01243_10243_12043_12403
Counting sequence:
1, 1, 2, 6, 24, 116, 634, 3766, 23741, 156468, 1067369, 7483996, 53664321, 392040003, 2909452383, 21884916567, 166551065975, 1280512620450, 9934195134525, 77689117933037, 611930053106215, 4851186505864916, 38684210845126113, 310120428595937231, 2498268285651016096, 20215567071520197919, 164254734667129462396, 1339675393546933285469, 10965049298886799954903, 90041637834640374883253, 741654290214448258101071, 6126297811748128598919680, 50740489165764777308783359, 421308232463664095231465294, 3506462611205713089459951745, 29248482535366630603008370458, 244482756905203149020963722785, 2047643143738967563552266236973, 17182082792502725963730260969026, 144434440501264415051811390126680, 1216186735748678802851893081793069, 10257187863843721196471656999394135, 86640612412595909291745428547792411, 732906945577944433406857699082234281, 6208424219822201361998267737403216846, 52661375977166084204546124653577182604, 447255935684017108388625484740532988703, 3803203444915071259527345052685522456746, 32378033087018347390392239192654717193333, 275954902398663209557243883486813340743266, 2354469391627661266740642953323635043284670, 20109300171792243012971994368971791815633614, 171922448880895840675846534812830965778241870, 1471240516463440874127180092726399603931292665, 12601866080071439279924865219530180318591813729, 108036777244959394038970461986031836628306772489, 927001036564524244822311044817878315400473217356, 7960633767556633228580087411710857389737898674930, 68416610842874611844489643554440035789140745993510, 588450921630505327496541263808014414838439984408942, 5065036671343970433152959935880736303926915912442155, 43628273025734688197256222952538157539422854900413492, 376059418481900952371573242789223354586899577627839256, 3243682631505151699809865438260458676362481510458214006, 27996551841292465392753525389595416292471579848919698504, 241794450604315982053125752071669641971595465730379583893, 2089562628141535838679078682693211687144982882759103067805, 18068570406389751980569538825223852938407832548067064834705, 156330579378172150472695903185452459719856468135487749839243, 1353345133858878758193161870207915172936535052847002723378348, 11722243174156162471268723324029615486755366744498849377611501, 101588316273232730638023676618207211152278492793010988921987543, 880848650861955788259329905500383238394022731506377030136628782, 7641475089685946107814651703650491345172619932410201735981673313, 66323222072972065141993763933713230496337169725453057987806052581, 575918331852814533983226609596399770521987125584470509779073018086, 5003312692925093915381146242637471457222985802676610407186766161529, 43486118352356083135667570417786163406108667619641685837299639058588, 378124564805618438120406039321925736635590874128653468795223325446359, 3289315854012506462815201652423714656291310433358047994568960005085530, 28625828723900943405444943194205786833105856912733670171511114633285604, 249222874333138774088148177706012878347523643841875804397063328443565560, 2170654861291933318826315219322200439163627909824401852544606102481515528, 18913092574508008677004395991236769570364197531001182590659967797922171649, 164853899036453453649108645935268622631060784347109969513178200178180538135, 1437463891881711658560763090797610357968675126655178795878340675110081267423, 12538684931335907535953052398698583046513663030568646810555194337364361505294, 109410944144533657956561447077409012374608416375304673453694478376559958649492, 955036128328298335110203186292324675390543275497566761521942928230162964238149, 8339225938187052146805147087302741798069502637352349059264601140428142323172526, 72840906371787494015097318265008732528424191451474641064691095948528737414622558, 636451722420547179417321487175325051648535941437713683395750296904208164201496424, 