0123_135024_145023_235014_245013_345012<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 23, 103, 508, 2656, 14381, 79533, 445638, 2517738, 14301411, 81529971, 465953088, 2667737988, 15293841113, 87765930841, 504055136842, 2896728015886, 16655920477871, 95813593245951, 551389144800452, 3174263519294056, 18279604502597893, 105297510195292933, 606718962427522958, 3496773540297994866, 20158186528602785403, 116234191345536441099, 670362966897150710664, 3867012338251741896204, 22311394955910344338353, 128753803701134269026993, 743143079657766239273874, 4290035905451770265845014, 24769819142546724304500039, 143039387251628466097317783, 826146324388013649490429068, 4772265581786192468836904304, 27571247569590822379321969629, 159312704850414620580912750429, 920671457593299934801947381078, 5321295877146349812433185983226, 30760037653105431844582954225683, 177832604728881944251746352812963, 1028227947252297535789839543979728, 5945924459356847981302448379377556, 34387443112663366631005517949382281, 198897580396649945669127395681723913, 1150553693890743909036824130518383578, 6656267538513620130885909027880674078, 38512338986339282082181948376423588831, 222850225142545812541065914812029756463, 1289641993705766202493413884844148568404, 7463921404147770744553627854158900065144, 43202182379481876144663461610714943049909, 250082916108060009493261564440296357772213, 1447775037348744852423487141744012393307678, 8382159280557305022758922911343686114356354, 48534166776388182030063193829238177700642219, 281044571728421590868600855941245481757826619, 1627563418496990577972331031840440759349529368, 9426162094302215559964999527982572750609643548, 54596568910872993763002480748227159600582831969, 316248507998127875805508266617185308963620156769, 1831991937488857717701159823846307725048102511394, 10613285417609903192419375792471740840692660907558, 61490304038643243862571349250052015995137029581431, 356281497614800214288073742726054989168021736769223, 2064472358467877729063402446302727326336430612192028, 11963366656650573619561410586011072398041060541987968, 69330714358531354121364649782548182230072724592101261, 401814180846443686772693468701270421456866776939767821, 2328904008185389414605722410498286589438791776310761958, 13499077753452126226414651602157296595008075439456210698, 78249621703696793175971457899481546166196634484364736323, 453613011349077978161257314842292497928721039337531957971, 2629743292558010476766064149368833941526372428875800297568, 15246329709438689803848137919686160107505367099731971905444, 88397681425593032642469658608885123508154908350771354916409, 512553952810613621773970886097435156162479752389247338277049, 2972083392012619306046043699608996154795688588622905150714218, 17234736291704649792918234274560405165100445645374822393452078, 99947080416301874061367181384802026173986831052474295395217679, 579638176859608610829675246554952025274006786843513841289901919, 3361745595540916129685368102631464563084717768781908773913590244, 19498145430148393849130240107944838013442900825852513329570988168, 113094628841356129243731397260868455917943778107341230654595356773, 656010051013851475413324139989100484019594619414802047915762797669, 3805383955420323140773642216503443803159981667162275240388702238894, 22075248100713577277077094221691563881041422566031700829783520373394, 128065302621925109554829109024383552358230578557800000953305043313883, 742977748784289354234101386117564477305936812341636184817533943810411, 4310605196244745112709303742000304703757496928438613952982449778501288, 25010275952131024562287907628119623066223389735653571803775367956647468, 145116302202019483286240113936093493501159208442972847027771308541545233, 842036863438534290404454656574624577058650701986775025654781008456935441, 4886106099046706610485152329505772919067766165445435882231379299962085042, 28353800603212510358223986289807681181056557043729790074075783256623551286, 164541702846517233687596452222545137509549847241666234786778551654629089191<br /><br />


















  Specification 1<br />
  Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob<br />
  Tree: http://permpal.com/tree/24085/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[21,x]*F[3,x]<br />
  
    F[3,x] = F[1,x]+F[22,x]+F[4,x]<br />
  
    F[4,x] = F[21,x]*F[5,x]<br />
  
    F[5,x] = F[6,x,1]<br />
  
    F[6,x,k[0]] = F[7,x,1,k[0]]<br />
  
    F[7,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]<br />
  
    F[8,x,k[0],k[1]] = F[1,x]+F[17,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[9,x,k[0],k[1]]<br />
  
    F[9,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[13,x,k[0]]<br />
  
    F[10,x,k[0],k[1]] = (F[11,x,k[0],k[1]]*k[1]-F[11,x,k[0],1])/(-1+k[1])<br />
  
    F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]<br />
  
    F[12,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[13,x,k[0]]<br />
  
    F[13,x,k[0]] = k[0]*x<br />
  
    F[14,x,k[0],k[1]] = F[13,x,k[1]]*F[15,x,k[0],k[1]]<br />
  
    F[15,x,k[0],k[1]] = (-F[16,x,1,k[1]]*k[1]+F[16,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])<br />
  
