01243_01342_01432_02341_02431_03421_10243_10342_10432_20143
Counting sequence:
1, 1, 2, 6, 24, 110, 534, 2678, 13748, 71869, 381216, 2046630, 11100266, 60732086, 334799979, 1857897041, 10370176027, 58182823083, 327950571901, 1856195345959, 10545485247264, 60115556470047, 343759054613180, 1971307632199647, 11334111167922859, 65322808190073424, 377318402246885159, 2183970907874524084, 12665394553256492246, 73581264351674953499, 428194980497479861945, 2495718971724112025614, 14567592497353566207800, 85149054108273195162445, 498352975830165086550561, 2920301178326293449312354, 17132564561396469833491369, 100622331261058954777392334, 591587308050175313153774502, 3481552006139361841414670483, 20508565183820967023021619591, 120916714308471245743658374029, 713522665437730345097396344648, 4213883761341999407724178916921, 24905472579522525356580518839303, 147309121831508589596955397494653, 871913156503041986433109815868611, 5164312958663720566510874913194434, 30608031889363329314874162432580050, 181522442450549384658656672739092051, 1077175671212254402529020668687076455, 6395785363642078225076305684645795429, 37996429513939065735097529440621895486, 225852146616345279400897852729902425263, 1343165862872431439680018286223625639452, 7991917277707442265417602973554470994868, 47575195132504733479114727626198201493248, 283342154278966566785491278456533105860749, 1688246830239641820220222401713561811690537, 10063482654959884738212633207783278634627606, 60012547621215270362965284217453681623464860, 358023326347513803171158251787381152040177065, 2136734003594258205347846002853333517881863424, 12757163560483162608004958481890515348957448197, 76193373927850248292282385756786977560789540787, 455234150404110564720424398585611295995947708664, 2720835965280292018973682685671361897686086746290, 16267294792282002595365918107706051200061310707981, 97290294070277190835188222261994826784674255409527, 582050720071680147430220689146781563508661494161152, 3483255952731620402059793401644660046542972974922921, 20851603481111544984125036066484991456893633887482088, 124858888534928835897723263702732162431524070746044230, 747862883018018415915858214356003687151803567172355528, 4480677752292389967511490068497031759351465392645241271, 26852300492483333371793941211646135828038770011649207810, 160965315872751166871564336942626508148335655189636754692, 965146444123023872774382040862762851188376794440392748578, 5788438423795108244723838329037817004352497325556983664545, 34724357060510311871908789254935308198210716146420724828734, 208357434447917844202193872873395793239494200825630910073666, 1250498792844708340403644380186080203558784698556507059016420, 7506796218149261700492678028473510737131555767421476375600071, 45073441962373383278167590526161319049260055542693837034414691, 270694432635151139404456185996587962144932970553396149525643764, 1626028905765407646148967722821703753982713644908810923277569074, 9769345012244854306213179860818266162552021071389516080471475786, 58706861313023865234922197324856544171799952438274238510305439521, 352855227392270082985893162209905817712791975916390983145538804059, 2121224545016378995601038225822924629481481053399595826433505038817, 12754319853926854891422596405686878193279487756517984910769189382037, 76702015175265937778305774346610883243208315632720475231680485999740, 461353000066817027038954492308586323731581513922221338636957361274615, 2775462591522276719594549854702222791068129817287706762458041800870764, 16699799750347470913055265386211257958496048842240528082471863796344054, 100498471669573021165304413921499891070857572689535129295200721929885983, 604892862267704734083283216292387711296984086424570878978485851581164322, 3641386835480250951538456012029323590683587114824296608961697017231984361, 21924168028610518595769250036312438365714362905161152360067107704231801766, 132021908154703466032458166501873522015404209976422903663553135644138396262, 795122682318223909953088364950055647678022665207757043546510225512839806331
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24566/
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[49,x]+F[5,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[46,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[38,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[45,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[37,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[26,x,k[0],k[1]]+F[30,x,k[1]]
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[25,x,k[0]]*k[0]-F[25,x,k[1]]*k[1])/(-k[1]+k[0])
F[25,x,k[0]] = F[15,x,1,k[0]]
F[26,x,k[0],k[1]] = F[19,x,k[0]]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = (F[28,x,k[0]]*k[0]-F[28,x,k[1]]*k[1])/(-k[1]+k[0])
F[28,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[29,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[30,x,k[0]] = F[19,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[36,x,k[0]]
F[33,x,k[0]] = F[3,x]*F[34,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[29,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[19,x,k[0]]*F[28,x,k[0]]
F[36,x,k[0]] = F[19,x,k[0]]*F[32,x,k[0]]
F[37,x,k[0],k[1]] = F[19,x,k[0]]*F[22,x,k[1],k[0]]
F[38,x,k[0],k[1]] = F[3,x]*F[39,x,k[0],k[1]]
F[39,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[40,x,k[0],k[1]] = F[19,x,k[0]]*F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,1,k[0],k[1]]
F[42,x,k[0],k[1],k[2]] = (F[43,x,k[0]*k[1],k[2]]*k[0]-F[43,x,k[1],k[2]])/(-1+k[0])
F[43,x,k[0],k[1]] = 1/(-1+k[0])*(F[44,x,k[0],k[1]]*k[0]-F[44,x,1,k[1]])
F[44,x,k[0],k[1]] = (F[32,x,k[0]]*k[0]-F[32,x,k[1]]*k[1])/(-k[1]+k[0])
F[45,x,k[0],k[1]] = F[19,x,k[0]]*F[43,x,k[1],k[0]]
F[46,x,k[0]] = F[19,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,1,k[0]]
F[48,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[49,x] = F[3,x]*F[50,x]
F[50,x] = F[51,x,1]
F[51,x,k[0]] = F[1,x]+F[52,x,k[0]]+F[54,x,k[0]]+F[8,x,k[0]]
F[52,x,k[0]] = F[3,x]*F[53,x,k[0]]
F[53,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[54,x,k[0]] = F[19,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,1,k[0]]
