107.19/27.40 YES 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [a] -> [], [a, b] -> [b, c, a], [c, c] -> [b, a, c, a]) 107.19/27.41 reason 107.19/27.41 remap for 3 rules 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [0] -> [], [0, 1] -> [1, 2, 0], [2, 2] -> [1, 0, 2, 0]) 107.19/27.41 reason 107.19/27.41 reverse each lhs and rhs 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [0] -> [], [1, 0] -> [0, 2, 1], [2, 2] -> [0, 2, 0, 1]) 107.19/27.41 reason 107.19/27.41 DP transform 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1], [1#, 0] |-> [0#, 2, 1], [1#, 0] |-> [2#, 1], [1#, 0] |-> [1#], [2#, 2] |-> [0#, 2, 0, 1], [2#, 2] |-> [2#, 0, 1], [2#, 2] |-> [0#, 1], [2#, 2] |-> [1#]) 107.19/27.41 reason 107.19/27.41 remap for 10 rules 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1], [3, 0] |-> [4, 2, 1], [3, 0] |-> [5, 1], [3, 0] |-> [3], [5, 2] |-> [4, 2, 0, 1], [5, 2] |-> [5, 0, 1], [5, 2] |-> [4, 1], [5, 2] |-> [3]) 107.19/27.41 reason 107.19/27.41 weights 107.19/27.41 Map [(3, 1/3), (5, 1/3)] 107.19/27.41 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1], [3, 0] |-> [5, 1], [3, 0] |-> [3], [5, 2] |-> [5, 0, 1], [5, 2] |-> [3]) 107.19/27.41 reason 107.19/27.41 EDG has 1 SCCs 107.19/27.41 property Termination 107.19/27.41 has value True 107.19/27.41 for SRS ( [3, 0] |-> [5, 1], [5, 2] |-> [3], [3, 0] |-> [3], [5, 2] |-> [5, 0, 1], [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.19/27.41 reason 107.48/27.43 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 107.48/27.43 interpretation 107.48/27.43 0 Wk / 3A - - 4A \ 107.48/27.43 | 0A 0A 2A - | 107.48/27.43 | - - 7A - | 107.48/27.43 \ - - - 0A / 107.48/27.43 1 Wk / 0A - 0A - \ 107.48/27.43 | 0A - 0A 1A | 107.48/27.43 | - - - - | 107.48/27.43 \ - - - 0A / 107.48/27.43 2 Wk / - 0A 0A 0A \ 107.48/27.43 | 3A 3A 4A 4A | 107.48/27.43 | - - 0A - | 107.48/27.43 \ - - - 0A / 107.48/27.43 3 Wk / - 5A - 7A \ 107.48/27.43 | - 2A - 3A | 107.48/27.43 | - - - - | 107.48/27.43 \ - - - 0A / 107.48/27.43 5 Wk / - 3A - 6A \ 107.48/27.43 | 0A 0A 5A 2A | 107.48/27.43 | - - - - | 107.48/27.43 \ - - - 0A / 107.48/27.43 [3, 0] |-> [5, 1] 107.48/27.43 lhs rhs ge gt 107.48/27.43 Wk / 5A 5A 7A 7A \ Wk / 3A - 3A 6A \ True True 107.48/27.45 | 2A 2A 4A 3A | | 0A - 0A 2A | 107.48/27.45 | - - - - | | - - - - | 107.48/27.45 \ - - - 0A / \ - - - 0A / 107.48/27.45 [5, 2] |-> [3] 107.48/27.45 lhs rhs ge gt 107.48/27.45 Wk / 6A 6A 7A 7A \ Wk / - 5A - 7A \ True False 107.48/27.45 | 3A 3A 5A 4A | | - 2A - 3A | 107.48/27.45 | - - - - | | - - - - | 107.48/27.45 \ - - - 0A / \ - - - 0A / 107.48/27.45 [3, 0] |-> [3] 107.48/27.45 lhs rhs ge gt 107.48/27.45 Wk / 5A 5A 7A 7A \ Wk / - 5A - 7A \ True False 107.48/27.45 | 2A 2A 4A 3A | | - 2A - 3A | 107.48/27.45 | - - - - | | - - - - | 107.48/27.45 \ - - - 0A / \ - - - 0A / 107.48/27.45 [5, 2] |-> [5, 0, 1] 107.69/27.47 lhs rhs ge gt 107.69/27.47 Wk / 6A 6A 7A 7A \ Wk / 3A - 3A 6A \ True False 107.69/27.47 | 3A 3A 5A 4A | | 3A - 3A 4A | 107.69/27.47 | - - - - | | - - - - | 107.69/27.47 \ - - - 0A / \ - - - 0A / 107.69/27.47 [0] ->= [] 107.69/27.47 lhs rhs ge gt 107.69/27.47 Wk / 3A - - 