36.49/9.26 YES 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [a, a] -> [b], [a, b] -> [c, c], [b, c] -> [b, a, a]) 36.49/9.26 reason 36.49/9.26 remap for 3 rules 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [0, 0] -> [1], [0, 1] -> [2, 2], [1, 2] -> [1, 0, 0]) 36.49/9.26 reason 36.49/9.26 reverse each lhs and rhs 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [0, 0] -> [1], [1, 0] -> [2, 2], [2, 1] -> [0, 0, 1]) 36.49/9.26 reason 36.49/9.26 DP transform 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1], [0#, 0] |-> [1#], [1#, 0] |-> [2#, 2], [1#, 0] |-> [2#], [2#, 1] |-> [0#, 0, 1], [2#, 1] |-> [0#, 1]) 36.49/9.26 reason 36.49/9.26 remap for 8 rules 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1], [3, 0] |-> [4], [4, 0] |-> [5, 2], [4, 0] |-> [5], [5, 1] |-> [3, 0, 1], [5, 1] |-> [3, 1]) 36.49/9.26 reason 36.49/9.26 EDG has 1 SCCs 36.49/9.26 property Termination 36.49/9.26 has value True 36.49/9.26 for SRS ( [3, 0] |-> [4], [4, 0] |-> [5], [5, 1] |-> [3, 1], [5, 1] |-> [3, 0, 1], [4, 0] |-> [5, 2], [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1]) 36.49/9.26 reason 36.49/9.26 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 36.49/9.26 interpretation 36.49/9.26 0 / 0A 0A 3A \ 36.49/9.26 | 0A 0A 3A | 36.49/9.26 \ -3A 0A 0A / 36.49/9.26 1 / 0A 3A 3A \ 36.49/9.26 | -3A 0A 0A | 36.49/9.26 \ -3A 0A 0A / 36.49/9.26 2 / 0A 0A 0A \ 36.49/9.26 | 0A 0A 0A | 36.49/9.26 \ 0A 0A 0A / 36.49/9.26 3 / 43A 43A 46A \ 36.49/9.26 | 43A 43A 46A | 36.49/9.26 \ 43A 43A 46A / 36.49/9.26 4 / 43A 44A 44A \ 36.49/9.26 | 43A 44A 44A | 36.49/9.26 \ 43A 44A 44A / 36.49/9.26 5 / 43A 43A 44A \ 36.49/9.26 | 43A 43A 44A | 36.49/9.26 \ 43A 43A 44A / 36.49/9.26 [3, 0] |-> [4] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 43A 46A 46A \ / 43A 44A 44A \ True False 36.49/9.26 | 43A 46A 46A | | 43A 44A 44A | 36.49/9.26 \ 43A 46A 46A / \ 43A 44A 44A / 36.49/9.26 [4, 0] |-> [5] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 44A 44A 47A \ / 43A 43A 44A \ True True 36.49/9.26 | 44A 44A 47A | | 43A 43A 44A | 36.49/9.26 \ 44A 44A 47A / \ 43A 43A 44A / 36.49/9.26 [5, 1] |-> [3, 1] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 43A 46A 46A \ / 43A 46A 46A \ True False 36.49/9.26 | 43A 46A 46A | | 43A 46A 46A | 36.49/9.26 \ 43A 46A 46A / \ 43A 46A 46A / 36.49/9.26 [5, 1] |-> [3, 0, 1] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 43A 46A 46A \ / 43A 46A 46A \ True False 36.49/9.26 | 43A 46A 46A | | 43A 46A 46A | 36.49/9.26 \ 43A 46A 46A / \ 43A 46A 46A / 36.49/9.26 [4, 0] |-> [5, 2] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 44A 44A 47A \ / 44A 44A 44A \ True False 36.49/9.26 | 44A 44A 47A | | 44A 44A 44A | 36.49/9.26 \ 44A 44A 47A / \ 44A 44A 44A / 36.49/9.26 [0, 0] ->= [1] 36.49/9.26 lhs rhs ge gt 36.49/9.26 / 0A 3A 3A \ / 0A 3A 3A \ True False 36.78/9.30 | 0A 3A 3A | | -3A 0A 0A | 36.78/9.30 \ 0A 0A 3A / \ -3A 0A 0A / 36.78/9.30 [1, 0] ->= [2, 2] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 3A 3A 6A \ / 0A 0A 0A \ True False 36.78/9.30 | 0A 0A 3A | | 0A 0A 0A | 36.78/9.30 \ 0A 0A 3A / \ 0A 0A 0A / 36.78/9.30 [2, 1] ->= [0, 0, 1] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 0A 3A 3A \ / 0A 3A 3A \ True False 36.78/9.30 | 0A 3A 3A | | 0A 3A 3A | 36.78/9.30 \ 0A 3A 3A / \ 0A 3A 3A / 36.78/9.30 property Termination 36.78/9.30 has value True 36.78/9.30 for SRS ( [3, 0] |-> [4], [5, 1] |-> [3, 1], [5, 1] |-> [3, 0, 1], [4, 0] |-> [5, 2], [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1]) 36.78/9.30 reason 36.78/9.30 EDG has 1 SCCs 36.78/9.30 property Termination 36.78/9.30 has value True 36.78/9.30 for SRS ( [3, 0] |-> [4], [4, 