57.96/14.65 YES 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [a, b] -> [b, c, a], [b, c] -> [c, b, b], [b, a] -> [a, c, b]) 57.96/14.65 reason 57.96/14.65 remap for 3 rules 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [0, 1] -> [1, 2, 0], [1, 2] -> [2, 1, 1], [1, 0] -> [0, 2, 1]) 57.96/14.65 reason 57.96/14.65 DP transform 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1], [0#, 1] |-> [1#, 2, 0], [0#, 1] |-> [0#], [1#, 2] |-> [1#, 1], [1#, 2] |-> [1#], [1#, 0] |-> [0#, 2, 1], [1#, 0] |-> [1#]) 57.96/14.65 reason 57.96/14.65 remap for 9 rules 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1], [3, 1] |-> [4, 2, 0], [3, 1] |-> [3], [4, 2] |-> [4, 1], [4, 2] |-> [4], [4, 0] |-> [3, 2, 1], [4, 0] |-> [4]) 57.96/14.65 reason 57.96/14.65 weights 57.96/14.65 Map [(0, 1/1), (3, 1/1)] 57.96/14.65 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1], [3, 1] |-> [4, 2, 0], [3, 1] |-> [3], [4, 2] |-> [4, 1], [4, 2] |-> [4], [4, 0] |-> [3, 2, 1]) 57.96/14.65 reason 57.96/14.65 EDG has 2 SCCs 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [3, 1] |-> [3], [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1]) 57.96/14.65 reason 57.96/14.65 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 57.96/14.65 interpretation 57.96/14.65 0 Wk / 0A 0A - 0A \ 57.96/14.65 | 0A - - 1A | 57.96/14.65 | 0A - 0A 0A | 57.96/14.65 \ - - - 0A / 57.96/14.65 1 Wk / 7A 0A 7A 7A \ 57.96/14.65 | - 0A 0A - | 57.96/14.65 | - - 0A - | 57.96/14.65 \ - - - 0A / 57.96/14.65 2 Wk / - - 0A 0A \ 57.96/14.65 | - 6A 7A 5A | 57.96/14.65 | - - - 0A | 57.96/14.65 \ - - - 0A / 57.96/14.65 3 Wk / 0A - - 0A \ 57.96/14.65 | - - - - | 57.96/14.65 | - - - - | 57.96/14.65 \ - - - 0A / 57.96/14.65 [3, 1] |-> [3] 57.96/14.65 lhs rhs ge gt 57.96/14.65 Wk / 7A 0A 7A 7A \ Wk / 0A - - 0A \ True True 57.96/14.65 | - - - - | | - - - - | 57.96/14.65 | - - - - | | - - - - | 57.96/14.65 \ - - - 0A / \ - - - 0A / 57.96/14.65 [0, 1] ->= [1, 2, 0] 57.96/14.65 lhs rhs ge gt 57.96/14.65 Wk / 7A 0A 7A 7A \ Wk / 7A - 7A 7A \ True False 57.96/14.65 | 7A 0A 7A 7A | | 7A - 7A 7A | 57.96/14.65 | 7A 0A 7A 7A | | - - - 0A | 57.96/14.65 \ - - - 0A / \ - - - 0A / 57.96/14.65 [1, 2] ->= [2, 1, 1] 57.96/14.65 lhs rhs ge gt 57.96/14.65 Wk / - 6A 7A 7A \ Wk / - - 0A 0A \ True False 57.96/14.65 | - 6A 7A 5A | | - 6A 7A 5A | 57.96/14.65 | - - - 0A | | - - - 0A | 57.96/14.65 \ - - - 0A / \ - - - 0A / 57.96/14.65 [1, 0] ->= [0, 2, 1] 57.96/14.65 lhs rhs ge gt 57.96/14.65 Wk / 7A 7A 7A 7A \ Wk / - 6A 7A 5A \ True False 57.96/14.65 | 0A - 0A 1A | | - - 0A 1A | 57.96/14.65 | 0A - 0A 0A | | - - 0A 0A | 57.96/14.65 \ - - - 0A / \ - - - 0A / 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.65 for SRS ( [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1]) 57.96/14.65 reason 57.96/14.65 EDG has 0 SCCs 57.96/14.65 57.96/14.65 property Termination 57.96/14.65 has value True 57.96/14.67 for SRS ( [4, 2] |-> [4, 1], [4, 2] |-> [4], [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1]) 57.96/14.67 