F[56,x,k[0],k[1]] = (F[31,x,k[0]*k[1]]*k[0]-F[31,x,k[1]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{5}\! \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_{46}\! \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_{38}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \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_{37}\! \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_{26}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}\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) = \frac{F_{25}\! \left(x , y_{0}\right) y_{0}-F_{25}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{28}\! \left(x , y_{0}\right) y_{0}-F_{28}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{30}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = -\frac{-F_{32}\! \left(x , y_{0}\right) y_{0}+F_{32}\! \left(x , 1\right)}{-1+y_{0}}
F_{32}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \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_{40}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , 1, y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{43}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{43}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}
F_{43}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{32}\! \left(x , y_{0}\right) y_{0}-F_{32}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{1}, y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , 1, y_{0}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{49}\! \left(x \right) = F_{3}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{51}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{53}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = -\frac{-F_{51}\! \left(x , y_{0}\right) y_{0}+F_{51}\! \left(x , 1\right)}{-1+y_{0}}
F_{54}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , 1, y_{0}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{31}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{31}\! \left(x , y_{1}\right)}{-1+y_{0}}
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_49(x) + F_5(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_46(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_38(x, k_0, k_1) + F_40(x, k_0, k_1) + F_45(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_37(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_26(x, k_0, k_1) + F_30(x, k_1))
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), (-k_0*F_25(x, k_0) + k_1*F_25(x, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0), F_15(x, 1, k_0))
Eq(F_26(x, k_0, k_1), F_19(x, k_0)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), (-k_0*F_28(x, k_0) + k_1*F_28(x, k_1))/(-k_0 + k_1))
Eq(F_28(x, k_0), F_1(x) + F_10(x, k_0) + F_29(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_30(x, k_0), F_19(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_36(x, k_0))
Eq(F_33(x, k_0), F_3(x)*F_34(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_10(x, k_0) + F_29(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_19(x, k_0)*F_28(x, k_0))
Eq(F_36(x, k_0), F_19(x, k_0)*F_32(x, k_0))
Eq(F_37(x, k_0, k_1), F_19(x, k_0)*F_22(x, k_1, k_0))
Eq(F_38(x, k_0, k_1), F_3(x)*F_39(x, k_0, k_1))
Eq(F_39(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_40(x, k_0, k_1), F_19(x, k_0)*F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, 1, k_0, k_1))
Eq(F_42(x, k_0, k_1, k_2), (-k_0*k_1*F_43(x, k_0*k_1, k_2) + k_1*F_43(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_43(x, k_0, k_1), (k_0*F_44(x, k_0, k_1) - F_44(x, 1, k_1))/(k_0 - 1))
Eq(F_44(x, k_0, k_1), (-k_0*F_32(x, k_0) + k_1*F_32(x, k_1))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1), F_19(x, k_0)*F_43(x, k_1, k_0))
Eq(F_46(x, k_0), F_19(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, 1, k_0))
Eq(F_48(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_49(x), F_3(x)*F_50(x))
Eq(F_50(x), F_51(x, 1))
Eq(F_51(x, k_0), F_1(x) + F_52(x, k_0) + F_54(x, k_0) + F_8(x, k_0))
Eq(F_52(x, k_0), F_3(x)*F_53(x, k_0))
Eq(F_53(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_54(x, k_0), F_19(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, 1, k_0))
Eq(F_56(x, k_0, k_1), (-k_0*k_1*F_31(x, k_0*k_1) + k_1*F_31(x, k_1))/(-k_0*k_1 + k_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, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 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, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [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, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 0]]}, {"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, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[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, 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, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [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, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 0]]}, {"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, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], 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3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 4], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 4], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 4], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 3], [0, 4], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 4], [0, 4], [0, 0], [0, 0]]}, {"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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 4], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 4], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 4], [0, 0], [0, 0]]}, {"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, 2]]}, {"patt": [0], "pos": [[0, 3]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0], [0, 0]]}, {"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, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"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]]}], "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]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25257/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[98,x,k[0]]
F[10,x,k[0]] = F[11,x]+F[13,x,k[0]]
F[11,x] = 1/F[4,x]*F[12,x]
F[12,x] = F[2,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[92,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[26,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[0,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x]+F[24,x,k[0]]
