10243_10342_10432_20341_20431_30421

Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3297, 18924, 111537, 670952, 4103156, 25439025, 159569991, 1011080015, 6463370327, 41641771550, 270165428174, 1763816351046, 11580808045301, 76429716408738, 506791868050868, 3374985815738160, 22565280763354463, 151427544114191689, 1019642441270416792, 6887567529555038476, 46662239372348647746, 317002812878554969746, 2159149180742039267596, 14741965731802814408954, 100883181563425316864149, 691855888691126020513822, 4754378157991437545698674, 32734447902170459337311021, 225790352955506130461916044, 1560105928121609986134009615, 10797258460418784259921625345, 74842580700401113591347210626, 519550189310673573489507460036, 3611766611911295475046668744402, 25141851354906913681426203966113, 175240344002762848817420446498580, 1222941782351824497868284495969903, 8544555101219195572222973299918410, 59767307094550740454855907023738449, 418512445489575255173494095478090900, 2933625181403384964569634348540818942, 20584231125499995531976695287160901306, 144571171145055560901998095816291671909, 1016318829596790698718440664338810323655, 7150963255932157940369942774621012874105, 50358329763800462356078251908679019362034, 354925282579716963617636704088407162025946, 2503506716350914039550019865740097604307512, 17672370236465549192440413307950833286022226, 124842851959752512984968510550920453323447453, 882560717826827563244196532213269990386917705, 6243487741393953458088029377898299536767360458, 44197928511024576368257796828368838998001346259, 313082821627053684341175202173747992335092817232, 2219168931056941011023510019601716735766267842324, 15739351213069266872817128658327805524730382436594, 111696753885532042699344274372223120238871219541695, 793128993510302191149488010288518962161966577064030, 5634939749631499469586272948247810833242297129703293, 40056209758977348354582010826667801096007100400318053, 284891049710863745054266405581477727962755162123133218, 2027261033827368924676701365502285117303474320012542487, 14432988397042730648623944232969484691200218605405808088, 102804621179688816620364439212184380610011614258299466391, 732610435887999835075129003454182358951431228903537708043, 5223146246746730304013972076554798342961565626676044602466, 37255006376253390349491346081172754291601135291449428711390, 265843118416210185247567616855080160734136558265140582679896, 1897796654843842144544509721130030177194710844131156380453408, 13553539875180601639160403023976129422395719342197624916833584, 96834500083704794858396894398745949849077426531667950887004842, 692113759962466416275847528791611440049960588966256248782485570, 4948694892389332347677705730371684579234938267983443414426808883, 35396937201086838672294002640010617431018559072398727399555713090, 253278679463981150762726330267887853202472655687996654853992942490, 1812949840589456761421321930477709675967605704137140505193194661049, 12981460261808320110709685219860514701379656489992640901086678729960, 92984044799151401475050285758708496921796386999381690611615015029775, 666249792051524985154136508162677803351852522982300854264669856017290, 4775361566480225592200952199543099704555059780103554515536691718407048, 34238349168126032412412245047923275810525329935515097725987587002273610, 245557794196703986399647388249107965127922984975812812936028122387247487, 1761676034148498139249124384350821810099215741290405424819691465022100375, 12642324847147173069389628775007391923448812546760570201798309932228251670, 90751470878603583337967061500948446737035327509634111944882341620276957798, 651633745797335871868453872861074185860834726837288234397347931509220035061, 4680303860500135077278146312759321693528740121249966314642513023685997059633, 33625025616105901087394239312048111402918445830848420862350195081365957362737, 241638909904764788253363262011869290814689827169326959506801547360764591175125, 1736938470487877228427550271086824243959967791990865389103367538719598583901983, 12488579594741846850994769335579365219097692969053783796155470320029139933794864, 89815335092613686774669148631997953360608273553405574307296497433167353158003580, 646092404812362990894668739487238456323013772114627429664427048298081668632799223, 4648827038674943195802080144584642394190393819217998910180091005649555211537343658

Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25349/
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[32,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[32,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = k[0]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[32,x]