5562795322099889796114542592840968634273382851361647558896499518267079580373186384, 48635708617856888488433837233873854813030915622962157951270498127132516206827684177, 425352631339926648257702509587236012787660980241867010444701165121088141278281087622, 3721105252522213198373820329312024477568823429832371037603741057817353922344413549612, 32562749710697712231588661296559766377247018699970173156732863445160606743822900006597, 285032175721780797673391639024787203616184139100751075838475557487084064515425549909613, 2495674247001717023324182742847681525207670322430567540704576330203329601939907074599448, 21857509128501027803286557875353618870610378851327329615538079352860529959914605482365229, 191482831897664505045326992267713149076871125074170701054411142363904356619126553435832391
Specification 1
Strategy pack name: row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24877/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[88,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[6,x]+F[85,x]+F[86,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[79,x,k[0]]+F[81,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[15,x,1,k[0]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[74,x,k[1]]
F[16,x,k[0],k[1]] = F[11,x]*F[17,x,k[0],k[1]]
F[17,x,k[0],k[1]] = F[18,x,1,k[0],k[1]]
F[18,x,k[0],k[1],k[2]] = F[1,x]+F[19,x,k[0],k[1],k[2]]+F[21,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[35,x,k[0],k[2]]+F[36,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = F[11,x]*F[20,x,k[0],k[1],k[2]]
F[20,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[18,x,k[0],k[1],k[2]]*k[0]-F[18,x,1,k[1],k[2]])
F[21,x,k[0],k[1],k[2]] = F[11,x]*F[22,x,k[0],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = (F[23,x,k[0],k[2]]*k[0]-F[23,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[34,x,k[0]]
F[25,x,k[0],k[1],k[2]] = (F[26,x,k[0],1,k[2]]*k[0]-F[26,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = (F[27,x,k[0],k[1]]*k[0]*k[1]-F[27,x,k[0],k[2]/k[0]]*k[2])/(k[0]*k[1]-k[2])
F[27,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[11,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[28,x,k[0],k[1]]*k[0]-F[28,x,1,k[1]])
F[31,x,k[0],k[1]] = F[11,x]*F[23,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]*F[34,x,k[0]]
F[33,x,k[0],k[1]] = (F[27,x,k[0],1]*k[0]-F[27,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[34,x,k[0]] = k[0]*x
F[35,x,k[0],k[1]] = F[28,x,k[0],k[1]]*F[34,x,k[1]]
F[36,x,k[0],k[1],k[2]] = F[34,x,k[1]]*F[37,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = F[1,x]+F[35,x,k[0],k[2]]+F[36,x,k[0],k[1],k[2]]+F[38,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]+F[44,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1],k[2]] = F[11,x]*F[39,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[37,x,k[0],k[1],k[2]]*k[0]-F[37,x,1,k[1],k[2]])
F[40,x,k[0],k[1],k[2]] = F[41,x,k[0],k[1],1,k[2]]
F[41,x,k[0],k[1],k[2],k[3]] = F[42,x,k[0],k[1],k[1]*k[2],k[3]]
F[42,x,k[0],k[1],k[2],k[3]] = F[11,x]*F[43,x,k[0],k[1],k[2],k[3]]
F[43,x,k[0],k[1],k[2],k[3]] = (F[22,x,k[0],k[2],k[3]]*k[0]-F[22,x,k[1],k[2],k[3]]*k[1])/(-k[1]+k[0])
F[44,x,k[0],k[1],k[2]] = F[45,x,k[0],k[1],1,k[2]]
F[45,x,k[0],k[1],k[2],k[3]] = F[46,x,k[0],k[1],k[1]*k[2],k[3]]
F[46,x,k[0],k[1],k[2],k[3]] = F[34,x,k[0]]*F[47,x,k[0],k[1],k[2],k[3]]
F[47,x,k[0],k[1],k[2],k[3]] = (F[25,x,k[0],k[1],k[3]]*k[1]-F[25,x,k[0],k[2],k[3]]*k[2])/(-k[2]+k[1])
F[48,x,k[0],k[1],k[2]] = F[34,x,k[1]]*F[49,x,k[0],k[1],k[2]]
F[49,x,k[0],k[1],k[2]] = F[50,x,k[0],k[1],1,k[2]]
F[50,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[2])*(F[51,x,k[0],k[1],k[2],k[3]]*k[2]-F[51,x,k[0],k[1],1,k[3]])
F[51,x,k[0],k[1],k[2],k[3]] = F[1,x]+F[35,x,k[0],k[3]]+F[41,x,k[0],k[1],k[2],k[3]]+F[45,x,k[0],k[1],k[2],k[3]]+F[52,x,k[0],k[1],k[2],k[3]]+F[54,x,k[0],k[1],k[2],k[3]]+F[56,x,k[0],k[1],k[2],k[3]]
F[52,x,k[0],k[1],k[2],k[3]] = F[11,x]*F[53,x,k[0],k[1],k[2],k[3]]