F[23,x] = -F[0,x]+F[11,x]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[28,x,k[0]] = F[27,x,k[0]]+F[90,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[34,x,k[0]]
F[35,x,k[0]] = F[34,x,k[0]]+F[88,x,k[0]]
F[36,x,k[0]] = F[35,x,k[0]]+F[61,x,k[0]]
F[37,x,k[0]] = F[36,x,k[0]]*F[4,x]
F[37,x,k[0]] = F[38,x,k[0]]
F[39,x,k[0]] = F[38,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[41,x,k[0]]+F[9,x,k[0]]
F[42,x,k[0]] = F[21,x,k[0]]*F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[4,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]+F[60,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[21,x,k[0]]*F[48,x,k[0]]
F[49,x,k[0]] = F[48,x,k[0]]+F[55,x,k[0]]
F[50,x,k[0]] = F[4,x]*F[49,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[4,x]*F[54,x,k[0]]
F[54,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[56,x,k[0]] = F[55,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[51,x,k[0]]
F[59,x,k[0]] = F[4,x]*F[58,x,k[0]]
F[59,x,k[0]] = F[22,x,k[0]]
F[60,x,k[0]] = -k[0]*(F[43,x,1]-F[43,x,k[0]])/(-1+k[0])
F[61,x,k[0]] = k[0]*F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[4,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,1,k[0]]
F[65,x,k[0],k[1]] = (F[66,x,k[0]*k[1]]*k[0]-F[66,x,k[1]])/(-1+k[0])
F[66,x,k[0]] = F[67,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[67,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[4,x]*F[71,x,k[0]]
F[71,x,k[0]] = 1/(-1+k[0])*(F[72,x,k[0]]*k[0]-F[72,x,1])
F[72,x,k[0]] = F[73,x,k[0]]
F[74,x,k[0]] = F[4,x]*F[73,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[76,x,k[0]] = F[21,x,k[0]]*F[75,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[4,x]*F[80,x,k[0]]
F[80,x,k[0]] = -k[0]*(F[19,x,1]-F[19,x,k[0]])/(-1+k[0])
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[4,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[85,x,k[0]]
F[84,x,k[0]] = -k[0]*(F[77,x,1]-F[77,x,k[0]])/(-1+k[0])
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[4,x]*F[87,x,k[0]]
F[87,x,k[0]] = -k[0]*(F[45,x,1]-F[45,x,k[0]])/(-1+k[0])
F[89,x,k[0]] = F[4,x]*F[88,x,k[0]]
F[54,x,k[0]] = F[41,x,k[0]]+F[89,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[92,x,k[0]] = k[0]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[4,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,1,k[0]]
F[96,x,k[0],k[1]] = (F[97,x,k[0]*k[1]]*k[0]-F[97,x,k[1]])/(-1+k[0])
F[97,x,k[0]] = F[17,x,k[0]]+F[41,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[4,x]
F[100,x,k[0]] = F[101,x,k[0]]+F[39,x,k[0]]
F[101,x,k[0]] = k[0]*F[102,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[4,x]
F[104,x,k[0]] = F[105,x,1,k[0]]
F[105,x,k[0],k[1]] = (F[106,x,k[0]*k[1]]*k[0]-F[106,x,k[1]])/(-1+k[0])
F[106,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \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 , y\right)+F_{98}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{2}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
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_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}
F_{56}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = -\frac{y \left(F_{43}\! \left(x , 1\right)-F_{43}\! \left(x , y\right)\right)}{-1+y}
F_{61}\! \left(x , y\right) = y F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , 1, y\right)
F_{65}\! \left(x , y , z\right) = -\frac{-F_{66}\! \left(x , y z \right) y +F_{66}\! \left(x , z\right)}{-1+y}
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = -\frac{-F_{72}\! \left(x , y\right) y +F_{72}\! \left(x , 1\right)}{-1+y}
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = -\frac{y \left(F_{19}\! \left(x , 1\right)-F_{19}\! \left(x , y\right)\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = -\frac{y \left(F_{77}\! \left(x , 1\right)-F_{77}\! \left(x , y\right)\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = -\frac{y \left(F_{45}\! \left(x , 1\right)-F_{45}\! \left(x , y\right)\right)}{-1+y}
F_{89}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = y F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , 1, y\right)
F_{96}\! \left(x , y , z\right) = -\frac{-F_{97}\! \left(x , y z \right) y +F_{97}\! \left(x , z\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = y F_{102}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , 1, y\right)
F_{105}\! \left(x , y , z\right) = -\frac{-F_{106}\! \left(x , y z \right) y +F_{106}\! \left(x , z\right)}{-1+y}
F_{106}\! \left(x , y\right) = -\frac{-y F_{97}\! \left(x , y\right)+F_{97}\! \left(x , 1\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_98(x, k_0))
Eq(F_10(x, k_0), F_11(x) + F_13(x, k_0))
Eq(F_11(x), F_12(x)/F_4(x))
Eq(F_12(x), F_2(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_92(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_26(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_0(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x) + F_24(x, k_0))
Eq(F_23(x), -F_0(x) + F_11(x))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_28(x, k_0), F_27(x, k_0) + F_90(x, k_0))
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_31(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_35(x, k_0), F_34(x, k_0) + F_88(x, k_0))
Eq(F_36(x, k_0), F_35(x, k_0) + F_61(x, k_0))
Eq(F_37(x, k_0), F_36(x, k_0)*F_4(x))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_39(x, k_0), F_38(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x, k_0) + F_9(x, k_0))
Eq(F_42(x, k_0), F_21(x, k_0)*F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_4(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0) + F_60(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_21(x, k_0)*F_48(x, k_0))
Eq(F_49(x, k_0), F_48(x, k_0) + F_55(x, k_0))
Eq(F_50(x, k_0), F_4(x)*F_49(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_4(x)*F_54(x, k_0))
Eq(F_54(x, k_0), (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_56(x, k_0), F_55(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_51(x, k_0))
Eq(F_59(x, k_0), F_4(x)*F_58(x, k_0))
Eq(F_59(x, k_0), F_22(x, k_0))
Eq(F_60(x, k_0), -F_43(x, 1) + (k_0*F_43(x, k_0) - F_43(x, 1))/(k_0 - 1))
Eq(F_61(x, k_0), k_0*F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_4(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, 1, k_0))
Eq(F_65(x, k_0, k_1), (-k_0*k_1*F_66(x, k_0*k_1) + k_1*F_66(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_67(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_4(x)*F_71(x, k_0))
