24.76/6.28 YES 24.76/6.28 property Termination 24.76/6.28 has value True 24.76/6.28 for SRS ( [b, b, b] -> [a], [a, a] -> [a, b, a], [a, a, a] -> [b, a, a]) 24.76/6.28 reason 24.76/6.28 remap for 3 rules 24.76/6.29 property Termination 24.76/6.29 has value True 24.76/6.30 for SRS ( [0, 0, 0] -> [1], [1, 1] -> [1, 0, 1], [1, 1, 1] -> [0, 1, 1]) 24.76/6.30 reason 24.76/6.30 reverse each lhs and rhs 24.76/6.30 property Termination 24.76/6.30 has value True 24.76/6.30 for SRS ( [0, 0, 0] -> [1], [1, 1] -> [1, 0, 1], [1, 1, 1] -> [1, 1, 0]) 24.76/6.30 reason 24.76/6.30 DP transform 24.76/6.30 property Termination 24.76/6.30 has value True 24.87/6.32 for SRS ( [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0], [0#, 0, 0] |-> [1#], [1#, 1] |-> [1#, 0, 1], [1#, 1] |-> [0#, 1], [1#, 1, 1] |-> [1#, 1, 0], [1#, 1, 1] |-> [1#, 0], [1#, 1, 1] |-> [0#]) 24.87/6.32 reason 24.87/6.32 remap for 9 rules 24.87/6.32 property Termination 24.87/6.32 has value True 24.87/6.32 for SRS ( [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0], [2, 0, 0] |-> [3], [3, 1] |-> [3, 0, 1], [3, 1] |-> [2, 1], [3, 1, 1] |-> [3, 1, 0], [3, 1, 1] |-> [3, 0], [3, 1, 1] |-> [2]) 24.87/6.32 reason 24.87/6.32 EDG has 1 SCCs 24.87/6.32 property Termination 24.87/6.32 has value True 24.95/6.33 for SRS ( [2, 0, 0] |-> [3], [3, 1, 1] |-> [2], [3, 1, 1] |-> [3, 0], [3, 1, 1] |-> [3, 1, 0], [3, 1] |-> [2, 1], [3, 1] |-> [3, 0, 1], [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.33 reason 24.95/6.34 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 24.95/6.34 interpretation 24.95/6.34 0 / 0A 2A \ 24.95/6.34 \ 0A 2A / 24.95/6.34 1 / 2A 2A \ 24.95/6.34 \ 0A 0A / 24.95/6.34 2 / 8A 10A \ 24.95/6.34 \ 8A 10A / 24.95/6.34 3 / 11A 11A \ 24.95/6.34 \ 11A 11A / 24.95/6.34 [2, 0, 0] |-> [3] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 12A 14A \ / 11A 11A \ True True 24.95/6.34 \ 12A 14A / \ 11A 11A / 24.95/6.34 [3, 1, 1] |-> [2] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 15A 15A \ / 8A 10A \ True True 24.95/6.34 \ 15A 15A / \ 8A 10A / 24.95/6.34 [3, 1, 1] |-> [3, 0] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 15A 15A \ / 11A 13A \ True True 24.95/6.34 \ 15A 15A / \ 11A 13A / 24.95/6.34 [3, 1, 1] |-> [3, 1, 0] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 15A 15A \ / 13A 15A \ True False 24.95/6.34 \ 15A 15A / \ 13A 15A / 24.95/6.34 [3, 1] |-> [2, 1] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 13A 13A \ / 10A 10A \ True True 24.95/6.34 \ 13A 13A / \ 10A 10A / 24.95/6.34 [3, 1] |-> [3, 0, 1] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 13A 13A \ / 13A 13A \ True False 24.95/6.34 \ 13A 13A / \ 13A 13A / 24.95/6.34 [0, 0, 0] ->= [1] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 4A 6A \ / 2A 2A \ True True 24.95/6.34 \ 4A 6A / \ 0A 0A / 24.95/6.34 [1, 1] ->= [1, 0, 1] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 4A 4A \ / 4A 4A \ True False 24.95/6.34 \ 2A 2A / \ 2A 2A / 24.95/6.34 [1, 1, 1] ->= [1, 1, 0] 24.95/6.34 lhs rhs ge gt 24.95/6.34 / 6A 6A \ / 4A 6A \ True False 24.95/6.34 \ 4A 4A / \ 2A 4A / 24.95/6.34 property Termination 24.95/6.34 has value True 24.95/6.35 for SRS ( [3, 1, 1] |-> [3, 1, 0], [3, 1] |-> [3, 0, 1], [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.35 reason 24.95/6.36 EDG has 1 SCCs 24.95/6.36 property Termination 24.95/6.36 has value True 24.95/6.36 for SRS ( [3, 1, 1] |-> [3, 1, 0], [3, 1] |-> [3, 0, 1], [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.36 reason 24.95/6.36 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 24.95/6.36 interpretation 24.95/6.36 0 / 0A 2A \ 24.95/6.36 \ 0A 2A / 24.95/6.36 1 / 4A 4A \ 24.95/6.36 \ 2A 2A / 24.95/6.36 3 / 20A 20A \ 24.95/6.36 \ 20A 20A / 