F[53,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[0])*(F[51,x,k[0],k[1],k[2],k[3]]*k[0]-F[51,x,1,k[1],k[2],k[3]])
F[54,x,k[0],k[1],k[2],k[3]] = F[34,x,k[1]]*F[55,x,k[0],k[1],k[2],k[3]]
F[55,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[2])*(F[51,x,k[0],k[1],k[2],k[3]]*k[2]-F[51,x,k[0],k[1],1,k[3]])
F[56,x,k[0],k[1],k[2],k[3]] = F[34,x,k[2]]*F[51,x,k[0],k[1],k[2],k[3]]
F[57,x,k[0],k[1]] = F[11,x]*F[58,x,k[0],k[1]]
F[58,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[59,x,k[0],k[1]] = F[34,x,k[0]]*F[60,x,k[0],k[1]]
F[60,x,k[0],k[1]] = F[61,x,1,k[0],k[1]]
F[61,x,k[0],k[1],k[2]] = F[62,x,k[0]*k[1],k[1],k[2]]
F[63,x,k[0],k[1],k[2]] = F[62,x,k[0],k[0]*k[1],k[2]]
F[63,x,k[0],k[1],k[2]] = F[1,x]+F[64,x,k[0],k[1],k[2]]+F[66,x,k[0],k[1],k[2]]+F[69,x,k[0],k[1],k[2]]+F[72,x,k[0],k[1],k[2]]+F[74,x,k[2]]
F[64,x,k[0],k[1],k[2]] = F[11,x]*F[65,x,k[0],k[1],k[2]]
F[65,x,k[0],k[1],k[2]] = F[51,x,1,k[0],k[1],k[2]]
F[66,x,k[0],k[1],k[2]] = F[67,x,k[0],k[0]*k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = F[11,x]*F[68,x,k[0],k[1],k[2]]
F[68,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[62,x,k[0],k[1],k[2]]*k[0]-F[62,x,1,k[1],k[2]])
F[69,x,k[0],k[1],k[2]] = F[70,x,k[0],k[0]*k[1],k[2]]
F[70,x,k[0],k[1],k[2]] = F[34,x,k[0]]*F[71,x,k[0],k[1],k[2]]
F[71,x,k[0],k[1],k[2]] = (F[63,x,k[0],1,k[2]]*k[0]-F[63,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[72,x,k[0],k[1],k[2]] = F[73,x,k[0],k[0]*k[1],k[2]]
F[73,x,k[0],k[1],k[2]] = F[34,x,k[1]]*F[62,x,k[0],k[1],k[2]]
F[74,x,k[0]] = F[34,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[1,x]+F[74,x,k[0]]+F[76,x,k[0]]+F[78,x,k[0]]
F[76,x,k[0]] = F[11,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[28,x,1,k[0]]
F[78,x,k[0]] = F[11,x]*F[14,x,k[0]]
F[79,x,k[0]] = F[11,x]*F[80,x,k[0]]
F[80,x,k[0]] = 1/(-1+k[0])*(F[77,x,k[0]]*k[0]-F[77,x,1])
F[81,x,k[0]] = F[34,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,1,k[0]]
F[83,x,k[0],k[1]] = (-F[84,x,1,k[1]]*k[1]+F[84,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[84,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[85,x] = F[78,x,1]
F[86,x] = F[11,x]*F[87,x]
F[87,x] = F[77,x,1]
F[88,x] = F[11,x]*F[89,x]
F[89,x] = F[90,x,1]
F[90,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[91,x,k[0]]+F[93,x,k[0]]
F[91,x,k[0]] = F[11,x]*F[92,x,k[0]]
F[92,x,k[0]] = 1/(-1+k[0])*(F[90,x,k[0]]*k[0]-F[90,x,1])
F[93,x,k[0]] = F[34,x,k[0]]*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[1]]
F[96,x,k[0],k[1]] = F[1,x]+F[102,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[97,x,k[0],k[1]]+F[99,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[11,x]*F[98,x,k[0],k[1]]
F[98,x,k[0],k[1]] = 1/(-1+k[0])*(F[96,x,k[0],k[1]]*k[0]-F[96,x,1,k[1]])
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]*F[34,x,k[0]]
F[100,x,k[0],k[1]] = (F[101,x,k[0],1]*k[0]-F[101,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[101,x,k[0],k[1]] = F[96,x,k[0],k[0]*k[1]]
F[102,x,k[0],k[1]] = F[34,x,k[1]]*F[96,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{88}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y_{0}\right) = -\frac{-F_{8}\! \left(x , y_{0}\right) y_{0}+F_{8}\! \left(x , 1\right)}{-1+y_{0}}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = -\frac{-F_{14}\! \left(x , y_{0}\right) y_{0}+F_{14}\! \left(x , 1\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, y_{0}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , 1, y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{0}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{23}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{23}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{14}\! \left(x , y_{0}\right) y_{0}-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{34}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{26}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{27}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{27}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{27}\! \left(x , y_{0}, 1\right) y_{0}-F_{27}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{34}\! \left(x , y_{0}\right) = y_{0} x