Eq(F_71(x, k_0), (k_0*F_72(x, k_0) - F_72(x, 1))/(k_0 - 1))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_74(x, k_0), F_4(x)*F_73(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_76(x, k_0), F_21(x, k_0)*F_75(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_4(x)*F_80(x, k_0))
Eq(F_80(x, k_0), -F_19(x, 1) + (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_4(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_85(x, k_0))
Eq(F_84(x, k_0), -F_77(x, 1) + (k_0*F_77(x, k_0) - F_77(x, 1))/(k_0 - 1))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_4(x)*F_87(x, k_0))
Eq(F_87(x, k_0), -F_45(x, 1) + (k_0*F_45(x, k_0) - F_45(x, 1))/(k_0 - 1))
Eq(F_89(x, k_0), F_4(x)*F_88(x, k_0))
Eq(F_54(x, k_0), F_41(x, k_0) + F_89(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_92(x, k_0), k_0*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_4(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, 1, k_0))
Eq(F_96(x, k_0, k_1), (-k_0*k_1*F_97(x, k_0*k_1) + k_1*F_97(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_97(x, k_0), F_17(x, k_0) + F_41(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_4(x))
Eq(F_100(x, k_0), F_101(x, k_0) + F_39(x, k_0))
Eq(F_101(x, k_0), k_0*F_102(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_4(x))
Eq(F_104(x, k_0), F_105(x, 1, k_0))
Eq(F_105(x, k_0, k_1), (-k_0*k_1*F_106(x, k_0*k_1) + k_1*F_106(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_106(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Pack JSON:
{"name": "point_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": "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:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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": "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 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], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 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": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 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": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 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": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"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], [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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"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], [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": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 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], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 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": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 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": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 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, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"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], [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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 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], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 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0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 3], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 1], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [2, 2], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 3], [3, 3], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 3], [3, 3], [3, 3], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 3], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 1], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [2, 2], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"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, 0], [2, 2], [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, 0], [2, 1], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"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, 3], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 3], [3, 3], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 3], [3, 3], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 3], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 3], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 3, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25583/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[78,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[107,x,k[0]]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[49,x,k[0]]
F[14,x,k[0]] = F[102,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,1,k[0]]
F[16,x,k[0],k[1]] = (F[17,x,k[0]*k[1]]*k[0]-F[17,x,k[1]])/(-1+k[0])
F[17,x,k[0]] = F[0,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[49,x,k[0]]
F[20,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[82,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[77,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[5,x]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[49,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]+F[71,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]+F[51,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]*F[49,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[9,x,k[0]] = F[34,x,k[0]]+F[35,x]
F[35,x] = F[36,x]+F[38,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x,1]
F[41,x,k[0]] = F[42,x,k[0]]+F[9,x,k[0]]
F[43,x,k[0]] = F[42,x,k[0]]*F[49,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[50,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[23,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = k[0]*x
F[50,x,k[0]] = -k[0]*(F[44,x,1]-F[44,x,k[0]])/(-1+k[0])
F[51,x,k[0]] = k[0]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[4,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,1,k[0]]
F[55,x,k[0],k[1]] = (F[56,x,k[0]*k[1]]*k[0]-F[56,x,k[1]])/(-1+k[0])
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[49,x,k[0]]*F[58,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[64,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[63,x,k[0]]
F[63,x,k[0]] = -k[0]*(F[18,x,1]-F[18,x,k[0]])/(-1+k[0])
