12.24/3.10 YES 12.24/3.10 property Termination 12.24/3.10 has value True 12.24/3.10 for SRS ( [b, a, a, a] -> [a, b, b, b], [b, a, a, a] -> [b, b, b, a], [a, b, b, a] -> [a, a, a, a]) 12.24/3.10 reason 12.24/3.10 remap for 3 rules 12.24/3.10 property Termination 12.24/3.10 has value True 12.24/3.10 for SRS ( [0, 1, 1, 1] -> [1, 0, 0, 0], [0, 1, 1, 1] -> [0, 0, 0, 1], [1, 0, 0, 1] -> [1, 1, 1, 1]) 12.24/3.10 reason 12.24/3.10 DP transform 12.24/3.10 property Termination 12.24/3.10 has value True 12.24/3.10 for SRS ( [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1], [0#, 1, 1, 1] |-> [1#, 0, 0, 0], [0#, 1, 1, 1] |-> [0#, 0, 0], [0#, 1, 1, 1] |-> [0#, 0], [0#, 1, 1, 1] |-> [0#], [0#, 1, 1, 1] |-> [0#, 0, 0, 1], [0#, 1, 1, 1] |-> [0#, 0, 1], [0#, 1, 1, 1] |-> [0#, 1], [1#, 0, 0, 1] |-> [1#, 1, 1, 1], [1#, 0, 0, 1] |-> [1#, 1, 1], [1#, 0, 0, 1] |-> [1#, 1]) 12.24/3.10 reason 12.24/3.10 remap for 13 rules 12.24/3.10 property Termination 12.24/3.10 has value True 12.24/3.10 for SRS ( [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1], [2, 1, 1, 1] |-> [3, 0, 0, 0], [2, 1, 1, 1] |-> [2, 0, 0], [2, 1, 1, 1] |-> [2, 0], [2, 1, 1, 1] |-> [2], [2, 1, 1, 1] |-> [2, 0, 0, 1], [2, 1, 1, 1] |-> [2, 0, 1], [2, 1, 1, 1] |-> [2, 1], [3, 0, 0, 1] |-> [3, 1, 1, 1], [3, 0, 0, 1] |-> [3, 1, 1], [3, 0, 0, 1] |-> [3, 1]) 12.24/3.10 reason 12.24/3.10 weights 12.24/3.10 Map [(0, 1/12), (1, 1/12), (2, 1/1)] 12.24/3.10 12.24/3.10 property Termination 12.24/3.10 has value True 12.24/3.11 for SRS ( [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1], [2, 1, 1, 1] |-> [2, 0, 0, 1], [3, 0, 0, 1] |-> [3, 1, 1, 1]) 12.24/3.11 reason 12.24/3.11 EDG has 2 SCCs 12.24/3.11 property Termination 12.24/3.11 has value True 12.24/3.11 for SRS ( [2, 1, 1, 1] |-> [2, 0, 0, 1], [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1]) 12.24/3.11 reason 12.24/3.11 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 12.24/3.11 interpretation 12.24/3.11 0 / 6A 6A 9A \ 12.24/3.11 | 6A 6A 9A | 12.24/3.11 \ 6A 6A 6A / 12.24/3.11 1 / 9A 12A 12A \ 12.24/3.11 | 6A 9A 9A | 12.24/3.11 \ 6A 9A 9A / 12.24/3.11 2 / 12A 13A 13A \ 12.24/3.11 | 12A 13A 13A | 12.24/3.11 \ 12A 13A 13A / 12.24/3.11 [2, 1, 1, 1] |-> [2, 0, 0, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 39A 42A 42A \ / 37A 40A 40A \ True True 12.24/3.11 | 39A 42A 42A | | 37A 40A 40A | 12.24/3.11 \ 39A 42A 42A / \ 37A 40A 40A / 12.24/3.11 [0, 1, 1, 1] ->= [1, 0, 0, 0] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 33A 36A 36A \ / 33A 33A 36A \ True False 12.24/3.11 | 33A 36A 36A | | 30A 30A 33A | 12.24/3.11 \ 33A 36A 36A / \ 30A 30A 33A / 12.24/3.11 [0, 1, 1, 1] ->= [0, 0, 0, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 33A 36A 36A \ / 30A 33A 33A \ True True 12.24/3.11 | 33A 36A 36A | | 30A 33A 33A | 12.24/3.11 \ 