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}\right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{37}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{41}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}, y_{3}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{11}\! \left(x \right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{22}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{45}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{46}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}, y_{3}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{34}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{25}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{1}-F_{25}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{2}}{-y_{2}+y_{1}}
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}\right) F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{50}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{2}+F_{51}\! \left(x , y_{0}, y_{1}, 1, y_{3}\right)}{-1+y_{2}}
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}, y_{3}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{56}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{11}\! \left(x \right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}+F_{51}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{34}\! \left(x , y_{1}\right) F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{2}+F_{51}\! \left(x , y_{0}, y_{1}, 1, y_{3}\right)}{-1+y_{2}}
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{34}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \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_{59}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{61}\! \left(x , 1, y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{2}\right)
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{51}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{67}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{62}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{70}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{0}\right) F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{63}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{63}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{73}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{74}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{74}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{28}\! \left(x , 1, y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{14}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = -\frac{-F_{77}\! \left(x , y_{0}\right) y_{0}+F_{77}\! \left(x , 1\right)}{-1+y_{0}}
F_{81}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{83}\! \left(x , 1, y_{0}\right)
F_{83}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{84}\! \left(x , 1, y_{1}\right) y_{1}-F_{84}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{85}\! \left(x \right) = F_{78}\! \left(x , 1\right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x , 1\right)
F_{90}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = -\frac{-F_{90}\! \left(x , y_{0}\right) y_{0}+F_{90}\! \left(x , 1\right)}{-1+y_{0}}
F_{93}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{95}\! \left(x , 1, y_{0}\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{96}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{98}\! \left(x , y_{0}, y_{1}\right)
