39.33/9.96 YES 39.33/9.96 property Termination 39.33/9.97 has value True 39.49/9.99 for SRS ( [c, c, b] -> [a, c, b], [a, c, b, a] -> [b, c, c], [b, a, c] -> [a, b, c, a], [b, c, a] -> [c, a, b]) 39.49/9.99 reason 39.49/9.99 remap for 4 rules 39.49/9.99 property Termination 39.49/9.99 has value True 39.49/9.99 for SRS ( [0, 0, 1] -> [2, 0, 1], [2, 0, 1, 2] -> [1, 0, 0], [1, 2, 0] -> [2, 1, 0, 2], [1, 0, 2] -> [0, 2, 1]) 39.49/9.99 reason 39.49/9.99 reverse each lhs and rhs 39.49/9.99 property Termination 39.49/9.99 has value True 39.49/10.00 for SRS ( [1, 0, 0] -> [1, 0, 2], [2, 1, 0, 2] -> [0, 0, 1], [0, 2, 1] -> [2, 0, 1, 2], [2, 0, 1] -> [1, 2, 0]) 39.49/10.00 reason 39.49/10.00 DP transform 39.49/10.00 property Termination 39.49/10.00 has value True 39.49/10.04 for SRS ( [1, 0, 0] ->= [1, 0, 2], [2, 1, 0, 2] ->= [0, 0, 1], [0, 2, 1] ->= [2, 0, 1, 2], [2, 0, 1] ->= [1, 2, 0], [1#, 0, 0] |-> [1#, 0, 2], [1#, 0, 0] |-> [0#, 2], [1#, 0, 0] |-> [2#], [2#, 1, 0, 2] |-> [0#, 0, 1], [2#, 1, 0, 2] |-> [0#, 1], [2#, 1, 0, 2] |-> [1#], [0#, 2, 1] |-> [2#, 0, 1, 2], [0#, 2, 1] |-> [0#, 1, 2], [0#, 2, 1] |-> [1#, 2], [0#, 2, 1] |-> [2#], [2#, 0, 1] |-> [1#, 2, 0], [2#, 0, 1] |-> [2#, 0], [2#, 0, 1] |-> [0#]) 39.49/10.04 reason 39.49/10.04 remap for 17 rules 39.49/10.04 property Termination 39.49/10.04 has value True 39.67/10.05 for SRS ( [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1], [3, 1, 1] |-> [3, 1, 2], [3, 1, 1] |-> [4, 2], [3, 1, 1] |-> [5], [5, 0, 1, 2] |-> [4, 1, 0], [5, 0, 1, 2] |-> [4, 0], [5, 0, 1, 2] |-> [3], [4, 2, 0] |-> [5, 1, 0, 2], [4, 2, 0] |-> [4, 0, 2], [4, 2, 0] |-> [3, 2], [4, 2, 0] |-> [5], [5, 1, 0] |-> [3, 2, 1], [5, 1, 0] |-> [5, 1], [5, 1, 0] |-> [4]) 39.67/10.05 reason 39.67/10.05 weights 39.67/10.05 Map [(0, 3/1), (3, 2/1)] 39.67/10.05 39.67/10.05 property Termination 39.67/10.05 has value True 39.67/10.05 for SRS ( [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1], [3, 1, 1] |-> [3, 1, 2], [5, 0, 1, 2] |-> [4, 1, 0], [5, 0, 1, 2] |-> [4, 0], [4, 2, 0] |-> [5, 1, 0, 2], [4, 2, 0] |-> [4, 0, 2]) 39.67/10.05 reason 39.67/10.05 EDG has 2 SCCs 39.67/10.05 property Termination 39.67/10.05 has value True 39.73/10.06 for SRS ( [3, 1, 1] |-> [3, 1, 2], [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 39.73/10.06 reason 39.73/10.07 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 39.73/10.07 interpretation 39.73/10.07 0 / 27A 30A 30A \ 39.73/10.07 | 27A 30A 30A | 39.73/10.07 \ 27A 30A 30A / 39.73/10.07 1 / 0A 3A 3A \ 39.73/10.07 | 0A 0A 3A | 39.73/10.07 \ 0A 0A 0A / 39.73/10.07 2 / 0A 0A 3A \ 39.73/10.07 | -3A 0A 0A | 39.73/10.07 \ -3A 0A 0A / 39.73/10.07 3 / 17A 17A 18A \ 39.73/10.07 | 17A 17A 18A | 39.73/10.07 \ 17A 17A 18A / 39.73/10.07 [3, 1, 1] |-> [3, 1, 2] 39.73/10.07 lhs rhs ge gt 39.73/10.07 / 20A 21A 23A \ / 18A 20A 21A \ True True 39.73/10.07 | 20A 21A 23A | | 18A 20A 21A | 39.73/10.07 \ 20A 21A 23A / \ 18A 20A 21A / 39.73/10.07 [0, 1, 1] ->= [0, 1, 2] 39.73/10.08 lhs rhs ge gt 39.73/10.08 / 33A 33A 33A \ / 30A 33A 33A \ True False 39.73/10.08 | 33A 33A 33A | | 30A 33A 33A | 39.73/10.08 \ 33A 33A 33A / \ 30A 33A 33A / 39.73/10.08 [2, 0, 1, 2] ->= [1, 1, 0] 39.73/10.08 lhs rhs ge gt 39.73/10.08 / 33A 36A 36A \ / 33A 36A 36A \ True False 39.73/10.08 | 30A 33A 33A | | 30A 33A 33A | 39.73/10.08 \ 30A 33A 33A / \ 30A 33A 33A / 39.73/10.08 [1, 2, 0] ->= [2, 1, 0, 2] 39.73/10.08 lhs rhs ge gt 39.73/10.08 / 30A 33A 33A \ / 30A 33A 33A \ True False 39.73/10.08 | 30A 33A 33A | | 30A 33A 33A | 39.73/10.08 \ 30A 33A 33A / \ 30A 33A 33A / 39.73/10.08 [2, 1, 0] ->= [0, 2, 1] 39.73/10.08 lhs rhs ge gt 39.73/10.08 / 30A 33A 33A \ / 30A 30A 33A \ True False 39.73/10.08 | 30A 33A 33A | | 30A 30A 33A | 39.73/10.08 \ 30A 33A 33A / \ 30A 30A 33A / 39.73/10.08 property Termination 39.73/10.08 has value True 39.73/10.08 for SRS ( [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 39.73/10.08 reason 39.73/10.08 EDG has 0 SCCs 39.73/10.08 39.73/10.08 property Termination 39.73/10.08 has value True 39.73/10.09 for SRS ( [5, 0, 1, 2] |-> [4, 1, 0], [4, 2, 0] |-> [4, 0, 2], [4, 2, 0] |-> [5, 1, 0, 2], [5, 0, 1, 2] |-> [4, 0], [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 39.73/10.09 reason 39.73/10.09 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 39.73/10.09 interpretation 39.73/10.09 0 / 2A 2A \ 39.73/10.09 \ 0A 0A / 39.73/10.09 1 / 0A 0A \ 39.73/10.09 \ 0A 0A / 39.73/10.09 2 / 0A 0A \ 39.73/10.09 \ 0A 0A / 39.73/10.09 4 / 13A 14A \ 39.73/10.09 \ 13A 14A / 39.73/10.10 5 / 14A 14A \ 39.73/10.10 \ 14A 14A / 39.73/10.10 [5, 0, 1, 2] |-> [4, 1, 0] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 16A 16A \ / 16A 16A \ True False 39.73/10.10 \ 16A 16A / \ 16A 16A / 39.73/10.10 [4, 2, 0] |-> [4, 0, 2] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 16A 16A \ / 15A 15A \ True True 39.73/10.10 \ 16A 16A / \ 15A 15A / 39.73/10.10 [4, 2, 0] |-> [5, 1, 0, 2] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 16A 16A \ / 16A 16A \ True False 39.73/10.10 \ 16A 16A / \ 16A 16A / 39.73/10.10 [5, 0, 1, 2] |-> [4, 0] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 16A 16A \ / 15A 15A \ True True 39.73/10.10 \ 16A 16A / \ 15A 15A / 39.73/10.10 [0, 1, 1] ->= [0, 1, 2] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 2A 2A \ / 2A 2A \ True False 39.73/10.10 \ 0A 0A / \ 0A 0A / 39.73/10.10 [2, 0, 1, 2] ->= [1, 1, 0] 39.73/10.10 lhs rhs ge gt 39.73/10.10 / 2A 2A \ / 2A 2A \ True False 39.73/10.10 \ 2A 2A / \ 2A 2A / 39.73/10.10 [1, 2, 0] ->= [2, 1, 0, 2] 39.73/10.10 lhs rhs ge gt 39.73/10.11 / 2A 2A \ / 2A 2A \ True False 39.73/10.11 \ 2A 2A / \ 2A 2A / 39.73/10.11 [2, 1, 0] ->= [0, 2, 1] 39.73/10.11 lhs rhs ge gt 39.73/10.11 / 2A 2A \ / 2A 2A \ True False 39.73/10.11 \ 2A 2A / \ 0A 0A / 39.73/10.11 property Termination 39.73/10.11 has value True 40.91/10.39 for SRS ( [5, 0, 1, 2] |-> [4, 1, 0], [4, 2, 0] |-> [5, 1, 0, 2], [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 40.91/10.41 reason 41.27/10.45 EDG has 1 SCCs 41.27/10.47 property Termination 41.27/10.49 has value True 41.77/10.62 for SRS ( [5, 0, 1, 2] |-> [4, 1, 0], [4, 2, 0] |-> [5, 1, 0, 2], [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 41.77/10.62 