F[15,x,k[0]] = F[113,x,k[0]]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]+F[99,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[35,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]+F[26,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[64,x,k[0]]
F[23,x,k[0]] = F[24,x]+F[49,x,k[0]]
F[24,x] = F[1,x]+F[25,x]+F[48,x]
F[25,x] = F[26,x]*F[32,x]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[28,x,k[0]]+F[4,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[36,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[31,x,k[0]]+F[33,x,k[0]]
F[30,x] = 0
F[31,x,k[0]] = F[28,x,k[0]]*F[32,x]
F[32,x] = x
F[33,x,k[0]] = F[34,x,k[0]]*F[35,x,k[0]]
F[34,x,k[0]] = F[0,x]+F[29,x,k[0]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[32,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[28,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[1,x]+F[43,x,k[0]]+F[47,x,k[0]]
F[43,x,k[0]] = F[32,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[32,x]*F[42,x,k[0]]*F[44,x,k[0]]
F[47,x,k[0]] = F[35,x,k[0]]*F[42,x,k[0]]
F[48,x] = F[24,x]*F[32,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[30,x]+F[51,x,k[0]]+F[52,x,k[0]]
F[51,x,k[0]] = F[20,x,k[0]]*F[32,x]
F[52,x,k[0]] = F[35,x,k[0]]*F[53,x,k[0]]
F[53,x,k[0]] = F[1,x]+F[52,x,k[0]]+F[54,x,k[0]]+F[59,x,k[0]]
F[54,x,k[0]] = F[32,x]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[62,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[32,x]*F[56,x,k[0]]
F[59,x,k[0]] = F[35,x,k[0]]*F[57,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[18,x,k[0]]*F[32,x]
F[62,x,k[0]] = k[0]*F[63,x,k[0]]
F[63,x,k[0]] = F[61,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[32,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[146,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[140,x,k[0]]+F[142,x]+F[22,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[32,x]*F[69,x,k[0]]
F[70,x,k[0]] = F[135,x,k[0]]+F[69,x,k[0]]
F[71,x,k[0]] = F[32,x]*F[70,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[126,x,k[0]]+F[73,x,k[0]]
F[74,x,k[0]] = F[116,x,k[0]]+F[73,x,k[0]]
F[75,x,k[0]] = F[32,x]*F[74,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[114,x,k[0]]+F[118,x,k[0]]+F[75,x,k[0]]
F[76,x,k[0]] = F[77,x]+F[82,x,k[0]]
F[77,x] = F[0,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[0,x]*F[32,x]*F[80,x]
F[80,x] = F[4,x]+F[81,x]
F[81,x] = F[5,x]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[35,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[93,x,k[0]]
F[86,x,k[0]] = F[35,x,k[0]]*F[85,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[88,x,k[0]] = F[77,x]+F[87,x,k[0]]
F[88,x,k[0]] = F[57,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[32,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[13,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[56,x,k[0]]*F[57,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = k[0]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[32,x]*F[97,x,k[0]]
F[98,x,k[0]] = F[35,x,k[0]]*F[97,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[106,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]+F[30,x]
F[102,x,k[0]] = F[32,x]*F[99,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[35,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]+F[105,x,k[0]]+F[57,x,k[0]]
F[105,x,k[0]] = F[18,x,k[0]]*F[32,x]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[101,x,k[0]]*F[32,x]*F[56,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[32,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]
F[111,x,k[0]] = F[17,x,k[0]]*F[29,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[42,x,k[0]]*F[99,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[32,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[117,x,k[0]]
F[116,x,k[0]] = F[20,x,k[0]]+F[4,x]
F[117,x,k[0]] = F[61,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[35,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]+F[53,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]*F[32,x]
F[122,x,k[0]] = F[123,x,k[0]]+F[125,x,k[0]]
F[123,x,k[0]] = F[12,x,k[0]]+F[124,x,k[0]]
F[124,x,k[0]] = F[53,x,k[0]]*F[56,x,k[0]]
F[125,x,k[0]] = F[13,x,k[0]]
F[126,x,k[0]] = F[127,x]
F[127,x] = F[128,x]*F[32,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[28,x,1]
F[132,x] = F[133,x]
F[133,x] = F[134,x,1]
F[134,x,k[0]] = F[28,x,k[0]]*F[44,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[32,x]
F[137,x,k[0]] = F[138,x,k[0]]+F[139,x,k[0]]
F[138,x,k[0]] = F[17,x,k[0]]*F[27,x,k[0]]
F[139,x,k[0]] = F[44,x,k[0]]*F[99,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[123,x,k[0]]*F[35,x,k[0]]
F[142,x] = F[143,x]*F[32,x]
F[143,x] = F[144,x,1]
F[144,x,k[0]] = F[145,x,k[0]]+F[41,x,k[0]]
F[145,x,k[0]] = F[34,x,k[0]]*F[4,x]
F[146,x,k[0]] = F[147,x,k[0]]
F[148,x,k[0]] = F[147,x,k[0]]+F[151,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]*F[32,x]