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[68,x,k[0]]
F[67,x,k[0]] = -k[0]*(F[60,x,1]-F[60,x,k[0]])/(-1+k[0])
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[4,x]*F[70,x,k[0]]
F[70,x,k[0]] = -k[0]*(F[46,x,1]-F[46,x,k[0]])/(-1+k[0])
F[72,x,k[0]] = F[71,x,k[0]]+F[75,x,k[0]]
F[72,x,k[0]] = F[31,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[49,x,k[0]]*F[54,x,k[0]]
F[76,x,k[0]] = F[49,x,k[0]]*F[75,x,k[0]]
F[76,x,k[0]] = F[11,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[21,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[4,x]*F[81,x,k[0]]
F[81,x,k[0]] = 1/(-1+k[0])*(F[42,x,k[0]]*k[0]-F[42,x,1])
F[82,x,k[0]] = F[83,x,k[0]]
F[84,x,k[0]] = F[83,x,k[0]]+F[9,x,k[0]]
F[85,x,k[0]] = F[100,x,k[0]]+F[84,x,k[0]]
F[86,x,k[0]] = F[85,x,k[0]]+F[98,x,k[0]]
F[87,x,k[0]] = F[4,x]*F[86,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[4,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]+F[91,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[91,x,k[0]] = k[0]*F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,1,k[0]]
F[95,x,k[0],k[1]] = (F[96,x,k[0]*k[1]]*k[0]-F[96,x,k[1]])/(-1+k[0])
F[96,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
F[97,x,k[0]] = F[20,x,k[0]]+F[42,x,k[0]]
F[98,x,k[0]] = k[0]*F[99,x,k[0]]
F[99,x,k[0]] = F[53,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]*F[4,x]
F[101,x,k[0]] = F[79,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[21,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[49,x,k[0]]
F[105,x,k[0]] = F[106,x,1,k[0]]
F[106,x,k[0],k[1]] = (F[42,x,k[0]*k[1]]*k[0]-F[42,x,k[1]])/(-1+k[0])
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[91,x,k[0]]
F[110,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \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 , y\right)+F_{78}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , 1, y\right)
F_{16}\! \left(x , y , z\right) = -\frac{-F_{17}\! \left(x , y z \right) y +F_{17}\! \left(x , z\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{5}\! \left(x \right)
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_{49}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x , 1\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = y x
F_{50}\! \left(x , y\right) = -\frac{y \left(F_{44}\! \left(x , 1\right)-F_{44}\! \left(x , y\right)\right)}{-1+y}
F_{51}\! \left(x , y\right) = y F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , 1, y\right)
F_{55}\! \left(x , y , z\right) = -\frac{-F_{56}\! \left(x , y z \right) y +F_{56}\! \left(x , z\right)}{-1+y}
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{y \left(F_{18}\! \left(x , 1\right)-F_{18}\! \left(x , y\right)\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = -\frac{y \left(F_{46}\! \left(x , 1\right)-F_{46}\! \left(x , y\right)\right)}{-1+y}
F_{72}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-F_{42}\! \left(x , y\right) y +F_{42}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = y F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , 1, y\right)
F_{95}\! \left(x , y , z\right) = -\frac{-F_{96}\! \left(x , y z \right) y +F_{96}\! \left(x , z\right)}{-1+y}
F_{96}\! \left(x , y\right) = -\frac{-F_{97}\! \left(x , y\right) y +F_{97}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = y F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , 1, y\right)
F_{106}\! \left(x , y , z\right) = -\frac{-F_{42}\! \left(x , y z \right) y +F_{42}\! \left(x , z\right)}{-1+y}
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_78(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_107(x, k_0) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_49(x, k_0))
Eq(F_14(x, k_0), F_102(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, 1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*k_1*F_17(x, k_0*k_1) + k_1*F_17(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_17(x, k_0), F_0(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_49(x, k_0))
Eq(F_20(x, k_0), F_17(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_82(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_77(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_5(x))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_49(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0) + F_71(x, k_0))
Eq(F_32(x, k_0), F_31(x, k_0) + F_51(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0)*F_49(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_9(x, k_0), F_34(x, k_0) + F_35(x))
Eq(F_35(x), F_36(x) + F_38(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x, 1))
Eq(F_41(x, k_0), F_42(x, k_0) + F_9(x, k_0))
Eq(F_43(x, k_0), F_42(x, k_0)*F_49(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_50(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_23(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), k_0*x)
Eq(F_50(x, k_0), -F_44(x, 1) + (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_51(x, k_0), k_0*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_4(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, 1, k_0))
Eq(F_55(x, k_0, k_1), (-k_0*k_1*F_56(x, k_0*k_1) + k_1*F_56(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_49(x, k_0)*F_58(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_64(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_63(x, k_0))
Eq(F_63(x, k_0), -F_18(x, 1) + (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_68(x, k_0))
Eq(F_67(x, k_0), -F_60(x, 1) + (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_4(x)*F_70(x, k_0))
Eq(F_70(x, k_0), -F_46(x, 1) + (k_0*F_46(x, k_0) - F_46(x, 1))/(k_0 - 1))
Eq(F_72(x, k_0), F_71(x, k_0) + F_75(x, k_0))
Eq(F_72(x, k_0), F_31(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_49(x, k_0)*F_54(x, k_0))
Eq(F_76(x, k_0), F_49(x, k_0)*F_75(x, k_0))
Eq(F_76(x, k_0), F_11(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_21(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_4(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (k_0*F_42(x, k_0) - F_42(x, 1))/(k_0 - 1))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_84(x, k_0), F_83(x, k_0) + F_9(x, k_0))
Eq(F_85(x, k_0), F_100(x, k_0) + F_84(x, k_0))
Eq(F_86(x, k_0), F_85(x, k_0) + F_98(x, k_0))
Eq(F_87(x, k_0), F_4(x)*F_86(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_4(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0) + F_91(x, k_0))