0] |-> [5, 2], [5, 1] |-> [3, 0, 1], [5, 1] |-> [3, 1], [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1]) 36.78/9.30 reason 36.78/9.30 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 36.78/9.30 interpretation 36.78/9.30 0 / 0A 0A 3A \ 36.78/9.30 | 0A 0A 3A | 36.78/9.30 \ -3A 0A 0A / 36.78/9.30 1 / 0A 3A 3A \ 36.78/9.30 | -3A 0A 0A | 36.78/9.30 \ -3A 0A 0A / 36.78/9.30 2 / 0A 0A 0A \ 36.78/9.30 | 0A 0A 0A | 36.78/9.30 \ 0A 0A 0A / 36.78/9.30 3 / 22A 22A 25A \ 36.78/9.30 | 22A 22A 25A | 36.78/9.30 \ 22A 22A 25A / 36.78/9.30 4 / 22A 25A 25A \ 36.78/9.30 | 22A 25A 25A | 36.78/9.30 \ 22A 25A 25A / 36.78/9.30 5 / 24A 24A 24A \ 36.78/9.30 | 24A 24A 24A | 36.78/9.30 \ 24A 24A 24A / 36.78/9.30 [3, 0] |-> [4] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 22A 25A 25A \ / 22A 25A 25A \ True False 36.78/9.30 | 22A 25A 25A | | 22A 25A 25A | 36.78/9.30 \ 22A 25A 25A / \ 22A 25A 25A / 36.78/9.30 [4, 0] |-> [5, 2] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 25A 25A 28A \ / 24A 24A 24A \ True True 36.78/9.30 | 25A 25A 28A | | 24A 24A 24A | 36.78/9.30 \ 25A 25A 28A / \ 24A 24A 24A / 36.78/9.30 [5, 1] |-> [3, 0, 1] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 24A 27A 27A \ / 22A 25A 25A \ True True 36.78/9.30 | 24A 27A 27A | | 22A 25A 25A | 36.78/9.30 \ 24A 27A 27A / \ 22A 25A 25A / 36.78/9.30 [5, 1] |-> [3, 1] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 24A 27A 27A \ / 22A 25A 25A \ True True 36.78/9.30 | 24A 27A 27A | | 22A 25A 25A | 36.78/9.30 \ 24A 27A 27A / \ 22A 25A 25A / 36.78/9.30 [0, 0] ->= [1] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 0A 3A 3A \ / 0A 3A 3A \ True False 36.78/9.30 | 0A 3A 3A | | -3A 0A 0A | 36.78/9.30 \ 0A 0A 3A / \ -3A 0A 0A / 36.78/9.30 [1, 0] ->= [2, 2] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 3A 3A 6A \ / 0A 0A 0A \ True False 36.78/9.30 | 0A 0A 3A | | 0A 0A 0A | 36.78/9.30 \ 0A 0A 3A / \ 0A 0A 0A / 36.78/9.30 [2, 1] ->= [0, 0, 1] 36.78/9.30 lhs rhs ge gt 36.78/9.30 / 0A 3A 3A \ / 0A 3A 3A \ True False 36.78/9.30 | 0A 3A 3A | | 0A 3A 3A | 36.78/9.30 \ 0A 3A 3A / \ 0A 3A 3A / 36.78/9.30 property Termination 36.78/9.30 has value True 36.78/9.30 for SRS ( [3, 0] |-> [4], [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1]) 36.78/9.30 reason 36.78/9.30 weights 36.78/9.30 Map [(3, 1/1)] 36.78/9.30 36.78/9.30 property Termination 36.78/9.30 has value True 36.78/9.30 for SRS ( [0, 0] ->= [1], [1, 0] ->= [2, 2], [2, 1] ->= [0, 0, 1]) 36.78/9.30 reason 36.78/9.30 EDG has 0 SCCs 36.78/9.30 36.78/9.30 ************************************************** 36.78/9.30 summary 36.78/9.30 ************************************************** 36.78/9.30 SRS with 3 rules on 3 letters Remap { tracing = False} 36.78/9.30 SRS with 3 rules on 3 letters reverse each lhs and rhs 36.78/9.30 SRS with 3 rules on 3 letters DP transform 36.78/9.30 SRS with 8 rules on 6 letters Remap { tracing = False} 36.78/9.30 SRS with 8 rules on 6 letters EDG 36.78/9.31 SRS with 8 rules on 6 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 36.78/9.31 SRS with 7 rules on 6 letters EDG 36.78/9.31 SRS with 7 rules on 6 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 36.78/9.31 SRS with 4 rules on 5 letters weights 36.78/9.31 SRS with 3 rules on 3 letters EDG 36.78/9.31 36.78/9.31 ************************************************** 36.78/9.31 (3, 3)\Deepee(8, 6)\Matrix{\Arctic}{3}(7, 6)\Matrix{\Arctic}{3}(4, 5)\Weight(3, 3)\EDG[] 36.78/9.31 ************************************************** 37.17/9.39 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]} 37.17/9.39 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 37.33/9.49 EOF