F[149,x,k[0]] = F[150,x,k[0]]
F[150,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[152,x,k[0]] = F[151,x,k[0]]*F[32,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = 1/(-1+k[0])*(F[154,x,k[0]]*k[0]-F[154,x,1])
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[157,x,k[0]]*F[32,x]
F[156,x,k[0]] = F[56,x,k[0]]
F[157,x,k[0]] = F[57,x,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_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{32}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = y F_{13}\! \left(x , y\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_{32}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{32}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = x
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_{0}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = y x
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{42}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{48}\! \left(x \right) = F_{24}\! \left(x \right) F_{32}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{62}\! \left(x , y\right) = y F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{142}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{77}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = y F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{97}\! \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_{108}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{32}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{32}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x , 1\right)
F_{134}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{32}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x , 1\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = -\frac{-F_{89}\! \left(x , y\right) y +F_{89}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = -\frac{-y F_{154}\! \left(x , y\right)+F_{154}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{157}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_32(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_32(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), k_0*F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_32(x))
Eq(F_15(x, k_0), F_113(x, k_0) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0) + F_99(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_35(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0) + F_26(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_64(x, k_0))
Eq(F_23(x, k_0), F_24(x) + F_49(x, k_0))
Eq(F_24(x), F_1(x) + F_25(x) + F_48(x))
Eq(F_25(x), F_26(x)*F_32(x))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_28(x, k_0) + F_4(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_36(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_30(x), 0)
Eq(F_31(x, k_0), F_28(x, k_0)*F_32(x))
Eq(F_32(x), x)
Eq(F_33(x, k_0), F_34(x, k_0)*F_35(x, k_0))
Eq(F_34(x, k_0), F_0(x) + F_29(x, k_0))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_32(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), F_29(x, k_0)*F_4(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_28(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_1(x) + F_43(x, k_0) + F_47(x, k_0))
Eq(F_43(x, k_0), F_32(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_32(x)*F_42(x, k_0)*F_44(x, k_0))
Eq(F_47(x, k_0), F_35(x, k_0)*F_42(x, k_0))
Eq(F_48(x), F_24(x)*F_32(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_30(x) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_51(x, k_0), F_20(x, k_0)*F_32(x))
Eq(F_52(x, k_0), F_35(x, k_0)*F_53(x, k_0))
Eq(F_53(x, k_0), F_1(x) + F_52(x, k_0) + F_54(x, k_0) + F_59(x, k_0))
Eq(F_54(x, k_0), F_32(x)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_62(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_32(x)*F_56(x, k_0))
Eq(F_59(x, k_0), F_35(x, k_0)*F_57(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_18(x, k_0)*F_32(x))
Eq(F_62(x, k_0), k_0*F_63(x, k_0))
Eq(F_63(x, k_0), F_61(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_32(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_146(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_140(x, k_0) + F_142(x) + F_22(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_32(x)*F_69(x, k_0))
Eq(F_70(x, k_0), F_135(x, k_0) + F_69(x, k_0))
Eq(F_71(x, k_0), F_32(x)*F_70(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_126(x, k_0) + F_73(x, k_0))
Eq(F_74(x, k_0), F_116(x, k_0) + F_73(x, k_0))
Eq(F_75(x, k_0), F_32(x)*F_74(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_114(x, k_0) + F_118(x, k_0) + F_75(x, k_0))
Eq(F_76(x, k_0), F_77(x) + F_82(x, k_0))
Eq(F_77(x), F_0(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_0(x)*F_32(x)*F_80(x))
