791429952, 6818253845096097888, 42078690426590838648, 260192590875330830184, 1611809331094556001992, 10001531699630723383128, 62159360466240510325864, 386893252849411449435238, 2411468731776815694315880, 15050212402720321867863740, 94046318368650459247673540, 588368589233121400589682796, 3685007643340128358801086212, 23103799142550630445170882032, 144997756213821279891544218420, 910857727956409536862598893868, 5727053878714549424494954841516, 36040012430021305916463807297600, 226983509271868647971801235395372, 1430682705929494647229499446104432, 9024372153384943490376808140478356, 56964106143825662441272278385169336, 359818145732719544203709341430482508, 2274311767190180322457764573458824356, 14384359475866308608327274590110836420, 91031933907404081744072470633855120432, 576433852698545461671344833800439810052, 3652144887425502324853466826134066544128, 23151557748656347090466390590436216968028, 146837684316343163165610082531405406113272, 931776566409619175392688363796735611109220, 5915552066197450792065318294845518450532912, 37573418876791821833055773179609504543917484, 238759771474358758108552268521539481955410680, 1517854087962252829677615832680152510876289908, 9653417157662161202040196700724875558854693096, 61419794362287507611995660963272027173166049244, 390936498430054675334859396288434314427470228040, 2489254299748973126109229478263034197918583253108, 15855953420541648389533756969437266649759099599134, 101034710746554713697717142190595527871924144693244, 644019932203674312820515448324725604245632532788940, 4106520627260663270329504737303292313617302416528256, 26193312631579770767652969012479912204342098458237396, 167126174426054971166645914152574413077667167905677928, 1066675278361563923403807734312835438754567080438370320, 6810044482435316409711077104915497666883184991915264512, 43490463219694988666593687128214479666550454468954229652, 277818419214435189598626520095967605445000869247168760352, 1775201463256970737947564022854853978381508215532157817360, 11346206682678909413655481463241497879038620879373093825768, 72538256591069787196288007483602108100455006022182203873528, 463867539439507237498877072250838369004170646549899098065144, 2967074673311958795061565066029113485965958501903882065346936, 18983132579250485512903306158839726446981001558902672324051032, 121481342481942860639356157562444939510836266864956838157930868, 777590713081397941512084249290856295887491306420929868483279928, 4978401322604002410834828018374612966858575541383656604225577296, 31880399859179958652585755956225008003485753981795564908164589456, 204197481016474569654505852095535861962982387474397686437190951736, 1308180254268112941675615287140198566336014564115250341960500990672, 8382494713862477444256238730597653796997849614666111076912148810296, 53723642312666134531957265314775436965944419963341476863788448635328, 344383323822615661274611023188245370386207203413442863897606581400312, 2208011793451591864104984646698478290402637758273756859646613707873360, 14159288978474489094621086503486304548896623060134002655470394242022344, 90815611958600361220576463771800678091055390014564174702525028697190720, 582581757971230979212962442679045075946523193310504881719615431146208464, 3737910445695850148172114158953391833989749956735765077428963951271042352, 23986945083657026841377741860252973757018314731463759058466188422622748872, 153954885092972727127803340229896632658032169198272043712759384567892839888, 988286779960296136021772142419686566443604560801761461925570547031226255244, 6345151821712895763152188070198455954644490567402229000575296735210055132064, 40744515281445259948947747405422237304669273820411288533163121315059713009760, 261675478465219918578469328183956969622699335491810769023927086525284344118936

Implicit equation for the generating function in Maple syntax:
(4*x-1)*F(x)^4+(-16*x+6)*F(x)^3+(x^2+24*x-13)*F(x)^2+(-16*x+12)*F(x)+4*x-4 = 0

Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) F \! \left(x \right)^{4}+\left(-16 x +6\right) F \! \left(x \right)^{3}+\left(x^{2}+24 x -13\right) F \! \left(x \right)^{2}+\left(-16 x +12\right) F \! \left(x \right)+4 x -4 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(6) = 540
a(7) = 2772
a(8) = 14704
a(9) = 79974
a(10) = 443592
a(11) = 2499596
a(12) = 14268740
a(13) = 82339972
a(14) = 479549860
a(15) = 2815097792
a(16) = 16639456452
a(17) = 98947148126
a(18) = 591537712636
a(19) = 3553227623724