    F[16,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]<br />
  
    F[17,x,k[0],k[1]] = F[13,x,k[1]]*F[18,x,k[0],k[1]]<br />
  
    F[18,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])<br />
  
    F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[21,x]<br />
  
    F[20,x,k[0],k[1]] = (F[8,x,k[0],k[1]]*k[1]-F[8,x,k[0],1])/(-1+k[1])<br />
  
    F[21,x] = x<br />
  
    F[22,x] = F[21,x]*F[23,x]<br />
  
    F[23,x] = F[24,x,1]<br />
  
    F[24,x,k[0]] = (F[25,x,k[0]]*k[0]-F[25,x,1])/(-1+k[0])<br />
  
    F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]+F[27,x,k[0]]<br />
  
    F[26,x,k[0]] = F[13,x,k[0]]*F[6,x,k[0]]<br />
  
    F[27,x,k[0]] = F[21,x]*F[24,x,k[0]]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)<br />
  
    F_{6}\! \left(x , y\right) = F_{7}\! \left(x , 1, y\right)<br />
  
    F_{7}\! \left(x , y , z\right) = F_{8}\! \left(x , y z , z\right)<br />
  
    F_{8}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)<br />
  
    F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right) F_{13}\! \left(x , y\right)<br />
  
    F_{10}\! \left(x , y , z\right) = \frac{z F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , y , 1\right)}{-1+z}<br />
  
    F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)<br />
  
    F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{13}\! \left(x , y\right)<br />
  
    F_{13}\! \left(x , y\right) = y x<br />
  
    F_{14}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{15}\! \left(x , y , z\right)<br />
  
    F_{15}\! \left(x , y , z\right) = \frac{-z F_{16}\! \left(x , 1, z\right)+y F_{16}\! \left(x , \frac{y}{z}, z\right)}{-z +y}<br />
  
    F_{16}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)<br />
  
    F_{17}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{18}\! \left(x , y , z\right)<br />
  
    F_{18}\! \left(x , y , z\right) = \frac{-z F_{7}\! \left(x , 1, z\right)+y F_{7}\! \left(x , \frac{y}{z}, z\right)}{-z +y}<br />
  
    F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{21}\! \left(x \right)<br />
  
    F_{20}\! \left(x , y , z\right) = \frac{z F_{8}\! \left(x , y , z\right)-F_{8}\! \left(x , y , 1\right)}{-1+z}<br />
  
    F_{21}\! \left(x \right) = x<br />
  
    F_{22}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)<br />
  
    F_{24}\! \left(x , y\right) = \frac{y F_{25}\! \left(x , y\right)-F_{25}\! \left(x , 1\right)}{-1+y}<br />
  
    F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)<br />
  
    F_{26}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{6}\! \left(x , y\right)<br />
  
    F_{27}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_21(x)*F_3(x))<br />
  
    Eq(F_3(x), F_1(x) + F_22(x) + F_4(x))<br />
  
    Eq(F_4(x), F_21(x)*F_5(x))<br />
  
    Eq(F_5(x), F_6(x, 1))<br />
  
    Eq(F_6(x, k_0), F_7(x, 1, k_0))<br />
  
    Eq(F_7(x, k_0, k_1), F_8(x, k_0*k_1, k_1))<br />
  
    Eq(F_8(x, k_0, k_1), F_1(x) + F_17(x, k_0, k_1) + F_19(x, k_0, k_1) + F_9(x, k_0, k_1))<br />
  
    Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_1)*F_13(x, k_0))<br />
  
    Eq(F_10(x, k_0, k_1), (-k_1*F_11(x, k_0, k_1) + F_11(x, k_0, 1))/(1 - k_1))<br />
  
    Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1))<br />
  
    Eq(F_12(x, k_0, k_1), F_11(x, k_0, k_1)*F_13(x, k_0))<br />
  
    Eq(F_13(x, k_0), k_0*x)<br />
  
    Eq(F_14(x, k_0, k_1), F_13(x, k_1)*F_15(x, k_0, k_1))<br />
  
    Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0/k_1, k_1) + k_1*F_16(x, 1, k_1))/(-k_0 + k_1))<br />
  