Eq(F_80(x), F_4(x) + F_81(x))
Eq(F_81(x), F_5(x))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_35(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_93(x, k_0))
Eq(F_86(x, k_0), F_35(x, k_0)*F_85(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_88(x, k_0), F_77(x) + F_87(x, k_0))
Eq(F_88(x, k_0), F_57(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_32(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_13(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_56(x, k_0)*F_57(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), k_0*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_32(x)*F_97(x, k_0))
Eq(F_98(x, k_0), F_35(x, k_0)*F_97(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_108(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_106(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0) + F_30(x))
Eq(F_102(x, k_0), F_32(x)*F_99(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_35(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0) + F_105(x, k_0) + F_57(x, k_0))
Eq(F_105(x, k_0), F_18(x, k_0)*F_32(x))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_101(x, k_0)*F_32(x)*F_56(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_32(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0))
Eq(F_111(x, k_0), F_17(x, k_0)*F_29(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_42(x, k_0)*F_99(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_32(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_117(x, k_0))
Eq(F_116(x, k_0), F_20(x, k_0) + F_4(x))
Eq(F_117(x, k_0), F_61(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_35(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0) + F_53(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0)*F_32(x))
Eq(F_122(x, k_0), F_123(x, k_0) + F_125(x, k_0))
Eq(F_123(x, k_0), F_12(x, k_0) + F_124(x, k_0))
Eq(F_124(x, k_0), F_53(x, k_0)*F_56(x, k_0))
Eq(F_125(x, k_0), F_13(x, k_0))
Eq(F_126(x, k_0), F_127(x))
Eq(F_127(x), F_128(x)*F_32(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_28(x, 1))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x, 1))
Eq(F_134(x, k_0), F_28(x, k_0)*F_44(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_32(x))
Eq(F_137(x, k_0), F_138(x, k_0) + F_139(x, k_0))
Eq(F_138(x, k_0), F_17(x, k_0)*F_27(x, k_0))
Eq(F_139(x, k_0), F_44(x, k_0)*F_99(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_123(x, k_0)*F_35(x, k_0))
Eq(F_142(x), F_143(x)*F_32(x))
Eq(F_143(x), F_144(x, 1))
Eq(F_144(x, k_0), F_145(x, k_0) + F_41(x, k_0))
Eq(F_145(x, k_0), F_34(x, k_0)*F_4(x))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_148(x, k_0), F_147(x, k_0) + F_151(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0)*F_32(x))
Eq(F_149(x, k_0), F_150(x, k_0))
Eq(F_150(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_151(x, k_0)*F_32(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), (k_0*F_154(x, k_0) - F_154(x, 1))/(k_0 - 1))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_157(x, k_0)*F_32(x))
Eq(F_156(x, k_0), F_56(x, k_0))
Eq(F_157(x, k_0), F_57(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "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, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[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], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 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], [0, 0], 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0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0], [2, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 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], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 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], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 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], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": 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0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [4, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [5, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [4, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [5, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [4, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [5, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [4, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [5, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [4, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2], [5, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}, "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], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 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, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 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, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 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, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "ComponentToPointAssumptionStrategy", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false, "assumption": {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25504/