a(n+20) = 4096*n*(2*n-1)*(2*n+1)/(n+20)/(n+19)/(2*n+39)*a(n)+512*(2*n+1)*(916*n^2+712*n-9)/(n+20)/(n+19)/(2*n+39)*a(n+1)-192*(42060*n^3+208560*n^2+343911*n+187897)/(n+20)/(n+19)/(2*n+39)*a(n+2)-48*(432732*n^3+4881254*n^2+16662860*n+17918773)/(n+20)/(n+19)/(2*n+39)*a(n+3)+4*(25400764*n^3+306795900*n^2+1230413339*n+1639326000)/(n+20)/(n+19)/(2*n+39)*a(n+4)-2*(44453726*n^3+552325239*n^2+2292850891*n+3192582486)/(n+20)/(n+19)/(2*n+39)*a(n+5)-(112014674*n^3+2635668285*n^2+19272760981*n+44971622922)/(n+20)/(n+19)/(2*n+39)*a(n+6)+2*(149062195*n^3+3422417985*n^2+25922787338*n+64899906954)/(n+20)/(n+19)/(2*n+39)*a(n+7)-(257312554*n^3+6336497943*n^2+51982150787*n+142075461456)/(n+20)/(n+19)/(2*n+39)*a(n+8)+2*(53441668*n^3+1423814331*n^2+12690543599*n+37831782912)/(n+20)/(n+19)/(2*n+39)*a(n+9)-(3022790*n^3+79415085*n^2+716407897*n+2221131150)/(n+20)/(n+19)/(2*n+39)*a(n+10)-2*(7589803*n^3+252562797*n^2+2822211764*n+10582254672)/(n+20)/(n+19)/(2*n+39)*a(n+11)+3*(1791558*n^3+66969187*n^2+838710563*n+3515080212)/(n+20)/(n+19)/(2*n+39)*a(n+12)-2*(380062*n^3+16360809*n^2+231992765*n+1085753814)/(n+20)/(n+19)/(2*n+39)*a(n+13)-(396430*n^3+17215119*n^2+249931679*n+1212253350)/(n+20)/(n+19)/(2*n+39)*a(n+14)+2*(66845*n^3+3002127*n^2+44958874*n+224503194)/(n+20)/(n+19)/(2*n+39)*a(n+15)+(10922*n^3+528819*n^2+8543575*n+46047480)/(n+20)/(n+19)/(2*n+39)*a(n+16)-2*(2408*n^3+118971*n^2+1960519*n+10776756)/(n+20)/(n+19)/(2*n+39)*a(n+17)-(26*n^3+1479*n^2+27763*n+172098)/(n+20)/(n+19)/(2*n+39)*a(n+18)+54*(n+18)^2/(n+20)/(2*n+39)*a(n+19), n >= 20

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(6) = 540
a(7) = 2772
a(8) = 14704
a(9) = 79974
a(10) = 443592
a(11) = 2499596
a(12) = 14268740
a(13) = 82339972
a(14) = 479549860
a(15) = 2815097792
a(16) = 16639456452
a(17) = 98947148126
a(18) = 591537712636
a(19) = 3553227623724
a{\left(n + 20 \right)} = \frac{4096 n \left(2 n - 1\right) \left(2 n + 1\right) a{\left(n \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{54 \left(n + 18\right)^{2} a{\left(n + 19 \right)}}{\left(n + 20\right) \left(2 n + 39\right)} + \frac{512 \left(2 n + 1\right) \left(916 n^{2} + 712 n - 9\right) a{\left(n + 1 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(26 n^{3} + 1479 n^{2} + 27763 n + 172098\right) a{\left(n + 18 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(2408 n^{3} + 118971 n^{2} + 1960519 n + 10776756\right) a{\left(n + 17 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{\left(10922 n^{3} + 528819 n^{2} + 8543575 n + 46047480\right) a{\left(n + 16 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{192 \left(42060 n^{3} + 208560 n^{2} + 343911 n + 187897\right) a{\left(n + 2 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(66845 n^{3} + 3002127 n^{2} + 44958874 n + 224503194\right) a{\left(n + 15 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(380062 n^{3} + 16360809 n^{2} + 231992765 n + 1085753814\right) a{\left(n + 13 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(396430 n^{3} + 17215119 n^{2} + 249931679 n + 1212253350\right) a{\left(n + 14 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{48 \left(432732 n^{3} + 4881254 n^{2} + 16662860 n + 17918773\right) a{\left(n + 3 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{3 \left(1791558 n^{3} + 66969187 n^{2} + 838710563 n + 3515080212\right) a{\left(n + 12 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(3022790 n^{3} + 79415085 n^{2} + 716407897 n + 2221131150\right) a{\left(n + 10 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(7589803 n^{3} + 252562797 n^{2} + 2822211764 n + 10582254672\right) a{\left(n + 11 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{4 \left(25400764 n^{3} + 306795900 n^{2} + 1230413339 n + 1639326000\right) a{\left(n + 4 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{2 \left(44453726 n^{3} + 552325239 n^{2} + 2292850891 n + 3192582486\right) a{\left(n + 5 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(53441668 n^{3} + 1423814331 n^{2} + 12690543599 n + 37831782912\right) a{\left(n + 9 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(112014674 n^{3} + 2635668285 n^{2} + 19272760981 n + 44971622922\right) a{\left(n + 6 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} + \frac{2 \left(149062195 n^{3} + 3422417985 n^{2} + 25922787338 n + 64899906954\right) a{\left(n + 7 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)} - \frac{\left(257312554 n^{3} + 6336497943 n^{2} + 51982150787 n + 142075461456\right) a{\left(n + 8 \right)}}{\left(n + 19\right) \left(n + 20\right) \left(2 n + 39\right)}, \quad n \geq 20

Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24550/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[57,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[56,x]
F[15,x] = -F[52,x]+F[16,x]
F[16,x] = -F[20,x]+F[17,x]
F[17,x] = 1/F[11,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[0,x]+F[9,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = -F[22,x]+F[8,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[25,x]*F[4,x]
F[25,x] = F[0,x]+F[26,x]
F[26,x] = F[3,x]
F[27,x] = F[28,x]
F[28,x] = F[11,x]*F[29,x]
F[29,x] = F[30,x]+F[48,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]*F[34,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[21,x]
F[34,x] = 1/F[11,x]/F[4,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[40,x]+F[37,x]