4A \ Wk / 0A - - - \ True False 107.69/27.47 | 0A 0A 2A - | | - 0A - - | 107.69/27.47 | - - 7A - | | - - 0A - | 107.69/27.47 \ - - - 0A / \ - - - 0A / 107.69/27.47 [1, 0] ->= [0, 2, 1] 107.69/27.47 lhs rhs ge gt 107.69/27.47 Wk / 3A - 7A 4A \ Wk / 3A - 3A 4A \ True False 107.69/27.47 | 3A - 7A 4A | | 3A - 3A 4A | 107.69/27.47 | - - - - | | - - - - | 107.69/27.47 \ - - - 0A / \ - - - 0A / 107.69/27.47 [2, 2] ->= [0, 2, 0, 1] 107.69/27.49 lhs rhs ge gt 107.69/27.49 Wk / 3A 3A 4A 4A \ Wk / 3A - 3A 4A \ True False 107.69/27.49 | 6A 6A 7A 7A | | 6A - 6A 7A | 107.69/27.49 | - - 0A - | | - - - - | 107.69/27.49 \ - - - 0A / \ - - - 0A / 107.69/27.49 property Termination 107.69/27.49 has value True 107.69/27.49 for SRS ( [5, 2] |-> [3], [3, 0] |-> [3], [5, 2] |-> [5, 0, 1], [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.49 reason 107.69/27.49 weights 107.69/27.49 Map [(5, 1/1)] 107.69/27.49 107.69/27.49 property Termination 107.69/27.49 has value True 107.69/27.49 for SRS ( [3, 0] |-> [3], [5, 2] |-> [5, 0, 1], [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.49 reason 107.69/27.49 EDG has 2 SCCs 107.69/27.49 property Termination 107.69/27.49 has value True 107.69/27.49 for SRS ( [3, 0] |-> [3], [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.49 reason 107.69/27.49 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 107.69/27.49 interpretation 107.69/27.49 0 Wk / 1A - - 4A \ 107.69/27.49 | - 1A 1A 1A | 107.69/27.49 | 0A - 0A - | 107.69/27.49 \ - - - 0A / 107.69/27.49 1 Wk / 0A - - - \ 107.69/27.49 | 3A 5A 0A - | 107.69/27.49 | 0A - - - | 107.69/27.49 \ - - - 0A / 107.69/27.49 2 Wk / - - 0A 0A \ 107.69/27.49 | - - 3A 2A | 107.69/27.49 | 1A - 1A 4A | 107.69/27.49 \ - - - 0A / 107.69/27.50 3 Wk / 3A - - 6A \ 107.69/27.50 | - - - - | 107.69/27.50 | - - - - | 107.69/27.50 \ - - - 0A / 107.69/27.50 [3, 0] |-> [3] 107.69/27.50 lhs rhs ge gt 107.69/27.50 Wk / 4A - - 7A \ Wk / 3A - - 6A \ True True 107.69/27.50 | - - - - | | - - - - | 107.69/27.50 | - - - - | | - - - - | 107.69/27.50 \ - - - 0A / \ - - - 0A / 107.69/27.50 [0] ->= [] 107.69/27.50 lhs rhs ge gt 107.69/27.50 Wk / 1A - - 4A \ Wk / 0A - - - \ True False 107.69/27.50 | - 1A 1A 1A | | - 0A - - | 107.69/27.50 | 0A - 0A - | | - - 0A - | 107.69/27.50 \ - - - 0A / \ - - - 0A / 107.69/27.50 [1, 0] ->= [0, 2, 1] 107.69/27.52 lhs rhs ge gt 107.69/27.52 Wk / 1A - - 4A \ Wk / 1A - - 4A \ True False 107.69/27.52 | 4A 6A 6A 7A | | 4A - - 5A | 107.69/27.52 | 1A - - 4A | | 1A - - 4A | 107.69/27.52 \ - - - 0A / \ - - - 0A / 107.69/27.52 [2, 2] ->= [0, 2, 0, 1] 107.69/27.52 lhs rhs ge gt 107.69/27.52 Wk / 1A - 1A 4A \ Wk / 1A - - 4A \ True False 107.69/27.52 | 4A - 4A 7A | | 4A - - 6A | 107.69/27.52 | 2A - 2A 5A | | 2A - - 5A | 107.69/27.52 \ - - - 0A / \ - - - 0A / 107.69/27.52 property Termination 107.69/27.52 has value True 107.69/27.52 for SRS ( [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.52 reason 107.69/27.52 EDG has 0 SCCs 107.69/27.52 107.69/27.52 property Termination 107.69/27.52 has value True 107.69/27.52 for SRS ( [5, 2] |-> [5, 0, 1], [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.52 reason 