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[32,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[32,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = k[0]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[32,x]
F[15,x,k[0]] = F[113,x,k[0]]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]+F[99,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[35,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]+F[26,x]
F[22,x,k[0]] = F[23,x,k[0]]+F[64,x,k[0]]
F[23,x,k[0]] = F[24,x]+F[49,x,k[0]]
F[24,x] = F[1,x]+F[25,x]+F[48,x]
F[25,x] = F[26,x]*F[32,x]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = F[28,x,k[0]]+F[4,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[36,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[31,x,k[0]]+F[33,x,k[0]]
F[30,x] = 0
F[31,x,k[0]] = F[28,x,k[0]]*F[32,x]
F[32,x] = x
F[33,x,k[0]] = F[34,x,k[0]]*F[35,x,k[0]]
F[34,x,k[0]] = F[0,x]+F[29,x,k[0]]
F[35,x,k[0]] = k[0]*x
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[32,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = F[29,x,k[0]]*F[4,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[28,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[1,x]+F[43,x,k[0]]+F[47,x,k[0]]
F[43,x,k[0]] = F[32,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[32,x]*F[42,x,k[0]]*F[44,x,k[0]]
F[47,x,k[0]] = F[35,x,k[0]]*F[42,x,k[0]]
F[48,x] = F[24,x]*F[32,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[30,x]+F[51,x,k[0]]+F[52,x,k[0]]
F[51,x,k[0]] = F[20,x,k[0]]*F[32,x]
F[52,x,k[0]] = F[35,x,k[0]]*F[53,x,k[0]]
F[53,x,k[0]] = F[1,x]+F[52,x,k[0]]+F[54,x,k[0]]+F[59,x,k[0]]
F[54,x,k[0]] = F[32,x]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[62,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[32,x]*F[56,x,k[0]]
F[59,x,k[0]] = F[35,x,k[0]]*F[57,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[18,x,k[0]]*F[32,x]
F[62,x,k[0]] = k[0]*F[63,x,k[0]]
F[63,x,k[0]] = F[61,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[32,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[146,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[140,x,k[0]]+F[142,x]+F[22,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[32,x]*F[69,x,k[0]]
F[70,x,k[0]] = F[135,x,k[0]]+F[69,x,k[0]]
F[71,x,k[0]] = F[32,x]*F[70,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[126,x,k[0]]+F[73,x,k[0]]
F[74,x,k[0]] = F[116,x,k[0]]+F[73,x,k[0]]
F[75,x,k[0]] = F[32,x]*F[74,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[114,x,k[0]]+F[118,x,k[0]]+F[75,x,k[0]]
F[76,x,k[0]] = F[77,x]+F[82,x,k[0]]
F[77,x] = F[0,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[0,x]*F[32,x]*F[80,x]
F[80,x] = F[4,x]+F[81,x]
F[81,x] = F[5,x]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[35,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[93,x,k[0]]
F[86,x,k[0]] = F[35,x,k[0]]*F[85,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[88,x,k[0]] = F[77,x]+F[87,x,k[0]]
F[88,x,k[0]] = F[57,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[32,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[13,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[56,x,k[0]]*F[57,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = k[0]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[32,x]*F[97,x,k[0]]
F[98,x,k[0]] = F[35,x,k[0]]*F[97,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[108,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[106,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]+F[30,x]
F[102,x,k[0]] = F[32,x]*F[99,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[35,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]+F[105,x,k[0]]+F[57,x,k[0]]
F[105,x,k[0]] = F[18,x,k[0]]*F[32,x]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[101,x,k[0]]*F[32,x]*F[56,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]*F[32,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[112,x,k[0]]
F[111,x,k[0]] = F[17,x,k[0]]*F[29,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[42,x,k[0]]*F[99,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[32,x]
F[115,x,k[0]] = F[116,x,k[0]]+F[117,x,k[0]]
F[116,x,k[0]] = F[20,x,k[0]]+F[4,x]