F[37,x] = 1/F[11,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = -F[2,x]+F[19,x]
F[40,x] = -F[44,x]+F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[2,x]+F[39,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[46,x]+F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[11,x]*F[34,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]*F[8,x]
F[50,x] = 1/F[0,x]/F[11,x]*F[51,x]
F[51,x] = F[40,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[4,x]*F[54,x]
F[54,x] = F[15,x]+F[55,x]
F[55,x] = F[0,x]*F[2,x]
F[56,x] = F[43,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[61,x]+F[76,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = -F[66,x]+F[63,x]
F[63,x] = 1/F[11,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[5,x]
F[66,x] = F[67,x]
F[67,x] = F[11,x]*F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[4,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[0,x]*F[11,x]*F[4,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[11,x]*F[75,x]
F[75,x] = F[4,x]+F[62,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[84,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[14,x]*F[4,x]
F[81,x] = F[82,x]*F[9,x]
F[82,x] = F[83,x]
F[83,x] = F[0,x]*F[11,x]*F[4,x]
F[84,x] = F[73,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{57}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{3}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{21}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{56}\! \left(x \right) = F_{43}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{76}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{84}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right) F_{9}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{84}\! \left(x \right) = F_{73}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_57(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_56(x))
Eq(F_15(x), F_16(x) - F_52(x))
Eq(F_16(x), F_17(x) - F_20(x))
Eq(F_17(x), F_18(x)/F_11(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_0(x) + F_9(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), -F_22(x) + F_8(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_25(x)*F_4(x))
Eq(F_25(x), F_0(x) + F_26(x))
Eq(F_26(x), F_3(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_11(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_48(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x)*F_34(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_21(x))
Eq(F_34(x), F_35(x)/(F_11(x)*F_4(x)))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) - F_40(x))
Eq(F_37(x), F_38(x)/F_11(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_19(x) - F_2(x))
Eq(F_40(x), F_41(x) - F_44(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_2(x) + F_39(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_11(x)*F_34(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_50(x)*F_8(x))
Eq(F_50(x), F_51(x)/(F_0(x)*F_11(x)))
Eq(F_51(x), F_40(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_4(x)*F_54(x))
Eq(F_54(x), F_15(x) + F_55(x))
Eq(F_55(x), F_0(x)*F_2(x))
Eq(F_56(x), F_43(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_76(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) - F_66(x))
Eq(F_63(x), F_64(x)/F_11(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_5(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_11(x)*F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_4(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_11(x)*F_75(x))
Eq(F_75(x), F_4(x) + F_62(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_84(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_14(x)*F_4(x))
Eq(F_81(x), F_82(x)*F_9(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_84(x), F_73(x)*F_9(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": 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}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "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], "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, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[4, 2]]}]], "assumptions": []}], "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"}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25093/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[57,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[56,x]
F[15,x] = -F[52,x]+F[16,x]
F[16,x] = -F[20,x]+F[17,x]
F[17,x] = 1/F[11,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[0,x]+F[9,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = -F[22,x]+F[8,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[11,x]*F[25,x]*F[4,x]
F[25,x] = F[0,x]+F[26,x]
F[26,x] = F[3,x]
F[27,x] = F[28,x]
F[28,x] = F[11,x]*F[29,x]
F[29,x] = F[30,x]+F[48,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]*F[34,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[21,x]