    Eq(F_16(x, k_0, k_1), F_11(x, k_0*k_1, k_1))<br />
  
    Eq(F_17(x, k_0, k_1), F_13(x, k_1)*F_18(x, k_0, k_1))<br />
  
    Eq(F_18(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))<br />
  
    Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_21(x))<br />
  
    Eq(F_20(x, k_0, k_1), (-k_1*F_8(x, k_0, k_1) + F_8(x, k_0, 1))/(1 - k_1))<br />
  
    Eq(F_21(x), x)<br />
  
    Eq(F_22(x), F_21(x)*F_23(x))<br />
  
    Eq(F_23(x), F_24(x, 1))<br />
  
    Eq(F_24(x, k_0), (-k_0*F_25(x, k_0) + F_25(x, 1))/(1 - k_0))<br />
  
    Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0) + F_27(x, k_0))<br />
  
    Eq(F_26(x, k_0), F_13(x, k_0)*F_6(x, k_0))<br />
  
    Eq(F_27(x, k_0), F_21(x)*F_24(x, k_0))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;place_col&#34;: true, &#34;place_row&#34;: true, &#34;strategy_class&#34;: &#34;RowAndColumnPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.rearrange_assumption&#34;, &#34;strategy_class&#34;: &#34;RearrangeAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.assumption_insertion&#34;, &#34;strategy_class&#34;: &#34;AddAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.fusion.fusion&#34;, &#34;strategy_class&#34;: &#34;FusionFactory&#34;, &#34;tracked&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementCorroborationFactory&#34;}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;row_and_col_placements_tracked_fusion_req_corrob&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: 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&#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: 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4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 2], [0, 3]], [[1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 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&#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], 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{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 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&#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 1], [0, 2], [0, 4]], [[1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: 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[0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 0, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, 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{&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;assumption&#34;: {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}, &#34;class_module&#34;: &#34;tilings.strategies.rearrange_assumption&#34;, &#34;strategy_class&#34;: &#34;RearrangeAssumptionStrategy&#34;, &#34;sub_assumption&#34;: {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], 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[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1], [0, 2]], [[1, 0]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 1], [0, 3]], [[1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;tilings.strategies.fusion.fusion&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;FusionRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.fusion.fusion&#34;, &#34;col_idx&#34;: null, &#34;row_idx&#34;: 0, &#34;strategy_class&#34;: &#34;FusionStrategy&#34;, &#34;tracked&#34;: true}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}]}<br /><br />

  Specification 2<br />
  Strategy pack name: point_and_row_and_col_placements_tracked_fusion<br />
  Tree: http://permpal.com/tree/24086/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[22,x]*F[4,x]<br />
  
    F[4,x] = F[1,x]+F[23,x]+F[5,x]<br />
  
    F[5,x] = F[22,x]*F[6,x]<br />
  
    F[6,x] = F[7,x,1]<br />
  
    F[7,x,k[0]] = F[8,x,1,k[0]]<br />
  
    F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]<br />
  
    F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[20,x,k[0],k[1]]<br />
  
    F[10,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[14,x,k[0]]<br />
  
    F[11,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])/(-1+k[1])<br />
  
    F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]<br />
  
    F[13,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[14,x,k[0]]<br />
  
    F[14,x,k[0]] = k[0]*x<br />
  
    F[15,x,k[0],k[1]] = F[14,x,k[1]]*F[16,x,k[0],k[1]]<br />
  
    F[16,x,k[0],k[1]] = (-F[17,x,1,k[1]]*k[1]+F[17,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])<br />
  
    F[17,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]<br />
  
    F[18,x,k[0],k[1]] = F[14,x,k[1]]*F[19,x,k[0],k[1]]<br />
  
    F[19,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])<br />
  
    F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[22,x]<br />
  
    F[21,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])<br />
  
    F[22,x] = x<br />
  
    F[23,x] = F[22,x]*F[24,x]<br />
  
    F[24,x] = F[25,x,1]<br />
  
    F[25,x,k[0]] = (F[26,x,k[0]]*k[0]-F[26,x,1])/(-1+k[0])<br />
  
    F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[28,x,k[0]]<br />
  
    F[27,x,k[0]] = F[14,x,k[0]]*F[7,x,k[0]]<br />
  
    F[28,x,k[0]] = F[22,x]*F[25,x,k[0]]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{5}\! \left(x \right)<br />
  
    F_{5}\! \left(x \right) = F_{22}\! \left(x \right) F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)<br />
  
    F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)<br />
  
    F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , y z , z\right)<br />
  
    F_{9}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)<br />
  
    F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)<br />
  
    F_{11}\! \left(x , y , z\right) = -\frac{-z F_{12}\! \left(x , y , z\right)+F_{12}\! \left(x , y , 1\right)}{-1+z}<br />
  
    F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)<br />
  
    F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)<br />
  
    F_{14}\! \left(x , y\right) = y x<br />
  
    F_{15}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{16}\! \left(x , y , z\right)<br />
  
