40.40/10.23 YES 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [a] -> [], [a, b] -> [], [a, c] -> [c, c, a, a, b], [b, b] -> []) 40.40/10.23 reason 40.40/10.23 remap for 4 rules 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [0] -> [], [0, 1] -> [], [0, 2] -> [2, 2, 0, 0, 1], [1, 1] -> []) 40.40/10.23 reason 40.40/10.23 reverse each lhs and rhs 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [0] -> [], [1, 0] -> [], [2, 0] -> [1, 0, 0, 2, 2], [1, 1] -> []) 40.40/10.23 reason 40.40/10.23 DP transform 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= [], [2#, 0] |-> [1#, 0, 0, 2, 2], [2#, 0] |-> [0#, 0, 2, 2], [2#, 0] |-> [0#, 2, 2], [2#, 0] |-> [2#, 2], [2#, 0] |-> [2#]) 40.40/10.23 reason 40.40/10.23 remap for 9 rules 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= [], [3, 0] |-> [4, 0, 0, 2, 2], [3, 0] |-> [5, 0, 2, 2], [3, 0] |-> [5, 2, 2], [3, 0] |-> [3, 2], [3, 0] |-> [3]) 40.40/10.23 reason 40.40/10.23 weights 40.40/10.23 Map [(3, 3/1)] 40.40/10.23 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= [], [3, 0] |-> [3, 2], [3, 0] |-> [3]) 40.40/10.23 reason 40.40/10.23 EDG has 1 SCCs 40.40/10.23 property Termination 40.40/10.23 has value True 40.40/10.23 for SRS ( [3, 0] |-> [3, 2], [3, 0] |-> [3], [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= []) 40.40/10.23 reason 40.40/10.23 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 40.40/10.23 interpretation 40.40/10.23 0 Wk / 1A 1A 0A 6A \ 40.40/10.23 | - 1A 0A 2A | 40.40/10.23 | 0A 0A 0A 6A | 40.40/10.23 \ - - - 0A / 40.40/10.23 1 Wk / - - 0A 1A \ 40.40/10.23 | - - 0A 4A | 40.40/10.23 | 0A 0A 0A - | 40.40/10.23 \ - - - 0A / 40.40/10.23 2 Wk / 0A 0A - 3A \ 40.40/10.23 | 0A - - 3A | 40.40/10.23 | 1A 1A 0A 5A | 40.40/10.23 \ - - - 0A / 40.40/10.23 3 Wk / 0A - - 3A \ 40.40/10.23 | 0A 1A - - | 40.40/10.23 | 1A - 0A 3A | 40.40/10.23 \ - - - 0A / 40.40/10.23 [3, 0] |-> [3, 2] 40.40/10.23 lhs rhs ge gt 40.40/10.23 Wk / 1A 1A 0A 6A \ Wk / 0A 0A - 3A \ True False 40.40/10.23 | 1A 2A 1A 6A | | 1A 0A - 4A | 40.40/10.23 | 2A 2A 1A 7A | | 1A 1A 0A 5A | 40.40/10.23 \ - - - 0A / \ - - - 0A / 40.40/10.23 [3, 0] |-> [3] 40.40/10.26 lhs rhs ge gt 40.40/10.26 Wk / 1A 1A 0A 6A \ Wk / 0A - - 3A \ True True 40.40/10.26 | 1A 2A 1A 6A | | 0A 1A - - | 40.40/10.26 | 2A 2A 1A 7A | | 1A - 0A 3A | 40.40/10.26 \ - - - 0A / \ - - - 0A / 40.40/10.26 [0] ->= [] 40.40/10.26 lhs rhs ge gt 40.40/10.26 Wk / 1A 1A 0A 6A \ Wk / 0A - - - \ True False 40.40/10.26 | - 1A 0A 2A | | - 0A - - | 40.40/10.26 | 0A 0A 0A 6A | | - - 0A - | 40.40/10.26 \ - - - 0A / \ - - - 0A / 40.40/10.26 [1, 0] ->= [] 40.40/10.26 lhs rhs ge gt 40.40/10.26 Wk / 0A 0A 0A 6A \ Wk / 0A - - - \ True False 40.40/10.26 | 0A 0A 0A 6A | | - 0A - - | 40.40/10.26 | 1A 1A 0A 6A | | - - 0A - | 40.40/10.26 \ - - - 0A / \ - - - 0A / 40.40/10.26 [2, 0] ->= [1, 0, 0, 2, 2] 40.40/10.27 lhs rhs ge gt 40.40/10.27 Wk / 1A 1A 0A 6A \ Wk / 1A 1A 0A 6A \ True False 40.40/10.27 | 1A 1A 0A 6A | | 1A 1A 0A 6A | 40.40/10.27 | 2A 2A 1A 7A | | 2A 2A 1A 7A | 40.40/10.27 \ - - - 0A / \ - - - 0A / 40.40/10.27 [1, 1] ->= [] 40.40/10.27 lhs rhs ge gt 40.40/10.27 Wk / 0A 0A 0A 1A \ Wk / 0A - - - \ True False 40.40/10.27 | 0A 0A 0A 4A | | - 0A - - | 40.40/10.27 | 0A 0A 0A 4A | | - - 0A - | 40.40/10.27 \ - - - 0A / \ - - - 0A / 40.40/10.27 property Termination 40.40/10.27 has value True 40.40/10.27 