F[34,x] = 1/F[11,x]/F[4,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[40,x]+F[37,x]
F[37,x] = 1/F[11,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = -F[2,x]+F[19,x]
F[40,x] = -F[44,x]+F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[2,x]+F[39,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[46,x]+F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[11,x]*F[34,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]*F[8,x]
F[50,x] = 1/F[0,x]/F[11,x]*F[51,x]
F[51,x] = F[40,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[4,x]*F[54,x]
F[54,x] = F[15,x]+F[55,x]
F[55,x] = F[0,x]*F[2,x]
F[56,x] = F[43,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[61,x]+F[76,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = -F[66,x]+F[63,x]
F[63,x] = 1/F[11,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[5,x]
F[66,x] = F[67,x]
F[67,x] = F[11,x]*F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[4,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[0,x]*F[11,x]*F[4,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[11,x]*F[75,x]
F[75,x] = F[4,x]+F[62,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[84,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[14,x]*F[4,x]
F[81,x] = F[82,x]*F[9,x]
F[82,x] = F[83,x]
F[83,x] = F[0,x]*F[11,x]*F[4,x]
F[84,x] = F[73,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{57}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{3}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{21}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{56}\! \left(x \right) = F_{43}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{76}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{84}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right) F_{9}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{84}\! \left(x \right) = F_{73}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_57(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_56(x))
Eq(F_15(x), F_16(x) - F_52(x))
Eq(F_16(x), F_17(x) - F_20(x))
Eq(F_17(x), F_18(x)/F_11(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_0(x) + F_9(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), -F_22(x) + F_8(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_11(x)*F_25(x)*F_4(x))
Eq(F_25(x), F_0(x) + F_26(x))
Eq(F_26(x), F_3(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_11(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_48(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x)*F_34(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_21(x))
Eq(F_34(x), F_35(x)/(F_11(x)*F_4(x)))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) - F_40(x))
Eq(F_37(x), F_38(x)/F_11(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_19(x) - F_2(x))
Eq(F_40(x), F_41(x) - F_44(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_2(x) + F_39(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_11(x)*F_34(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_50(x)*F_8(x))
Eq(F_50(x), F_51(x)/(F_0(x)*F_11(x)))
Eq(F_51(x), F_40(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_4(x)*F_54(x))
Eq(F_54(x), F_15(x) + F_55(x))
Eq(F_55(x), F_0(x)*F_2(x))
Eq(F_56(x), F_43(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_76(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) - F_66(x))
Eq(F_63(x), F_64(x)/F_11(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_5(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_11(x)*F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_4(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_11(x)*F_75(x))
Eq(F_75(x), F_4(x) + F_62(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_84(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_14(x)*F_4(x))
Eq(F_81(x), F_82(x)*F_9(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_84(x), F_73(x)*F_9(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": 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}]], "symmetries": [], "iterative": false}
Specification JSON:
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0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 1], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 1], [5, 1], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[4, 2]]}]], "assumptions": []}], "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"}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25227/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[57,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[56,x]
F[15,x] = -F[52,x]+F[16,x]
F[16,x] = -F[22,x]+F[17,x]
F[17,x] = 1/F[11,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = -F[2,x]+F[21,x]
F[21,x] = -F[0,x]+F[9,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = -F[24,x]+F[8,x]
F[24,x] = F[0,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]*F[4,x]
F[27,x] = F[0,x]+F[28,x]
F[28,x] = F[3,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[48,x]
F[32,x] = F[33,x]