F[117,x,k[0]] = F[61,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[35,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]+F[53,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]*F[32,x]
F[122,x,k[0]] = F[123,x,k[0]]+F[125,x,k[0]]
F[123,x,k[0]] = F[12,x,k[0]]+F[124,x,k[0]]
F[124,x,k[0]] = F[53,x,k[0]]*F[56,x,k[0]]
F[125,x,k[0]] = F[13,x,k[0]]
F[126,x,k[0]] = F[127,x]
F[127,x] = F[128,x]*F[32,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[28,x,1]
F[132,x] = F[133,x]
F[133,x] = F[134,x,1]
F[134,x,k[0]] = F[28,x,k[0]]*F[44,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[32,x]
F[137,x,k[0]] = F[138,x,k[0]]+F[139,x,k[0]]
F[138,x,k[0]] = F[17,x,k[0]]*F[27,x,k[0]]
F[139,x,k[0]] = F[44,x,k[0]]*F[99,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[123,x,k[0]]*F[35,x,k[0]]
F[142,x] = F[143,x]*F[32,x]
F[143,x] = F[144,x,1]
F[144,x,k[0]] = F[145,x,k[0]]+F[41,x,k[0]]
F[145,x,k[0]] = F[34,x,k[0]]*F[4,x]
F[146,x,k[0]] = F[147,x,k[0]]
F[148,x,k[0]] = F[147,x,k[0]]+F[151,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]*F[32,x]
F[149,x,k[0]] = F[150,x,k[0]]
F[150,x,k[0]] = 1/(-1+k[0])*(F[89,x,k[0]]*k[0]-F[89,x,1])
F[152,x,k[0]] = F[151,x,k[0]]*F[32,x]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = 1/(-1+k[0])*(F[154,x,k[0]]*k[0]-F[154,x,1])
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[157,x,k[0]]*F[32,x]
F[156,x,k[0]] = F[56,x,k[0]]
F[157,x,k[0]] = F[57,x,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_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{32}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = y F_{13}\! \left(x , y\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_{32}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{32}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = x
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_{0}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = y x
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{42}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{48}\! \left(x \right) = F_{24}\! \left(x \right) F_{32}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{62}\! \left(x , y\right) = y F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{142}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{114}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{0}\! \left(x \right) F_{32}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{77}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = y F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{97}\! \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_{108}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{105}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{32}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{32}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x , 1\right)
F_{134}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{32}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x , 1\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = -\frac{-F_{89}\! \left(x , y\right) y +F_{89}\! \left(x , 1\right)}{-1+y}
F_{152}\! \left(x , y\right) = F_{151}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = -\frac{-y F_{154}\! \left(x , y\right)+F_{154}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{157}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_32(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_32(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), k_0*F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_32(x))
Eq(F_15(x, k_0), F_113(x, k_0) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0) + F_99(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_35(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0) + F_26(x))
Eq(F_22(x, k_0), F_23(x, k_0) + F_64(x, k_0))
Eq(F_23(x, k_0), F_24(x) + F_49(x, k_0))
Eq(F_24(x), F_1(x) + F_25(x) + F_48(x))
Eq(F_25(x), F_26(x)*F_32(x))
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), F_28(x, k_0) + F_4(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_36(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_30(x), 0)
Eq(F_31(x, k_0), F_28(x, k_0)*F_32(x))
Eq(F_32(x), x)
Eq(F_33(x, k_0), F_34(x, k_0)*F_35(x, k_0))
Eq(F_34(x, k_0), F_0(x) + F_29(x, k_0))
Eq(F_35(x, k_0), k_0*x)
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_32(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), F_29(x, k_0)*F_4(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_28(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_1(x) + F_43(x, k_0) + F_47(x, k_0))
Eq(F_43(x, k_0), F_32(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_32(x)*F_42(x, k_0)*F_44(x, k_0))
Eq(F_47(x, k_0), F_35(x, k_0)*F_42(x, k_0))