F_{98}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{96}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{96}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{99}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{101}\! \left(x , y_{0}, 1\right)-y_{1} F_{101}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{101}\! \left(x , y_{0}, y_{1}\right) = F_{96}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{102}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{1}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_88(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_6(x) + F_85(x) + F_86(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_79(x, k_0) + F_81(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_15(x, 1, k_0))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1) + F_74(x, k_1))
Eq(F_16(x, k_0, k_1), F_11(x)*F_17(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, 1, k_0, k_1))
Eq(F_18(x, k_0, k_1, k_2), F_1(x) + F_19(x, k_0, k_1, k_2) + F_21(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2) + F_35(x, k_0, k_2) + F_36(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), F_11(x)*F_20(x, k_0, k_1, k_2))
Eq(F_20(x, k_0, k_1, k_2), (k_0*F_18(x, k_0, k_1, k_2) - F_18(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_21(x, k_0, k_1, k_2), F_11(x)*F_22(x, k_0, k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*F_23(x, k_0, k_2) + k_1*F_23(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_34(x, k_0))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_26(x, k_0, 1, k_2) + k_1*F_26(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), (-k_0*k_1*F_27(x, k_0, k_1) + k_2*F_27(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1) + F_32(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_11(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_28(x, k_0, k_1) - F_28(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), F_11(x)*F_23(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1)*F_34(x, k_0))
Eq(F_33(x, k_0, k_1), (-k_0*F_27(x, k_0, 1) + k_1*F_27(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_34(x, k_0), k_0*x)
Eq(F_35(x, k_0, k_1), F_28(x, k_0, k_1)*F_34(x, k_1))
Eq(F_36(x, k_0, k_1, k_2), F_34(x, k_1)*F_37(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), F_1(x) + F_35(x, k_0, k_2) + F_36(x, k_0, k_1, k_2) + F_38(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2) + F_44(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1, k_2), F_11(x)*F_39(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), (k_0*F_37(x, k_0, k_1, k_2) - F_37(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_40(x, k_0, k_1, k_2), F_41(x, k_0, k_1, 1, k_2))
Eq(F_41(x, k_0, k_1, k_2, k_3), F_42(x, k_0, k_1, k_1*k_2, k_3))
Eq(F_42(x, k_0, k_1, k_2, k_3), F_11(x)*F_43(x, k_0, k_1, k_2, k_3))
Eq(F_43(x, k_0, k_1, k_2, k_3), (-k_0*F_22(x, k_0, k_2, k_3) + k_1*F_22(x, k_1, k_2, k_3))/(-k_0 + k_1))
Eq(F_44(x, k_0, k_1, k_2), F_45(x, k_0, k_1, 1, k_2))
Eq(F_45(x, k_0, k_1, k_2, k_3), F_46(x, k_0, k_1, k_1*k_2, k_3))
Eq(F_46(x, k_0, k_1, k_2, k_3), F_34(x, k_0)*F_47(x, k_0, k_1, k_2, k_3))
Eq(F_47(x, k_0, k_1, k_2, k_3), (-k_1*F_25(x, k_0, k_1, k_3) + k_2*F_25(x, k_0, k_2, k_3))/(-k_1 + k_2))
Eq(F_48(x, k_0, k_1, k_2), F_34(x, k_1)*F_49(x, k_0, k_1, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_50(x, k_0, k_1, 1, k_2))
Eq(F_50(x, k_0, k_1, k_2, k_3), (-k_2*F_51(x, k_0, k_1, k_2, k_3) + F_51(x, k_0, k_1, 1, k_3))/(1 - k_2))
Eq(F_51(x, k_0, k_1, k_2, k_3), F_1(x) + F_35(x, k_0, k_3) + F_41(x, k_0, k_1, k_2, k_3) + F_45(x, k_0, k_1, k_2, k_3) + F_52(x, k_0, k_1, k_2, k_3) + F_54(x, k_0, k_1, k_2, k_3) + F_56(x, k_0, k_1, k_2, k_3))
Eq(F_52(x, k_0, k_1, k_2, k_3), F_11(x)*F_53(x, k_0, k_1, k_2, k_3))
Eq(F_53(x, k_0, k_1, k_2, k_3), (k_0*F_51(x, k_0, k_1, k_2, k_3) - F_51(x, 1, k_1, k_2, k_3))/(k_0 - 1))
Eq(F_54(x, k_0, k_1, k_2, k_3), F_34(x, k_1)*F_55(x, k_0, k_1, k_2, k_3))
Eq(F_55(x, k_0, k_1, k_2, k_3), (k_2*F_51(x, k_0, k_1, k_2, k_3) - F_51(x, k_0, k_1, 1, k_3))/(k_2 - 1))
Eq(F_56(x, k_0, k_1, k_2, k_3), F_34(x, k_2)*F_51(x, k_0, k_1, k_2, k_3))