24.95/6.36 [3, 1, 1] |-> [3, 1, 0] 24.95/6.36 lhs rhs ge gt 24.95/6.36 / 28A 28A \ / 24A 26A \ True True 24.95/6.36 \ 28A 28A / \ 24A 26A / 24.95/6.36 [3, 1] |-> [3, 0, 1] 24.95/6.36 lhs rhs ge gt 24.95/6.36 / 24A 24A \ / 24A 24A \ True False 24.95/6.36 \ 24A 24A / \ 24A 24A / 24.95/6.36 [0, 0, 0] ->= [1] 24.95/6.36 lhs rhs ge gt 24.95/6.36 / 4A 6A \ / 4A 4A \ True False 24.95/6.36 \ 4A 6A / \ 2A 2A / 24.95/6.36 [1, 1] ->= [1, 0, 1] 24.95/6.36 lhs rhs ge gt 24.95/6.36 / 8A 8A \ / 8A 8A \ True False 24.95/6.37 \ 6A 6A / \ 6A 6A / 24.95/6.37 [1, 1, 1] ->= [1, 1, 0] 24.95/6.37 lhs rhs ge gt 24.95/6.37 / 12A 12A \ / 8A 10A \ True True 24.95/6.37 \ 10A 10A / \ 6A 8A / 24.95/6.37 property Termination 24.95/6.37 has value True 24.95/6.37 for SRS ( [3, 1] |-> [3, 0, 1], [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.37 reason 24.95/6.37 EDG has 1 SCCs 24.95/6.37 property Termination 24.95/6.37 has value True 24.95/6.37 for SRS ( [3, 1] |-> [3, 0, 1], [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.37 reason 24.95/6.37 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 24.95/6.37 interpretation 24.95/6.38 0 Wk / - 0A - 0A \ 24.95/6.38 | 0A 0A - - | 24.95/6.38 | - 4A - 0A | 24.95/6.38 \ - - - 0A / 24.95/6.38 1 Wk / 0A 0A - 0A \ 24.95/6.38 | - - - - | 24.95/6.38 | 0A - - 4A | 24.95/6.38 \ - - - 0A / 24.95/6.38 3 Wk / - - 0A 0A \ 24.95/6.38 | - - - - | 24.95/6.38 | - - - - | 24.95/6.38 \ - - - 0A / 24.95/6.38 [3, 1] |-> [3, 0, 1] 24.95/6.38 lhs rhs ge gt 24.95/6.38 Wk / 0A - - 4A \ Wk / - - - 0A \ True True 24.95/6.38 | - - - - | | - - - - | 24.95/6.38 | - - - - | | - - - - | 24.95/6.38 \ - - - 0A / \ - - - 0A / 24.95/6.38 [0, 0, 0] ->= [1] 24.95/6.38 lhs rhs ge gt 24.95/6.38 Wk / 0A 0A - 0A \ Wk / 0A 0A - 0A \ True False 24.95/6.38 | 0A 0A - 0A | | - - - - | 24.95/6.38 | 4A 4A - 4A | | 0A - - 4A | 24.95/6.38 \ - - - 0A / \ - - - 0A / 24.95/6.38 [1, 1] ->= [1, 0, 1] 24.95/6.38 lhs rhs ge gt 24.95/6.38 Wk / 0A 0A - 0A \ Wk / 0A 0A - 0A \ True False 24.95/6.38 | - - - - | | - - - - | 24.95/6.38 | 0A 0A - 4A | | - - - 4A | 24.95/6.38 \ - - - 0A / \ - - - 0A / 24.95/6.38 [1, 1, 1] ->= [1, 1, 0] 24.95/6.38 lhs rhs ge gt 24.95/6.38 Wk / 0A 0A - 0A \ Wk / 0A 0A - 0A \ True False 24.95/6.38 | - - - - | | - - - - | 24.95/6.38 | 0A 0A - 4A | | 0A 0A - 4A | 24.95/6.38 \ - - - 0A / \ - - - 0A / 24.95/6.38 property Termination 24.95/6.38 has value True 24.95/6.38 for SRS ( [0, 0, 0] ->= [1], [1, 1] ->= [1, 0, 1], [1, 1, 1] ->= [1, 1, 0]) 24.95/6.38 reason 24.95/6.38 EDG has 0 SCCs 24.95/6.38 24.95/6.38 ************************************************** 24.95/6.38 summary 24.95/6.38 ************************************************** 24.95/6.38 SRS with 3 rules on 2 letters Remap { tracing = False} 24.95/6.38 SRS with 3 rules on 2 letters reverse each lhs and rhs 24.95/6.38 SRS with 3 rules on 2 letters DP transform 24.95/6.38 SRS with 9 rules on 4 letters Remap { tracing = False} 24.95/6.39 SRS with 9 rules on 4 letters EDG 24.95/6.39 SRS with 9 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 24.95/6.39 SRS with 5 rules on 3 letters EDG 24.95/6.39 SRS with 5 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 24.95/6.39 SRS with 4 rules on 3 letters EDG 24.95/6.39 SRS with 4 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 24.95/6.39 SRS with 3 rules on 2 letters EDG 24.95/6.39 24.95/6.39 ************************************************** 24.95/6.39 (3, 2)\Deepee(9, 4)\Matrix{\Arctic}{2}(5, 3)\Matrix{\Arctic}{2}(4, 3)\Matrix{\Arctic}{4}(3, 2)\EDG[] 24.95/6.39 ************************************************** 24.95/6.42 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]} 24.95/6.42 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 25.44/6.51 EOF