21.84/5.53 YES 21.84/5.53 property Termination 21.84/5.53 has value True 21.84/5.53 for SRS ( [a, a] -> [b, a, c, b], [b, b] -> [a, a], [c, a] -> []) 21.84/5.53 reason 21.84/5.53 remap for 3 rules 21.84/5.53 property Termination 21.84/5.53 has value True 21.84/5.53 for SRS ( [0, 0] -> [1, 0, 2, 1], [1, 1] -> [0, 0], [2, 0] -> []) 21.84/5.53 reason 21.84/5.53 DP transform 21.84/5.53 property Termination 21.84/5.53 has value True 21.84/5.54 for SRS ( [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= [], [0#, 0] |-> [1#, 0, 2, 1], [0#, 0] |-> [0#, 2, 1], [0#, 0] |-> [2#, 1], [0#, 0] |-> [1#], [1#, 1] |-> [0#, 0], [1#, 1] |-> [0#]) 21.84/5.54 reason 21.84/5.54 remap for 9 rules 21.84/5.54 property Termination 21.84/5.54 has value True 21.94/5.55 for SRS ( [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= [], [3, 0] |-> [4, 0, 2, 1], [3, 0] |-> [3, 2, 1], [3, 0] |-> [5, 1], [3, 0] |-> [4], [4, 1] |-> [3, 0], [4, 1] |-> [3]) 21.94/5.55 reason 21.94/5.55 weights 21.94/5.55 Map [(3, 1/1), (4, 1/1)] 21.94/5.55 21.94/5.55 property Termination 21.94/5.55 has value True 21.94/5.56 for SRS ( [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= [], [3, 0] |-> [4, 0, 2, 1], [3, 0] |-> [3, 2, 1], [3, 0] |-> [4], [4, 1] |-> [3, 0], [4, 1] |-> [3]) 21.94/5.56 reason 21.94/5.56 EDG has 1 SCCs 21.94/5.56 property Termination 21.94/5.56 has value True 21.94/5.56 for SRS ( [3, 0] |-> [4, 0, 2, 1], [4, 1] |-> [3], [3, 0] |-> [4], [4, 1] |-> [3, 0], [3, 0] |-> [3, 2, 1], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 21.94/5.56 reason 21.94/5.56 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 21.94/5.56 interpretation 21.94/5.56 0 / 0A 2A \ 21.94/5.56 \ 0A 2A / 21.94/5.56 1 / 0A 2A \ 21.94/5.56 \ 0A 2A / 21.94/5.56 2 / 0A 0A \ 21.94/5.56 \ -2A -2A / 21.94/5.56 3 / 24A 24A \ 21.94/5.56 \ 24A 24A / 21.94/5.56 4 / 23A 24A \ 21.94/5.56 \ 23A 24A / 21.94/5.56 [3, 0] |-> [4, 0, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 24A 26A \ / 24A 26A \ True False 21.94/5.56 \ 24A 26A / \ 24A 26A / 21.94/5.56 [4, 1] |-> [3] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 24A 26A \ / 24A 24A \ True False 21.94/5.56 \ 24A 26A / \ 24A 24A / 21.94/5.56 [3, 0] |-> [4] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 24A 26A \ / 23A 24A \ True True 21.94/5.56 \ 24A 26A / \ 23A 24A / 21.94/5.56 [4, 1] |-> [3, 0] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 24A 26A \ / 24A 26A \ True False 21.94/5.56 \ 24A 26A / \ 24A 26A / 21.94/5.56 [3, 0] |-> [3, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 24A 26A \ / 24A 26A \ True False 21.94/5.56 \ 24A 26A / \ 24A 26A / 21.94/5.56 [0, 0] ->= [1, 0, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 2A 4A \ / 2A 4A \ True False 21.94/5.56 \ 2A 4A / \ 2A 4A / 21.94/5.56 [1, 1] ->= [0, 0] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 2A 4A \ / 2A 4A \ True False 21.94/5.56 \ 2A 4A / \ 2A 4A / 21.94/5.56 [2, 0] ->= [] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 0A 2A \ / 0A - \ True False 21.94/5.56 \ -2A 0A / \ - 0A / 21.94/5.56 property Termination 21.94/5.56 has value True 21.94/5.56 for SRS ( [3, 0] |-> [4, 0, 2, 1], [4, 1] |-> [3], [4, 1] |-> [3, 0], [3, 0] |-> [3, 2, 1], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 