Eq(F_57(x, k_0, k_1), F_11(x)*F_58(x, k_0, k_1))
Eq(F_58(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_59(x, k_0, k_1), F_34(x, k_0)*F_60(x, k_0, k_1))
Eq(F_60(x, k_0, k_1), F_61(x, 1, k_0, k_1))
Eq(F_61(x, k_0, k_1, k_2), F_62(x, k_0*k_1, k_1, k_2))
Eq(F_63(x, k_0, k_1, k_2), F_62(x, k_0, k_0*k_1, k_2))
Eq(F_63(x, k_0, k_1, k_2), F_1(x) + F_64(x, k_0, k_1, k_2) + F_66(x, k_0, k_1, k_2) + F_69(x, k_0, k_1, k_2) + F_72(x, k_0, k_1, k_2) + F_74(x, k_2))
Eq(F_64(x, k_0, k_1, k_2), F_11(x)*F_65(x, k_0, k_1, k_2))
Eq(F_65(x, k_0, k_1, k_2), F_51(x, 1, k_0, k_1, k_2))
Eq(F_66(x, k_0, k_1, k_2), F_67(x, k_0, k_0*k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), F_11(x)*F_68(x, k_0, k_1, k_2))
Eq(F_68(x, k_0, k_1, k_2), (k_0*F_62(x, k_0, k_1, k_2) - F_62(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_69(x, k_0, k_1, k_2), F_70(x, k_0, k_0*k_1, k_2))
Eq(F_70(x, k_0, k_1, k_2), F_34(x, k_0)*F_71(x, k_0, k_1, k_2))
Eq(F_71(x, k_0, k_1, k_2), (-k_0*F_63(x, k_0, 1, k_2) + k_1*F_63(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_72(x, k_0, k_1, k_2), F_73(x, k_0, k_0*k_1, k_2))
Eq(F_73(x, k_0, k_1, k_2), F_34(x, k_1)*F_62(x, k_0, k_1, k_2))
Eq(F_74(x, k_0), F_34(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_1(x) + F_74(x, k_0) + F_76(x, k_0) + F_78(x, k_0))
Eq(F_76(x, k_0), F_11(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_28(x, 1, k_0))
Eq(F_78(x, k_0), F_11(x)*F_14(x, k_0))
Eq(F_79(x, k_0), F_11(x)*F_80(x, k_0))
Eq(F_80(x, k_0), (k_0*F_77(x, k_0) - F_77(x, 1))/(k_0 - 1))
Eq(F_81(x, k_0), F_34(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, 1, k_0))
Eq(F_83(x, k_0, k_1), (-k_0*F_84(x, k_0/k_1, k_1) + k_1*F_84(x, 1, k_1))/(-k_0 + k_1))
Eq(F_84(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_85(x), F_78(x, 1))
Eq(F_86(x), F_11(x)*F_87(x))
Eq(F_87(x), F_77(x, 1))
Eq(F_88(x), F_11(x)*F_89(x))
Eq(F_89(x), F_90(x, 1))
Eq(F_90(x, k_0), F_1(x) + F_7(x, k_0) + F_91(x, k_0) + F_93(x, k_0))
Eq(F_91(x, k_0), F_11(x)*F_92(x, k_0))
Eq(F_92(x, k_0), (k_0*F_90(x, k_0) - F_90(x, 1))/(k_0 - 1))
Eq(F_93(x, k_0), F_34(x, k_0)*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), F_96(x, k_0*k_1, k_1))
Eq(F_96(x, k_0, k_1), F_1(x) + F_102(x, k_0, k_1) + F_29(x, k_0, k_1) + F_97(x, k_0, k_1) + F_99(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_11(x)*F_98(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), (k_0*F_96(x, k_0, k_1) - F_96(x, 1, k_1))/(k_0 - 1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1)*F_34(x, k_0))
Eq(F_100(x, k_0, k_1), (-k_0*F_101(x, k_0, 1) + k_1*F_101(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_101(x, k_0, k_1), F_96(x, k_0, k_0*k_1))
Eq(F_102(x, k_0, k_1), F_34(x, k_1)*F_96(x, k_0, k_1))
Pack JSON:
{"name": "row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 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": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 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], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 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, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 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, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 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], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 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, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 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, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "assumption": {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}]}, "sub_assumption": {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 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, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 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