Eq(F_90(x, k_0), (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), k_0*F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, 1, k_0))
Eq(F_95(x, k_0, k_1), (-k_0*k_1*F_96(x, k_0*k_1) + k_1*F_96(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_96(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_20(x, k_0) + F_42(x, k_0))
Eq(F_98(x, k_0), k_0*F_99(x, k_0))
Eq(F_99(x, k_0), F_53(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0)*F_4(x))
Eq(F_101(x, k_0), F_79(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_21(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_49(x, k_0))
Eq(F_105(x, k_0), F_106(x, 1, k_0))
Eq(F_106(x, k_0, k_1), (-k_0*k_1*F_42(x, k_0*k_1) + k_1*F_42(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_91(x, k_0))
Eq(F_110(x, k_0), -F_34(x, 1) + (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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": "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 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], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, 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"pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"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], [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": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 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], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], 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{"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"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], [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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 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"pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 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": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"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, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"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]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"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, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"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]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}]}
Specification 4
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/25828/
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[49,x]+F[5,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[46,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[38,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[45,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[37,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[26,x,k[0],k[1]]+F[30,x,k[1]]
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[25,x,k[0]]*k[0]-F[25,x,k[1]]*k[1])/(-k[1]+k[0])
F[25,x,k[0]] = F[15,x,1,k[0]]
F[26,x,k[0],k[1]] = F[19,x,k[0]]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = (F[28,x,k[0]]*k[0]-F[28,x,k[1]]*k[1])/(-k[1]+k[0])
F[28,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[29,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[30,x,k[0]] = F[19,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[36,x,k[0]]
F[33,x,k[0]] = F[3,x]*F[34,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[29,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[19,x,k[0]]*F[28,x,k[0]]
F[36,x,k[0]] = F[19,x,k[0]]*F[32,x,k[0]]
F[37,x,k[0],k[1]] = F[19,x,k[0]]*F[22,x,k[1],k[0]]
F[38,x,k[0],k[1]] = F[3,x]*F[39,x,k[0],k[1]]
F[39,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[40,x,k[0],k[1]] = F[19,x,k[0]]*F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,1,k[0],k[1]]
F[42,x,k[0],k[1],k[2]] = (F[43,x,k[0]*k[1],k[2]]*k[0]-F[43,x,k[1],k[2]])/(-1+k[0])
F[43,x,k[0],k[1]] = 1/(-1+k[0])*(F[44,x,k[0],k[1]]*k[0]-F[44,x,1,k[1]])
F[44,x,k[0],k[1]] = (F[32,x,k[0]]*k[0]-F[32,x,k[1]]*k[1])/(-k[1]+k[0])
F[45,x,k[0],k[1]] = F[19,x,k[0]]*F[43,x,k[1],k[0]]
F[46,x,k[0]] = F[19,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,1,k[0]]
F[48,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[49,x] = F[3,x]*F[50,x]
F[50,x] = F[51,x,1]
F[51,x,k[0]] = F[1,x]+F[52,x,k[0]]+F[54,x,k[0]]+F[8,x,k[0]]
F[52,x,k[0]] = F[3,x]*F[53,x,k[0]]
F[53,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[54,x,k[0]] = F[19,x,k[0]]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,1,k[0]]
F[56,x,k[0],k[1]] = (F[31,x,k[0]*k[1]]*k[0]-F[31,x,k[1]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{5}\! \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_{46}\! \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_{38}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \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_{37}\! \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_{26}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}\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) = \frac{F_{25}\! \left(x , y_{0}\right) y_{0}-F_{25}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{28}\! \left(x , y_{0}\right) y_{0}-F_{28}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{30}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = -\frac{-F_{32}\! \left(x , y_{0}\right) y_{0}+F_{32}\! \left(x , 1\right)}{-1+y_{0}}
F_{32}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \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_{40}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , 1, y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{43}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{43}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}
F_{43}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{32}\! \left(x , y_{0}\right) y_{0}-F_{32}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{1}, y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , 1, y_{0}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{49}\! \left(x \right) = F_{3}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{51}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{53}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = -\frac{-F_{51}\! \left(x , y_{0}\right) y_{0}+F_{51}\! \left(x , 1\right)}{-1+y_{0}}