21.94/5.56 reason 21.94/5.56 EDG has 1 SCCs 21.94/5.56 property Termination 21.94/5.56 has value True 21.94/5.56 for SRS ( [3, 0] |-> [4, 0, 2, 1], [4, 1] |-> [3, 0], [3, 0] |-> [3, 2, 1], [4, 1] |-> [3], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 21.94/5.56 reason 21.94/5.56 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 21.94/5.56 interpretation 21.94/5.56 0 / 0A 2A \ 21.94/5.56 \ 0A 2A / 21.94/5.56 1 / 0A 2A \ 21.94/5.56 \ 0A 2A / 21.94/5.56 2 / 0A 0A \ 21.94/5.56 \ -2A -2A / 21.94/5.56 3 / 15A 17A \ 21.94/5.56 \ 15A 17A / 21.94/5.56 4 / 15A 17A \ 21.94/5.56 \ 15A 17A / 21.94/5.56 [3, 0] |-> [4, 0, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 17A 19A \ / 17A 19A \ True False 21.94/5.56 \ 17A 19A / \ 17A 19A / 21.94/5.56 [4, 1] |-> [3, 0] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 17A 19A \ / 17A 19A \ True False 21.94/5.56 \ 17A 19A / \ 17A 19A / 21.94/5.56 [3, 0] |-> [3, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 17A 19A \ / 15A 17A \ True True 21.94/5.56 \ 17A 19A / \ 15A 17A / 21.94/5.56 [4, 1] |-> [3] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 17A 19A \ / 15A 17A \ True True 21.94/5.56 \ 17A 19A / \ 15A 17A / 21.94/5.56 [0, 0] ->= [1, 0, 2, 1] 21.94/5.56 lhs rhs ge gt 21.94/5.56 / 2A 4A \ / 2A 4A \ True False 21.94/5.56 \ 2A 4A / \ 2A 4A / 21.94/5.57 [1, 1] ->= [0, 0] 21.94/5.57 lhs rhs ge gt 21.94/5.57 / 2A 4A \ / 2A 4A \ True False 21.94/5.57 \ 2A 4A / \ 2A 4A / 21.94/5.57 [2, 0] ->= [] 21.94/5.57 lhs rhs ge gt 21.94/5.57 / 0A 2A \ / 0A - \ True False 21.94/5.57 \ -2A 0A / \ - 0A / 21.94/5.57 property Termination 21.94/5.57 has value True 21.94/5.57 for SRS ( [3, 0] |-> [4, 0, 2, 1], [4, 1] |-> [3, 0], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 21.94/5.57 reason 21.94/5.57 EDG has 1 SCCs 21.94/5.57 property Termination 21.94/5.57 has value True 21.94/5.57 for SRS ( [3, 0] |-> [4, 0, 2, 1], [4, 1] |-> [3, 0], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 21.94/5.57 reason 21.94/5.57 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 21.94/5.57 interpretation 21.94/5.57 0 / 0A 3A 3A \ 21.94/5.57 | 0A 0A 3A | 21.94/5.57 \ -3A 0A 0A / 21.94/5.57 1 / 0A 0A 3A \ 21.94/5.57 | 0A 0A 3A | 21.94/5.57 \ 0A 0A 3A / 21.94/5.57 2 / 0A 0A 0A \ 21.94/5.57 | -3A -3A -3A | 21.94/5.57 \ -3A -3A -3A / 21.94/5.57 3 / 42A 45A 45A \ 21.94/5.57 | 42A 45A 45A | 21.94/5.57 \ 42A 45A 45A / 21.94/5.57 4 / 42A 42A 45A \ 21.94/5.57 | 42A 42A 45A | 21.94/5.57 \ 42A 42A 45A / 21.94/5.58 [3, 0] |-> [4, 0, 2, 1] 21.94/5.58 lhs rhs ge gt 21.94/5.58 / 45A 45A 48A \ / 42A 42A 45A \ True True 21.94/5.58 | 45A 45A 48A | | 42A 42A 45A | 21.94/5.58 \ 45A 45A 48A / \ 42A 42A 45A / 21.94/5.58 [4, 1] |-> [3, 0] 21.94/5.58 lhs rhs ge gt 21.94/5.58 / 45A 45A 48A \ / 45A 45A 48A \ True False 21.94/5.62 | 45A 45A 48A | | 45A 45A 48A | 21.94/5.62 \ 45A 45A 48A / \ 45A 45A 48A / 21.94/5.62 [0, 0] ->= [1, 0, 2, 1] 21.94/5.62 lhs rhs ge gt 21.94/5.62 / 3A 3A 6A \ / 0A 0A 3A \ True False 21.94/5.62 | 0A 3A 3A | | 0A 0A 3A | 21.94/5.62 \ 0A 0A 3A / \ 0A 0A 3A / 21.94/5.62 [1, 1] ->= [0, 0] 21.94/5.62 lhs rhs ge gt 21.94/5.62 / 3A 3A 6A \ / 3A 3A 6A \ True False 21.94/5.62 | 3A 3A 6A | | 0A 3A 3A | 21.94/5.62 \ 3A 3A 6A / \ 0A 0A 3A / 21.94/5.62 [2, 