33A 36A 36A / \ 30A 33A 33A / 12.24/3.11 [1, 0, 0, 1] ->= [1, 1, 1, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 36A 39A 39A \ / 36A 39A 39A \ True False 12.24/3.11 | 33A 36A 36A | | 33A 36A 36A | 12.24/3.11 \ 33A 36A 36A / \ 33A 36A 36A / 12.24/3.11 property Termination 12.24/3.11 has value True 12.24/3.11 for SRS ( [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1]) 12.24/3.11 reason 12.24/3.11 EDG has 0 SCCs 12.24/3.11 12.24/3.11 property Termination 12.24/3.11 has value True 12.24/3.11 for SRS ( [3, 0, 0, 1] |-> [3, 1, 1, 1], [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1]) 12.24/3.11 reason 12.24/3.11 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 12.24/3.11 interpretation 12.24/3.11 0 / 0A 0A \ 12.24/3.11 \ 0A 0A / 12.24/3.11 1 / 0A 0A \ 12.24/3.11 \ -2A -2A / 12.24/3.11 3 / 20A 22A \ 12.24/3.11 \ 20A 22A / 12.24/3.11 [3, 0, 0, 1] |-> [3, 1, 1, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 22A 22A \ / 20A 20A \ True True 12.24/3.11 \ 22A 22A / \ 20A 20A / 12.24/3.11 [0, 1, 1, 1] ->= [1, 0, 0, 0] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 0A 0A \ / 0A 0A \ True False 12.24/3.11 \ 0A 0A / \ -2A -2A / 12.24/3.11 [0, 1, 1, 1] ->= [0, 0, 0, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 0A 0A \ / 0A 0A \ True False 12.24/3.11 \ 0A 0A / \ 0A 0A / 12.24/3.11 [1, 0, 0, 1] ->= [1, 1, 1, 1] 12.24/3.11 lhs rhs ge gt 12.24/3.11 / 0A 0A \ / 0A 0A \ True False 12.24/3.11 \ -2A -2A / \ -2A -2A / 12.24/3.11 property Termination 12.24/3.11 has value True 12.24/3.12 for SRS ( [0, 1, 1, 1] ->= [1, 0, 0, 0], [0, 1, 1, 1] ->= [0, 0, 0, 1], [1, 0, 0, 1] ->= [1, 1, 1, 1]) 12.24/3.12 reason 12.24/3.12 EDG has 0 SCCs 12.24/3.12 12.24/3.12 ************************************************** 12.24/3.12 summary 12.24/3.12 ************************************************** 12.24/3.12 SRS with 3 rules on 2 letters Remap { tracing = False} 12.24/3.12 SRS with 3 rules on 2 letters DP transform 12.24/3.12 SRS with 13 rules on 4 letters Remap { tracing = False} 12.24/3.12 SRS with 13 rules on 4 letters weights 12.24/3.12 SRS with 5 rules on 4 letters EDG 12.24/3.12 2 sub-proofs 12.24/3.12 1 SRS with 4 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = True} 12.24/3.12 SRS with 3 rules on 2 letters EDG 12.24/3.12 12.24/3.12 2 SRS with 4 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 12.24/3.12 SRS with 3 rules on 2 letters EDG 12.24/3.12 12.24/3.12 ************************************************** 12.24/3.12 (3, 2)\Deepee(13, 4)\Weight(5, 4)\EDG[(4, 3)\Matrix{\Arctic}{3}(3, 2)\EDG[],(4, 3)\Matrix{\Arctic}{2}(3, 2)\EDG[]] 12.24/3.12 ************************************************** 13.19/3.37 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]} 13.19/3.37 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 13.41/3.44 EOF