reason 41.77/10.62 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 41.77/10.62 interpretation 41.77/10.62 0 / 4A 4A \ 41.77/10.62 \ 2A 2A / 41.77/10.62 1 / 0A 0A \ 41.77/10.62 \ -2A 0A / 41.77/10.62 2 / 0A 0A \ 41.77/10.62 \ 0A 0A / 41.77/10.62 4 / 23A 25A \ 41.77/10.62 \ 23A 25A / 41.77/10.62 5 / 25A 27A \ 41.77/10.62 \ 25A 27A / 41.77/10.62 [5, 0, 1, 2] |-> [4, 1, 0] 41.77/10.62 lhs rhs ge gt 41.77/10.62 / 29A 29A \ / 27A 27A \ True True 41.77/10.62 \ 29A 29A / \ 27A 27A / 41.77/10.62 [4, 2, 0] |-> [5, 1, 0, 2] 41.77/10.62 lhs rhs ge gt 41.77/10.62 / 29A 29A \ / 29A 29A \ True False 41.77/10.62 \ 29A 29A / \ 29A 29A / 41.77/10.63 [0, 1, 1] ->= [0, 1, 2] 41.77/10.63 lhs rhs ge gt 41.77/10.63 / 4A 4A \ / 4A 4A \ True False 41.77/10.63 \ 2A 2A / \ 2A 2A / 41.77/10.63 [2, 0, 1, 2] ->= [1, 1, 0] 41.77/10.63 lhs rhs ge gt 41.77/10.63 / 4A 4A \ / 4A 4A \ True False 41.77/10.63 \ 4A 4A / \ 2A 2A / 41.77/10.63 [1, 2, 0] ->= [2, 1, 0, 2] 41.77/10.63 lhs rhs ge gt 41.77/10.63 / 4A 4A \ / 4A 4A \ True False 41.77/10.63 \ 4A 4A / \ 4A 4A / 41.77/10.63 [2, 1, 0] ->= [0, 2, 1] 41.77/10.63 lhs rhs ge gt 41.77/10.63 / 4A 4A \ / 4A 4A \ True False 41.77/10.63 \ 4A 4A / \ 2A 2A / 41.77/10.63 property Termination 41.77/10.63 has value True 41.77/10.63 for SRS ( [4, 2, 0] |-> [5, 1, 0, 2], [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 41.77/10.63 reason 41.77/10.63 weights 41.77/10.64 Map [(4, 1/1)] 41.77/10.64 41.77/10.64 property Termination 41.77/10.64 has value True 41.77/10.64 for SRS ( [0, 1, 1] ->= [0, 1, 2], [2, 0, 1, 2] ->= [1, 1, 0], [1, 2, 0] ->= [2, 1, 0, 2], [2, 1, 0] ->= [0, 2, 1]) 41.77/10.64 reason 41.77/10.64 EDG has 0 SCCs 41.77/10.64 41.77/10.64 ************************************************** 41.77/10.64 summary 41.77/10.64 ************************************************** 41.77/10.64 SRS with 4 rules on 3 letters Remap { tracing = False} 41.77/10.64 SRS with 4 rules on 3 letters reverse each lhs and rhs 42.06/10.66 SRS with 4 rules on 3 letters DP transform 42.06/10.66 SRS with 17 rules on 6 letters Remap { tracing = False} 42.06/10.66 SRS with 17 rules on 6 letters weights 42.12/10.67 SRS with 9 rules on 6 letters EDG 42.12/10.67 2 sub-proofs 42.12/10.68 1 SRS with 5 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 42.12/10.69 SRS with 4 rules on 3 letters EDG 42.12/10.69 42.12/10.69 2 SRS with 8 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 42.12/10.69 SRS with 6 rules on 5 letters EDG 42.12/10.69 SRS with 6 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 42.12/10.69 SRS with 5 rules on 5 letters weights 42.12/10.69 SRS with 4 rules on 3 letters EDG 42.12/10.69 42.12/10.69 ************************************************** 42.12/10.69 (4, 3)\Deepee(17, 6)\Weight(9, 6)\EDG[(5, 4)\Matrix{\Arctic}{3}(4, 3)\EDG[],(8, 5)\Matrix{\Arctic}{2}(6, 5)\Matrix{\Arctic}{2}(5, 5)\Weight(4, 3)\EDG[]] 42.12/10.69 ************************************************** 46.92/11.89 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]} 46.92/11.89 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 47.42/12.06 EOF