F_{54}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , 1, y_{0}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{31}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{31}\! \left(x , y_{1}\right)}{-1+y_{0}}
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_49(x) + F_5(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_46(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_38(x, k_0, k_1) + F_40(x, k_0, k_1) + F_45(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_37(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_26(x, k_0, k_1) + F_30(x, k_1))
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), (-k_0*F_25(x, k_0) + k_1*F_25(x, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0), F_15(x, 1, k_0))
Eq(F_26(x, k_0, k_1), F_19(x, k_0)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), (-k_0*F_28(x, k_0) + k_1*F_28(x, k_1))/(-k_0 + k_1))
Eq(F_28(x, k_0), F_1(x) + F_10(x, k_0) + F_29(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_30(x, k_0), F_19(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_36(x, k_0))
Eq(F_33(x, k_0), F_3(x)*F_34(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_10(x, k_0) + F_29(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_19(x, k_0)*F_28(x, k_0))
Eq(F_36(x, k_0), F_19(x, k_0)*F_32(x, k_0))
Eq(F_37(x, k_0, k_1), F_19(x, k_0)*F_22(x, k_1, k_0))
Eq(F_38(x, k_0, k_1), F_3(x)*F_39(x, k_0, k_1))
Eq(F_39(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_40(x, k_0, k_1), F_19(x, k_0)*F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, 1, k_0, k_1))
Eq(F_42(x, k_0, k_1, k_2), (-k_0*k_1*F_43(x, k_0*k_1, k_2) + k_1*F_43(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_43(x, k_0, k_1), (k_0*F_44(x, k_0, k_1) - F_44(x, 1, k_1))/(k_0 - 1))
Eq(F_44(x, k_0, k_1), (-k_0*F_32(x, k_0) + k_1*F_32(x, k_1))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1), F_19(x, k_0)*F_43(x, k_1, k_0))
Eq(F_46(x, k_0), F_19(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, 1, k_0))
Eq(F_48(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_49(x), F_3(x)*F_50(x))
Eq(F_50(x), F_51(x, 1))
Eq(F_51(x, k_0), F_1(x) + F_52(x, k_0) + F_54(x, k_0) + F_8(x, k_0))
Eq(F_52(x, k_0), F_3(x)*F_53(x, k_0))
Eq(F_53(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_54(x, k_0), F_19(x, k_0)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, 1, k_0))
Eq(F_56(x, k_0, k_1), (-k_0*k_1*F_31(x, k_0*k_1) + k_1*F_31(x, k_1))/(-k_0*k_1 + k_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, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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]]}], 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[0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 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": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0], [0, 0]]}, {"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, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {"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]]}], "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]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25917/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[78,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x]
F[11,x,k[0]] = F[107,x,k[0]]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[49,x,k[0]]
F[14,x,k[0]] = F[102,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,1,k[0]]
F[16,x,k[0],k[1]] = (F[17,x,k[0]*k[1]]*k[0]-F[17,x,k[1]])/(-1+k[0])
F[17,x,k[0]] = F[0,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[49,x,k[0]]
F[20,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[82,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[77,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[5,x]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[49,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]+F[71,x,k[0]]
F[32,x,k[0]] = F[31,x,k[0]]+F[51,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]*F[49,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[9,x,k[0]] = F[34,x,k[0]]+F[35,x]
F[35,x] = F[36,x]+F[38,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x,1]
F[41,x,k[0]] = F[42,x,k[0]]+F[9,x,k[0]]
F[43,x,k[0]] = F[42,x,k[0]]*F[49,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[50,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[23,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = k[0]*x
F[50,x,k[0]] = -k[0]*(F[44,x,1]-F[44,x,k[0]])/(-1+k[0])
F[51,x,k[0]] = k[0]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[4,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,1,k[0]]
F[55,x,k[0],k[1]] = (F[56,x,k[0]*k[1]]*k[0]-F[56,x,k[1]])/(-1+k[0])
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[49,x,k[0]]*F[58,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[64,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[63,x,k[0]]
F[63,x,k[0]] = -k[0]*(F[18,x,1]-F[18,x,k[0]])/(-1+k[0])
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[4,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[68,x,k[0]]
F[67,x,k[0]] = -k[0]*(F[60,x,1]-F[60,x,k[0]])/(-1+k[0])
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[4,x]*F[70,x,k[0]]
F[70,x,k[0]] = -k[0]*(F[46,x,1]-F[46,x,k[0]])/(-1+k[0])
F[72,x,k[0]] = F[71,x,k[0]]+F[75,x,k[0]]
F[72,x,k[0]] = F[31,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[49,x,k[0]]*F[54,x,k[0]]
F[76,x,k[0]] = F[49,x,k[0]]*F[75,x,k[0]]
F[76,x,k[0]] = F[11,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[21,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[4,x]*F[81,x,k[0]]
F[81,x,k[0]] = 1/(-1+k[0])*(F[42,x,k[0]]*k[0]-F[42,x,1])
F[82,x,k[0]] = F[83,x,k[0]]
F[84,x,k[0]] = F[83,x,k[0]]+F[9,x,k[0]]
F[85,x,k[0]] = F[100,x,k[0]]+F[84,x,k[0]]
F[86,x,k[0]] = F[85,x,k[0]]+F[98,x,k[0]]
F[87,x,k[0]] = F[4,x]*F[86,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[4,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]+F[91,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[41,x,k[0]]*k[0]-F[41,x,1])
F[91,x,k[0]] = k[0]*F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[95,x,1,k[0]]
F[95,x,k[0],k[1]] = (F[96,x,k[0]*k[1]]*k[0]-F[96,x,k[1]])/(-1+k[0])
F[96,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
F[97,x,k[0]] = F[20,x,k[0]]+F[42,x,k[0]]
F[98,x,k[0]] = k[0]*F[99,x,k[0]]
F[99,x,k[0]] = F[53,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]*F[4,x]