reason 57.96/14.67 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 57.96/14.67 interpretation 57.96/14.67 0 Wk / - - 0A 0A \ 57.96/14.67 | - - 0A 1A | 57.96/14.67 | - - 0A 1A | 57.96/14.67 \ - - - 0A / 57.96/14.67 1 Wk / 0A - - - \ 57.96/14.67 | 0A 0A - - | 57.96/14.67 | - - 5A 7A | 57.96/14.67 \ - - - 0A / 57.96/14.67 2 Wk / 4A 1A - - \ 57.96/14.67 | 5A 5A - 7A | 57.96/14.67 | - - - - | 57.96/14.67 \ - - - 0A / 57.96/14.67 4 Wk / 3A - - - \ 57.96/14.67 | - - - - | 57.96/14.67 | - - - - | 57.96/14.67 \ - - - 0A / 57.96/14.67 [4, 2] |-> [4, 1] 57.96/14.67 lhs rhs ge gt 57.96/14.67 Wk / 7A 4A - - \ Wk / 3A - - - \ True True 57.96/14.67 | - - - - | | - - - - | 57.96/14.67 | - - - - | | - - - - | 57.96/14.67 \ - - - 0A / \ - - - 0A / 57.96/14.67 [4, 2] |-> [4] 57.96/14.68 lhs rhs ge gt 57.96/14.68 Wk / 7A 4A - - \ Wk / 3A - - - \ True True 57.96/14.68 | - - - - | | - - - - | 57.96/14.68 | - - - - | | - - - - | 57.96/14.68 \ - - - 0A / \ - - - 0A / 57.96/14.68 [0, 1] ->= [1, 2, 0] 57.96/14.68 lhs rhs ge gt 57.96/14.68 Wk / - - 5A 7A \ Wk / - - 4A 4A \ True False 57.96/14.68 | - - 5A 7A | | - - 5A 7A | 57.96/14.68 | - - 5A 7A | | - - - 7A | 57.96/14.68 \ - - - 0A / \ - - - 0A / 57.96/14.68 [1, 2] ->= [2, 1, 1] 57.96/14.68 lhs rhs ge gt 57.96/14.68 Wk / 4A 1A - - \ Wk / 4A 1A - - \ True False 57.96/14.68 | 5A 5A - 7A | | 5A 5A - 7A | 57.96/14.68 | - - - 7A | | - - - - | 57.96/14.68 \ - - - 0A / \ - - - 0A / 57.96/14.69 [1, 0] ->= [0, 2, 1] 57.96/14.69 lhs rhs ge gt 57.96/14.69 Wk / - - 0A 0A \ Wk / - - - 0A \ True False 57.96/14.69 | - - 0A 1A | | - - - 1A | 57.96/14.69 | - - 5A 7A | | - - - 1A | 57.96/14.69 \ - - - 0A / \ - - - 0A / 57.96/14.69 property Termination 57.96/14.69 has value True 57.96/14.69 for SRS ( [0, 1] ->= [1, 2, 0], [1, 2] ->= [2, 1, 1], [1, 0] ->= [0, 2, 1]) 57.96/14.69 reason 57.96/14.69 EDG has 0 SCCs 57.96/14.69 57.96/14.69 ************************************************** 57.96/14.69 summary 57.96/14.69 ************************************************** 57.96/14.69 SRS with 3 rules on 3 letters Remap { tracing = False} 57.96/14.69 SRS with 3 rules on 3 letters DP transform 57.96/14.69 SRS with 9 rules on 5 letters Remap { tracing = False} 57.96/14.69 SRS with 9 rules on 5 letters weights 57.96/14.69 SRS with 8 rules on 5 letters EDG 57.96/14.69 2 sub-proofs 57.96/14.69 1 SRS with 4 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 57.96/14.69 SRS with 3 rules on 3 letters EDG 57.96/14.69 57.96/14.69 2 SRS with 5 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 57.96/14.69 SRS with 3 rules on 3 letters EDG 57.96/14.69 57.96/14.69 ************************************************** 57.96/14.70 (3, 3)\Deepee(9, 5)\Weight(8, 5)\EDG[(4, 4)\Matrix{\Arctic}{4}(3, 3)\EDG[],(5, 4)\Matrix{\Arctic}{4}(3, 3)\EDG[]] 57.96/14.70 ************************************************** 58.26/14.74 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]} 58.26/14.74 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 58.44/14.83 EOF