0] ->= [] 21.94/5.62 lhs rhs ge gt 21.94/5.62 / 0A 3A 3A \ / 0A - - \ True False 22.25/5.64 | -3A 0A 0A | | - 0A - | 22.25/5.64 \ -3A 0A 0A / \ - - 0A / 22.25/5.64 property Termination 22.25/5.64 has value True 22.25/5.65 for SRS ( [4, 1] |-> [3, 0], [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 22.25/5.65 reason 22.25/5.65 weights 22.25/5.66 Map [(4, 1/1)] 22.25/5.66 22.25/5.66 property Termination 22.25/5.66 has value True 22.25/5.66 for SRS ( [0, 0] ->= [1, 0, 2, 1], [1, 1] ->= [0, 0], [2, 0] ->= []) 22.25/5.66 reason 22.25/5.66 EDG has 0 SCCs 22.25/5.66 22.25/5.66 ************************************************** 22.25/5.66 summary 22.25/5.66 ************************************************** 22.25/5.66 SRS with 3 rules on 3 letters Remap { tracing = False} 22.25/5.67 SRS with 3 rules on 3 letters DP transform 22.25/5.67 SRS with 9 rules on 6 letters Remap { tracing = False} 22.25/5.67 SRS with 9 rules on 6 letters weights 22.25/5.67 SRS with 8 rules on 5 letters EDG 22.25/5.67 SRS with 8 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 22.25/5.67 SRS with 7 rules on 5 letters EDG 22.25/5.67 SRS with 7 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 22.25/5.67 SRS with 5 rules on 5 letters EDG 22.25/5.67 SRS with 5 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 22.45/5.68 SRS with 4 rules on 5 letters weights 22.45/5.69 SRS with 3 rules on 3 letters EDG 22.45/5.69 22.45/5.69 ************************************************** 22.45/5.69 (3, 3)\Deepee(9, 6)\Weight(8, 5)\Matrix{\Arctic}{2}(7, 5)\Matrix{\Arctic}{2}(5, 5)\Matrix{\Arctic}{3}(4, 5)\Weight(3, 3)\EDG[] 22.45/5.69 ************************************************** 22.81/5.79 let { done = Worker No_Strict_Rules;mo = Pre (Or_Else Count (IfSizeLeq 10000 GLPK Fail));wop = Or_Else (Worker (Weight { modus = mo})) Pass;weighted = \ m -> And_Then m wop;tiling = \ m w -> weighted (And_Then (Worker (Tiling { method = m,width = w})) (Worker Remap));when_small = \ m -> And_Then (Worker (SizeAtmost 100)) m;when_medium = \ m -> And_Then (Worker (SizeAtmost 10000)) m;solver = Minisatapi;qpi = \ dim bits -> weighted (when_small (Worker (QPI { tracing = True,dim = dim,bits = bits,solver = solver})));matrix = \ dom dim bits -> weighted (when_small (Worker (Matrix { monotone = Weak,domain = dom,dim = dim,bits = bits,tracing = False,solver = solver})));kbo = \ b -> weighted (when_small (Worker (KBO { bits = b,solver = solver})));mb = Worker (Matchbound { method = RFC,max_size = 100000});remove = First_Of ([ Worker (Weight { modus = mo})] <> ([ Seq [ qpi 2 4, qpi 3 4, qpi 4 4], Seq [ qpi 5 4, qpi 6 3, qpi 7 3]] <> ([ matrix Arctic 4 3, matrix Natural 4 3] <> [ kbo 1, And_Then (Worker Mirror) (kbo 1)])));remove_tile = Seq [ remove, tiling Overlap 3];dp = As_Transformer (Apply (And_Then (Worker (DP { tracing = False})) (Worker Remap)) (Apply wop (Branch (Worker (EDG { tracing = False})) remove_tile)));noh = [ Timeout 10 (Worker (Enumerate { closure = Forward})), Timeout 10 (Worker (Enumerate { closure = Backward}))];yeah = Tree_Search_Preemptive 0 done [ Worker (Weight { modus = mo}), mb, And_Then (Worker Mirror) mb, dp, And_Then (Worker Mirror) dp]} 22.81/5.79 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 23.01/5.89 EOF