F[101,x,k[0]] = F[79,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]+F[21,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[49,x,k[0]]
F[105,x,k[0]] = F[106,x,1,k[0]]
F[106,x,k[0],k[1]] = (F[42,x,k[0]*k[1]]*k[0]-F[42,x,k[1]])/(-1+k[0])
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[91,x,k[0]]
F[110,x,k[0]] = -k[0]*(F[34,x,1]-F[34,x,k[0]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \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 , y\right)+F_{78}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , 1, y\right)
F_{16}\! \left(x , y , z\right) = -\frac{-F_{17}\! \left(x , y z \right) y +F_{17}\! \left(x , z\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{5}\! \left(x \right)
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_{49}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x , 1\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = y x
F_{50}\! \left(x , y\right) = -\frac{y \left(F_{44}\! \left(x , 1\right)-F_{44}\! \left(x , y\right)\right)}{-1+y}
F_{51}\! \left(x , y\right) = y F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , 1, y\right)
F_{55}\! \left(x , y , z\right) = -\frac{-F_{56}\! \left(x , y z \right) y +F_{56}\! \left(x , z\right)}{-1+y}
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{y \left(F_{18}\! \left(x , 1\right)-F_{18}\! \left(x , y\right)\right)}{-1+y}
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = -\frac{y \left(F_{46}\! \left(x , 1\right)-F_{46}\! \left(x , y\right)\right)}{-1+y}
F_{72}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-F_{42}\! \left(x , y\right) y +F_{42}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}
F_{91}\! \left(x , y\right) = y F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , 1, y\right)
F_{95}\! \left(x , y , z\right) = -\frac{-F_{96}\! \left(x , y z \right) y +F_{96}\! \left(x , z\right)}{-1+y}
F_{96}\! \left(x , y\right) = -\frac{-F_{97}\! \left(x , y\right) y +F_{97}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = y F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , 1, y\right)
F_{106}\! \left(x , y , z\right) = -\frac{-F_{42}\! \left(x , y z \right) y +F_{42}\! \left(x , z\right)}{-1+y}
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_78(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x))
Eq(F_11(x, k_0), F_107(x, k_0) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_49(x, k_0))
Eq(F_14(x, k_0), F_102(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, 1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*k_1*F_17(x, k_0*k_1) + k_1*F_17(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_17(x, k_0), F_0(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_49(x, k_0))
Eq(F_20(x, k_0), F_17(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_82(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_77(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_5(x))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_49(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0) + F_71(x, k_0))
Eq(F_32(x, k_0), F_31(x, k_0) + F_51(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0)*F_49(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_9(x, k_0), F_34(x, k_0) + F_35(x))
Eq(F_35(x), F_36(x) + F_38(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x, 1))
Eq(F_41(x, k_0), F_42(x, k_0) + F_9(x, k_0))
Eq(F_43(x, k_0), F_42(x, k_0)*F_49(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_50(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_23(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), k_0*x)
Eq(F_50(x, k_0), -F_44(x, 1) + (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_51(x, k_0), k_0*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_4(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, 1, k_0))
Eq(F_55(x, k_0, k_1), (-k_0*k_1*F_56(x, k_0*k_1) + k_1*F_56(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_49(x, k_0)*F_58(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_64(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_63(x, k_0))
Eq(F_63(x, k_0), -F_18(x, 1) + (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_4(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_68(x, k_0))
Eq(F_67(x, k_0), -F_60(x, 1) + (k_0*F_60(x, k_0) - F_60(x, 1))/(k_0 - 1))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_4(x)*F_70(x, k_0))
Eq(F_70(x, k_0), -F_46(x, 1) + (k_0*F_46(x, k_0) - F_46(x, 1))/(k_0 - 1))
Eq(F_72(x, k_0), F_71(x, k_0) + F_75(x, k_0))
Eq(F_72(x, k_0), F_31(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_49(x, k_0)*F_54(x, k_0))
Eq(F_76(x, k_0), F_49(x, k_0)*F_75(x, k_0))
Eq(F_76(x, k_0), F_11(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_21(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_4(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (k_0*F_42(x, k_0) - F_42(x, 1))/(k_0 - 1))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_84(x, k_0), F_83(x, k_0) + F_9(x, k_0))
Eq(F_85(x, k_0), F_100(x, k_0) + F_84(x, k_0))
Eq(F_86(x, k_0), F_85(x, k_0) + F_98(x, k_0))
Eq(F_87(x, k_0), F_4(x)*F_86(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_4(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0) + F_91(x, k_0))
Eq(F_90(x, k_0), (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), k_0*F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_95(x, 1, k_0))
Eq(F_95(x, k_0, k_1), (-k_0*k_1*F_96(x, k_0*k_1) + k_1*F_96(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_96(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_20(x, k_0) + F_42(x, k_0))
Eq(F_98(x, k_0), k_0*F_99(x, k_0))
Eq(F_99(x, k_0), F_53(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0)*F_4(x))
Eq(F_101(x, k_0), F_79(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_21(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_49(x, k_0))
Eq(F_105(x, k_0), F_106(x, 1, k_0))
Eq(F_106(x, k_0, k_1), (-k_0*k_1*F_42(x, k_0*k_1) + k_1*F_42(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_91(x, k_0))
Eq(F_110(x, k_0), -F_34(x, 1) + (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 4, 2, 1], "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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "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": "ReverseRule", "original_rule": 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