107.69/27.52 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 107.69/27.52 interpretation 107.69/27.52 0 Wk / 0A 0A - 0A \ 107.69/27.52 | - 0A 0A - | 107.69/27.52 | 0A - 2A 3A | 107.69/27.52 \ - - - 0A / 107.69/27.52 1 Wk / - - 0A 0A \ 107.69/27.52 | - - 0A 0A | 107.69/27.52 | - - 0A 1A | 107.69/27.52 \ - - - 0A / 107.69/27.54 2 Wk / 2A 2A 0A - \ 107.69/27.54 | - 2A 2A 3A | 107.69/27.54 | - 0A - 1A | 107.69/27.54 \ - - - 0A / 107.69/27.54 5 Wk / 2A 2A 1A - \ 107.69/27.54 | - - - - | 107.69/27.54 | - - - - | 107.69/27.54 \ - - - 0A / 107.69/27.54 [5, 2] |-> [5, 0, 1] 107.69/27.54 lhs rhs ge gt 107.69/27.54 Wk / 4A 4A 4A 5A \ Wk / - - 3A 4A \ True True 107.69/27.54 | - - - - | | - - - - | 107.69/27.54 | - - - - | | - - - - | 107.69/27.54 \ - - - 0A / \ - - - 0A / 107.69/27.54 [0] ->= [] 107.69/27.54 lhs rhs ge gt 107.69/27.54 Wk / 0A 0A - 0A \ Wk / 0A - - - \ True False 107.69/27.54 | - 0A 0A - | | - 0A - - | 107.69/27.54 | 0A - 2A 3A | | - - 0A - | 107.69/27.54 \ - - - 0A / \ - - - 0A / 107.69/27.54 [1, 0] ->= [0, 2, 1] 107.69/27.54 lhs rhs ge gt 107.69/27.54 Wk / 0A - 2A 3A \ Wk / - - 2A 3A \ True False 107.69/27.54 | 0A - 2A 3A | | - - 2A 3A | 107.69/27.54 | 0A - 2A 3A | | - - 2A 3A | 107.69/27.54 \ - - - 0A / \ - - - 0A / 107.69/27.54 [2, 2] ->= [0, 2, 0, 1] 107.69/27.54 lhs rhs ge gt 107.69/27.54 Wk / 4A 4A 4A 5A \ Wk / - - 4A 5A \ True False 107.69/27.54 | - 4A 4A 5A | | - - 4A 5A | 107.69/27.54 | - 2A 2A 3A | | - - 2A 3A | 107.69/27.54 \ - - - 0A / \ - - - 0A / 107.69/27.54 property Termination 107.69/27.54 has value True 107.69/27.54 for SRS ( [0] ->= [], [1, 0] ->= [0, 2, 1], [2, 2] ->= [0, 2, 0, 1]) 107.69/27.54 reason 107.69/27.54 EDG has 0 SCCs 107.69/27.54 107.69/27.54 ************************************************** 107.69/27.54 summary 107.69/27.54 ************************************************** 107.69/27.54 SRS with 3 rules on 3 letters Remap { tracing = False} 107.69/27.54 SRS with 3 rules on 3 letters reverse each lhs and rhs 107.69/27.54 SRS with 3 rules on 3 letters DP transform 107.69/27.54 SRS with 10 rules on 6 letters Remap { tracing = False} 107.69/27.54 SRS with 10 rules on 6 letters weights 107.69/27.54 SRS with 7 rules on 5 letters EDG 107.69/27.54 SRS with 7 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 107.69/27.54 SRS with 6 rules on 5 letters weights 107.69/27.54 SRS with 5 rules on 5 letters EDG 107.69/27.54 2 sub-proofs 108.00/27.56 1 SRS with 4 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 108.00/27.56 SRS with 3 rules on 3 letters EDG 108.00/27.56 108.00/27.56 2 SRS with 4 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 108.00/27.56 SRS with 3 rules on 3 letters EDG 108.00/27.56 108.00/27.56 ************************************************** 108.00/27.56 (3, 3)\Deepee(10, 6)\Weight(7, 5)\Matrix{\Arctic}{4}(6, 5)\Weight(5, 5)\EDG[(4, 4)\Matrix{\Arctic}{4}(3, 3)\EDG[],(4, 4)\Matrix{\Arctic}{4}(3, 3)\EDG[]] 108.00/27.56 ************************************************** 108.38/27.67 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]} 108.38/27.67 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 108.87/27.80 EOF