Eq(F_48(x), F_24(x)*F_32(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_30(x) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_51(x, k_0), F_20(x, k_0)*F_32(x))
Eq(F_52(x, k_0), F_35(x, k_0)*F_53(x, k_0))
Eq(F_53(x, k_0), F_1(x) + F_52(x, k_0) + F_54(x, k_0) + F_59(x, k_0))
Eq(F_54(x, k_0), F_32(x)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_62(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_32(x)*F_56(x, k_0))
Eq(F_59(x, k_0), F_35(x, k_0)*F_57(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_18(x, k_0)*F_32(x))
Eq(F_62(x, k_0), k_0*F_63(x, k_0))
Eq(F_63(x, k_0), F_61(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_32(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_146(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_140(x, k_0) + F_142(x) + F_22(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_32(x)*F_69(x, k_0))
Eq(F_70(x, k_0), F_135(x, k_0) + F_69(x, k_0))
Eq(F_71(x, k_0), F_32(x)*F_70(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_126(x, k_0) + F_73(x, k_0))
Eq(F_74(x, k_0), F_116(x, k_0) + F_73(x, k_0))
Eq(F_75(x, k_0), F_32(x)*F_74(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_114(x, k_0) + F_118(x, k_0) + F_75(x, k_0))
Eq(F_76(x, k_0), F_77(x) + F_82(x, k_0))
Eq(F_77(x), F_0(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_0(x)*F_32(x)*F_80(x))
Eq(F_80(x), F_4(x) + F_81(x))
Eq(F_81(x), F_5(x))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_35(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_93(x, k_0))
Eq(F_86(x, k_0), F_35(x, k_0)*F_85(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_88(x, k_0), F_77(x) + F_87(x, k_0))
Eq(F_88(x, k_0), F_57(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_32(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_13(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_56(x, k_0)*F_57(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), k_0*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_32(x)*F_97(x, k_0))
Eq(F_98(x, k_0), F_35(x, k_0)*F_97(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_108(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_106(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0) + F_30(x))
Eq(F_102(x, k_0), F_32(x)*F_99(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_35(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0) + F_105(x, k_0) + F_57(x, k_0))
Eq(F_105(x, k_0), F_18(x, k_0)*F_32(x))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_101(x, k_0)*F_32(x)*F_56(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0)*F_32(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_112(x, k_0))
Eq(F_111(x, k_0), F_17(x, k_0)*F_29(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_42(x, k_0)*F_99(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_32(x))
Eq(F_115(x, k_0), F_116(x, k_0) + F_117(x, k_0))
Eq(F_116(x, k_0), F_20(x, k_0) + F_4(x))
Eq(F_117(x, k_0), F_61(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_35(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0) + F_53(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0)*F_32(x))
Eq(F_122(x, k_0), F_123(x, k_0) + F_125(x, k_0))
Eq(F_123(x, k_0), F_12(x, k_0) + F_124(x, k_0))
Eq(F_124(x, k_0), F_53(x, k_0)*F_56(x, k_0))
Eq(F_125(x, k_0), F_13(x, k_0))
Eq(F_126(x, k_0), F_127(x))
Eq(F_127(x), F_128(x)*F_32(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_28(x, 1))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x, 1))
Eq(F_134(x, k_0), F_28(x, k_0)*F_44(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_32(x))
Eq(F_137(x, k_0), F_138(x, k_0) + F_139(x, k_0))
Eq(F_138(x, k_0), F_17(x, k_0)*F_27(x, k_0))
Eq(F_139(x, k_0), F_44(x, k_0)*F_99(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_123(x, k_0)*F_35(x, k_0))
Eq(F_142(x), F_143(x)*F_32(x))
Eq(F_143(x), F_144(x, 1))
Eq(F_144(x, k_0), F_145(x, k_0) + F_41(x, k_0))
Eq(F_145(x, k_0), F_34(x, k_0)*F_4(x))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_148(x, k_0), F_147(x, k_0) + F_151(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0)*F_32(x))
Eq(F_149(x, k_0), F_150(x, k_0))
Eq(F_150(x, k_0), (k_0*F_89(x, k_0) - F_89(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_151(x, k_0)*F_32(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), (k_0*F_154(x, k_0) - F_154(x, 1))/(k_0 - 1))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_157(x, k_0)*F_32(x))
Eq(F_156(x, k_0), F_56(x, k_0))
Eq(F_157(x, k_0), F_57(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "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, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[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], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 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