F[33,x] = F[11,x]*F[34,x]*F[36,x]
F[34,x] = 1/F[11,x]*F[35,x]
F[35,x] = F[23,x]
F[36,x] = 1/F[11,x]/F[4,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[41,x]+F[39,x]
F[39,x] = 1/F[11,x]*F[40,x]
F[40,x] = F[20,x]
F[41,x] = -F[44,x]+F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[21,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[46,x]+F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[11,x]*F[36,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]*F[8,x]
F[50,x] = 1/F[0,x]/F[11,x]*F[51,x]
F[51,x] = F[41,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[4,x]*F[54,x]
F[54,x] = F[15,x]+F[55,x]
F[55,x] = F[0,x]*F[2,x]
F[56,x] = F[21,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[61,x]+F[77,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = -F[67,x]+F[63,x]
F[63,x] = 1/F[11,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[66,x]
F[66,x] = -F[0,x]+F[4,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[4,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[0,x]*F[11,x]*F[4,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[4,x]+F[62,x]
F[77,x] = F[78,x]
F[78,x] = F[11,x]*F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[85,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[14,x]*F[4,x]
F[82,x] = F[83,x]*F[9,x]
F[83,x] = F[84,x]
F[84,x] = F[0,x]*F[11,x]*F[4,x]
F[85,x] = F[74,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{57}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{3}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{23}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{41}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{56}\! \left(x \right) = F_{21}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{77}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{85}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right) F_{9}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{85}\! \left(x \right) = F_{74}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_57(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_56(x))
Eq(F_15(x), F_16(x) - F_52(x))
Eq(F_16(x), F_17(x) - F_22(x))
Eq(F_17(x), F_18(x)/F_11(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), -F_2(x) + F_21(x))
Eq(F_21(x), -F_0(x) + F_9(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), -F_24(x) + F_8(x))
Eq(F_24(x), F_0(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x)*F_4(x))
Eq(F_27(x), F_0(x) + F_28(x))
Eq(F_28(x), F_3(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_48(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_11(x)*F_34(x)*F_36(x))
Eq(F_34(x), F_35(x)/F_11(x))
Eq(F_35(x), F_23(x))
Eq(F_36(x), F_37(x)/(F_11(x)*F_4(x)))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x) - F_41(x))
Eq(F_39(x), F_40(x)/F_11(x))
Eq(F_40(x), F_20(x))
Eq(F_41(x), F_42(x) - F_44(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_21(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_11(x)*F_36(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_50(x)*F_8(x))
Eq(F_50(x), F_51(x)/(F_0(x)*F_11(x)))
Eq(F_51(x), F_41(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_4(x)*F_54(x))
Eq(F_54(x), F_15(x) + F_55(x))
Eq(F_55(x), F_0(x)*F_2(x))
Eq(F_56(x), F_21(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_77(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) - F_67(x))
Eq(F_63(x), F_64(x)/F_11(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_66(x))
Eq(F_66(x), -F_0(x) + F_4(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_4(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_4(x) + F_62(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_11(x)*F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_85(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_14(x)*F_4(x))
Eq(F_82(x), F_83(x)*F_9(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_85(x), F_74(x)*F_9(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": 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}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "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], "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, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 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0], [3, 0], [3, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 1], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 1], [3, 0], [5, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 4, 1], 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1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 1], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 1], [5, 1], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[4, 2]]}]], "assumptions": []}], "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"}}]}

Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25334/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[57,x]+F[8,x]