    F_{16}\! \left(x , y , z\right) = -\frac{z F_{17}\! \left(x , 1, z\right)-y F_{17}\! \left(x , \frac{y}{z}, z\right)}{-z +y}<br />
  
    F_{17}\! \left(x , y , z\right) = F_{12}\! \left(x , y z , z\right)<br />
  
    F_{18}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)<br />
  
    F_{19}\! \left(x , y , z\right) = -\frac{z F_{8}\! \left(x , 1, z\right)-y F_{8}\! \left(x , \frac{y}{z}, z\right)}{-z +y}<br />
  
    F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{22}\! \left(x \right)<br />
  
    F_{21}\! \left(x , y , z\right) = -\frac{-z F_{9}\! \left(x , y , z\right)+F_{9}\! \left(x , y , 1\right)}{-1+z}<br />
  
    F_{22}\! \left(x \right) = x<br />
  
    F_{23}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x , 1\right)<br />
  
    F_{25}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}<br />
  
    F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)<br />
  
    F_{27}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{7}\! \left(x , y\right)<br />
  
    F_{28}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_22(x)*F_4(x))<br />
  
    Eq(F_4(x), F_1(x) + F_23(x) + F_5(x))<br />
  
    Eq(F_5(x), F_22(x)*F_6(x))<br />
  
    Eq(F_6(x), F_7(x, 1))<br />
  
    Eq(F_7(x, k_0), F_8(x, 1, k_0))<br />
  
    Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))<br />
  
    Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_18(x, k_0, k_1) + F_20(x, k_0, k_1))<br />
  
    Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1)*F_14(x, k_0))<br />
  
    Eq(F_11(x, k_0, k_1), (-k_1*F_12(x, k_0, k_1) + F_12(x, k_0, 1))/(1 - k_1))<br />
  
    Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1))<br />
  
    Eq(F_13(x, k_0, k_1), F_12(x, k_0, k_1)*F_14(x, k_0))<br />
  
    Eq(F_14(x, k_0), k_0*x)<br />
  
    Eq(F_15(x, k_0, k_1), F_14(x, k_1)*F_16(x, k_0, k_1))<br />
  
    Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0/k_1, k_1) + k_1*F_17(x, 1, k_1))/(-k_0 + k_1))<br />
  
    Eq(F_17(x, k_0, k_1), F_12(x, k_0*k_1, k_1))<br />
  
    Eq(F_18(x, k_0, k_1), F_14(x, k_1)*F_19(x, k_0, k_1))<br />
  
    Eq(F_19(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))<br />
  
    Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_22(x))<br />
  
    Eq(F_21(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))<br />
  
    Eq(F_22(x), x)<br />
  
    Eq(F_23(x), F_22(x)*F_24(x))<br />
  
    Eq(F_24(x), F_25(x, 1))<br />
  
    Eq(F_25(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))<br />
  
    Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0) + F_28(x, k_0))<br />
  
    Eq(F_27(x, k_0), F_14(x, k_0)*F_7(x, k_0))<br />
  
    Eq(F_28(x, k_0), F_22(x)*F_25(x, k_0))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;place_col&#34;: true, &#34;place_row&#34;: true, &#34;strategy_class&#34;: &#34;RowAndColumnPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.rearrange_assumption&#34;, &#34;strategy_class&#34;: &#34;RearrangeAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.assumption_insertion&#34;, &#34;strategy_class&#34;: &#34;AddAssumptionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.fusion.fusion&#34;, &#34;strategy_class&#34;: &#34;FusionFactory&#34;, &#34;tracked&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_and_row_and_col_placements_tracked_fusion&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 2]], [[1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], 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&#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, 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[0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 2], [0, 3]], [[1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], 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{&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 2], [0, 2], [0, 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{&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 1], [0, 3]], [[1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 3], [0, 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[[0, 2], [0, 2], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: 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[0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], 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[[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 0], [0, 1], [0, 2], [0, 4]], [[1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 3, 5, 0, 2, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 3], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 4, 5, 0, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 3, 5, 0, 1, 4], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [2, 4, 5, 0, 1, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {&#34;patt&#34;: [3, 4, 5, 0, 1, 2], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}, {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}, {&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, 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4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 4]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 0], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 2, 3, 0], &#34;pos&#34;: [[0, 4], [0, 4], [0, 4], [0, 0]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 3, 4, 0, 2], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 1], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 3, 4, 0, 1], &#34;pos&#34;: [[0, 2], [0, 4], [0, 4], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 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false, &#34;indices&#34;: [0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}]}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [{&#34;assumption&#34;: &#34;TrackingAssumption&#34;, &#34;class_module&#34;: &#34;tilings.assumptions&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]}], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}]}<br /><br />