for SRS ( [3, 0] |-> [3, 2], [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= []) 40.40/10.27 reason 40.40/10.27 EDG has 1 SCCs 40.40/10.27 property Termination 40.40/10.27 has value True 40.40/10.27 for SRS ( [3, 0] |-> [3, 2], [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= []) 40.40/10.27 reason 40.40/10.27 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 40.40/10.27 interpretation 40.65/10.28 0 Wk / 0A 2A - 1A \ 40.65/10.28 | - 1A 0A 0A | 40.65/10.28 | 0A 3A 3A 4A | 40.65/10.28 \ - - - 0A / 40.65/10.28 1 Wk / 1A 2A 0A - \ 40.65/10.28 | 0A - - - | 40.65/10.28 | 0A 0A - 4A | 40.65/10.28 \ - - - 0A / 40.65/10.28 2 Wk / 0A - 3A 4A \ 40.65/10.28 | - 0A 0A 0A | 40.65/10.28 | - 0A 0A - | 40.65/10.28 \ - - - 0A / 40.65/10.28 3 Wk / - 2A 2A 4A \ 40.65/10.28 | - - - - | 40.65/10.28 | - - - - | 40.65/10.28 \ - - - 0A / 40.65/10.28 [3, 0] |-> [3, 2] 40.65/10.28 lhs rhs ge gt 40.65/10.28 Wk / 2A 5A 5A 6A \ Wk / - 2A 2A 4A \ True True 40.65/10.28 | - - - - | | - - - - | 40.65/10.28 | - - - - | | - - - - | 40.65/10.28 \ - - - 0A / \ - - - 0A / 40.65/10.28 [0] ->= [] 40.65/10.29 lhs rhs ge gt 40.65/10.29 Wk / 0A 2A - 1A \ Wk / 0A - - - \ True False 40.65/10.29 | - 1A 0A 0A | | - 0A - - | 40.65/10.29 | 0A 3A 3A 4A | | - - 0A - | 40.65/10.29 \ - - - 0A / \ - - - 0A / 40.65/10.29 [1, 0] ->= [] 40.65/10.29 lhs rhs ge gt 40.65/10.29 Wk / 1A 3A 3A 4A \ Wk / 0A - - - \ True False 40.65/10.29 | 0A 2A - 1A | | - 0A - - | 40.65/10.29 | 0A 2A 0A 4A | | - - 0A - | 40.65/10.29 \ - - - 0A / \ - - - 0A / 40.65/10.29 [2, 0] ->= [1, 0, 0, 2, 2] 40.65/10.29 lhs rhs ge gt 40.65/10.29 Wk / 3A 6A 6A 7A \ Wk / 3A 6A 6A 7A \ True False 40.65/10.29 | 0A 3A 3A 4A | | 0A 3A 3A 4A | 40.65/10.29 | 0A 3A 3A 4A | | 0A 3A 3A 4A | 40.65/10.29 \ - - - 0A / \ - - - 0A / 40.65/10.29 [1, 1] ->= [] 40.65/10.31 lhs rhs ge gt 40.65/10.31 Wk / 2A 3A 1A 4A \ Wk / 0A - - - \ True False 40.65/10.31 | 1A 2A 0A - | | - 0A - - | 40.65/10.31 | 1A 2A 0A 4A | | - - 0A - | 40.65/10.31 \ - - - 0A / \ - - - 0A / 40.65/10.31 property Termination 40.65/10.31 has value True 40.65/10.31 for SRS ( [0] ->= [], [1, 0] ->= [], [2, 0] ->= [1, 0, 0, 2, 2], [1, 1] ->= []) 40.65/10.31 reason 40.65/10.31 EDG has 0 SCCs 40.65/10.31 40.65/10.31 ************************************************** 40.65/10.31 summary 40.65/10.31 ************************************************** 40.65/10.31 SRS with 4 rules on 3 letters Remap { tracing = False} 40.65/10.31 SRS with 4 rules on 3 letters reverse each lhs and rhs 40.65/10.31 SRS with 4 rules on 3 letters DP transform 40.65/10.31 SRS with 9 rules on 6 letters Remap { tracing = False} 40.65/10.31 SRS with 9 rules on 6 letters weights 40.65/10.31 SRS with 6 rules on 4 letters EDG 40.65/10.31 SRS with 6 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 40.65/10.31 SRS with 5 rules on 4 letters EDG 40.65/10.31 SRS with 5 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 40.65/10.31 SRS with 4 rules on 3 letters EDG 40.65/10.31 40.65/10.31 ************************************************** 40.65/10.31 (4, 3)\Deepee(9, 6)\Weight(6, 4)\Matrix{\Arctic}{4}(5, 4)\Matrix{\Arctic}{4}(4, 3)\EDG[] 40.65/10.31 ************************************************** 41.09/10.41 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]} 41.09/10.41 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 41.25/10.50 EOF