F[8,x] = F[12,x]+F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[56,x]
F[15,x] = -F[52,x]+F[16,x]
F[16,x] = -F[22,x]+F[17,x]
F[17,x] = 1/F[11,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = -F[2,x]+F[21,x]
F[21,x] = -F[0,x]+F[9,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = -F[24,x]+F[8,x]
F[24,x] = F[0,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[27,x]*F[4,x]
F[27,x] = F[0,x]+F[28,x]
F[28,x] = F[3,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[48,x]
F[32,x] = F[33,x]
F[33,x] = F[11,x]*F[34,x]*F[36,x]
F[34,x] = 1/F[11,x]*F[35,x]
F[35,x] = F[23,x]
F[36,x] = 1/F[11,x]/F[4,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[41,x]+F[39,x]
F[39,x] = 1/F[11,x]*F[40,x]
F[40,x] = F[20,x]
F[41,x] = -F[44,x]+F[42,x]
F[42,x] = 1/F[11,x]*F[43,x]
F[43,x] = F[21,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[46,x]+F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[11,x]*F[36,x]*F[5,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[50,x]*F[8,x]
F[50,x] = 1/F[0,x]/F[11,x]*F[51,x]
F[51,x] = F[41,x]
F[52,x] = F[53,x]
F[53,x] = F[11,x]*F[4,x]*F[54,x]
F[54,x] = F[15,x]+F[55,x]
F[55,x] = F[0,x]*F[2,x]
F[56,x] = F[21,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[61,x]+F[77,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = -F[67,x]+F[63,x]
F[63,x] = 1/F[11,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[66,x]
F[66,x] = -F[0,x]+F[4,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[4,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[0,x]*F[11,x]*F[4,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[4,x]+F[62,x]
F[77,x] = F[78,x]
F[78,x] = F[11,x]*F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[85,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[14,x]*F[4,x]
F[82,x] = F[83,x]*F[9,x]
F[83,x] = F[84,x]
F[84,x] = F[0,x]*F[11,x]*F[4,x]
F[85,x] = F[74,x]*F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{57}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{3}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{23}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{11}\! \left(x \right) F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right) F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{41}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{56}\! \left(x \right) = F_{21}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{77}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{85}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right) F_{9}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{85}\! \left(x \right) = F_{74}\! \left(x \right) F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_57(x) + F_8(x))
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_56(x))
Eq(F_15(x), F_16(x) - F_52(x))
Eq(F_16(x), F_17(x) - F_22(x))
Eq(F_17(x), F_18(x)/F_11(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), -F_2(x) + F_21(x))
Eq(F_21(x), -F_0(x) + F_9(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), -F_24(x) + F_8(x))
Eq(F_24(x), F_0(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_27(x)*F_4(x))
Eq(F_27(x), F_0(x) + F_28(x))
Eq(F_28(x), F_3(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_48(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_11(x)*F_34(x)*F_36(x))
Eq(F_34(x), F_35(x)/F_11(x))
Eq(F_35(x), F_23(x))
Eq(F_36(x), F_37(x)/(F_11(x)*F_4(x)))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x) - F_41(x))
Eq(F_39(x), F_40(x)/F_11(x))
Eq(F_40(x), F_20(x))
Eq(F_41(x), F_42(x) - F_44(x))
Eq(F_42(x), F_43(x)/F_11(x))
Eq(F_43(x), F_21(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_11(x)*F_36(x)*F_5(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_50(x)*F_8(x))
Eq(F_50(x), F_51(x)/(F_0(x)*F_11(x)))
Eq(F_51(x), F_41(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_11(x)*F_4(x)*F_54(x))
Eq(F_54(x), F_15(x) + F_55(x))
Eq(F_55(x), F_0(x)*F_2(x))
Eq(F_56(x), F_21(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_77(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) - F_67(x))
Eq(F_63(x), F_64(x)/F_11(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_66(x))
Eq(F_66(x), -F_0(x) + F_4(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_4(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_4(x) + F_62(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_11(x)*F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_85(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_14(x)*F_4(x))
Eq(F_82(x), F_83(x)*F_9(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_0(x)*F_11(x)*F_4(x))
Eq(F_85(x), F_74(x)*F_9(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 3, 0, 4, 2], [1, 4, 0, 3, 2]], "symmetry": 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}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "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": 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