214.85/54.30 YES 214.85/54.30 property Termination 214.85/54.30 has value True 214.85/54.30 for SRS ( [b, b, a, b] -> [b, a, b, b, b, b], [b, a, b, b] -> [b, b, b], [b, b, b] -> [b, b, a, a, b, a, b]) 214.85/54.30 reason 214.85/54.30 remap for 3 rules 214.85/54.30 property Termination 214.85/54.30 has value True 214.85/54.30 for SRS ( [0, 0, 1, 0] -> [0, 1, 0, 0, 0, 0], [0, 1, 0, 0] -> [0, 0, 0], [0, 0, 0] -> [0, 0, 1, 1, 0, 1, 0]) 214.85/54.30 reason 214.85/54.30 reverse each lhs and rhs 214.85/54.30 property Termination 214.85/54.30 has value True 214.85/54.30 for SRS ( [0, 1, 0, 0] -> [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] -> [0, 0, 0], [0, 0, 0] -> [0, 1, 0, 1, 1, 0, 0]) 214.85/54.30 reason 214.85/54.30 DP transform 214.85/54.30 property Termination 214.85/54.30 has value True 214.85/54.32 for SRS ( [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0], [0#, 1, 0, 0] |-> [0#, 0, 0, 0, 1, 0], [0#, 1, 0, 0] |-> [0#, 0, 0, 1, 0], [0#, 1, 0, 0] |-> [0#, 0, 1, 0], [0#, 1, 0, 0] |-> [0#, 1, 0], [0#, 0, 1, 0] |-> [0#, 0, 0], [0#, 0, 1, 0] |-> [0#, 0], [0#, 0, 0] |-> [0#, 1, 0, 1, 1, 0, 0], [0#, 0, 0] |-> [0#, 1, 1, 0, 0]) 214.85/54.32 reason 214.85/54.32 remap for 11 rules 214.85/54.32 property Termination 214.85/54.32 has value True 214.85/54.32 for SRS ( [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0], [2, 1, 0, 0] |-> [2, 0, 0, 0, 1, 0], [2, 1, 0, 0] |-> [2, 0, 0, 1, 0], [2, 1, 0, 0] |-> [2, 0, 1, 0], [2, 1, 0, 0] |-> [2, 1, 0], [2, 0, 1, 0] |-> [2, 0, 0], [2, 0, 1, 0] |-> [2, 0], [2, 0, 0] |-> [2, 1, 0, 1, 1, 0, 0], [2, 0, 0] |-> [2, 1, 1, 0, 0]) 214.85/54.32 reason 214.85/54.32 EDG has 1 SCCs 214.85/54.32 property Termination 214.85/54.32 has value True 215.06/54.34 for SRS ( [2, 1, 0, 0] |-> [2, 0, 0, 0, 1, 0], [2, 0, 1, 0] |-> [2, 0], [2, 0, 1, 0] |-> [2, 0, 0], [2, 1, 0, 0] |-> [2, 1, 0], [2, 1, 0, 0] |-> [2, 0, 1, 0], [2, 1, 0, 0] |-> [2, 0, 0, 1, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 215.06/54.34 reason 215.06/54.34 Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 215.06/54.34 interpretation 215.06/54.34 0 / 0A 0A \ 215.06/54.34 \ -2A -2A / 215.06/54.34 1 / 0A 0A \ 215.06/54.34 \ 0A 0A / 215.06/54.34 2 / 27A 29A \ 215.06/54.34 \ 27A 29A / 215.06/54.34 [2, 1, 0, 0] |-> [2, 0, 0, 0, 1, 0] 215.06/54.34 lhs rhs ge gt 215.06/54.34 / 29A 29A \ / 27A 27A \ True True 215.06/54.34 \ 29A 29A / \ 27A 27A / 215.06/54.34 [2, 0, 1, 0] |-> [2, 0] 215.06/54.34 lhs rhs ge gt 215.06/54.34 / 27A 27A \ / 27A 27A \ True False 215.06/54.34 \ 27A 27A / \ 27A 27A / 215.06/54.34 [2, 0, 1, 0] |-> [2, 0, 0] 215.06/54.34 lhs rhs ge gt 215.06/54.34 / 27A 27A \ / 27A 27A \ True False 215.06/54.34 \ 27A 27A / \ 27A 27A / 215.06/54.35 [2, 1, 0, 0] |-> [2, 1, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 29A 29A \ / 29A 29A \ True False 215.06/54.35 \ 29A 29A / \ 29A 29A / 215.06/54.35 [2, 1, 0, 0] |-> [2, 0, 1, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 29A 29A \ / 27A 27A \ True True 215.06/54.35 \ 29A 29A / \ 27A 27A / 215.06/54.35 [2, 1, 0, 0] |-> [2, 0, 0, 1, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 29A 29A \ / 27A 27A \ True True 215.06/54.35 \ 29A 29A / \ 27A 27A / 215.06/54.35 [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 0A 0A \ / 0A 0A \ True False 215.06/54.35 \ -2A -2A / \ -2A -2A / 215.06/54.35 [0, 0, 1, 0] ->= [0, 0, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 0A 0A \ / 0A 0A \ True False 215.06/54.35 \ -2A -2A / \ -2A -2A / 215.06/54.35 [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0] 215.06/54.35 lhs rhs ge gt 215.06/54.35 / 0A 0A \ / 0A 0A \ True False 215.06/54.35 \ -2A -2A / \ -2A -2A / 215.06/54.35 property Termination 215.06/54.35 has value True 215.06/54.35 for SRS ( [2, 0, 1, 0] |-> [2, 0], [2, 0, 1, 0] |-> [2, 0, 0], [2, 1, 0, 0] |-> [2, 1, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 215.06/54.35 reason 215.06/54.35 EDG has 2 SCCs 215.06/54.35 property Termination 215.06/54.35 has value True 215.06/54.35 for SRS ( [2, 1, 0, 0] |-> [2, 1, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 215.06/54.35 reason 215.06/54.35 Matrix { monotone = Weak, domain = Natural, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 215.06/54.35 interpretation 215.06/54.35 0 Wk / 0 0 0 2 \ 215.06/54.35 | 0 0 0 1 | 215.06/54.35 | 0 1 1 0 | 215.06/54.35 \ 0 0 0 1 / 215.06/54.35 1 Wk / 0 0 0 0 \ 215.06/54.35 | 1 0 4 0 | 215.06/54.35 | 0 0 0 0 | 215.06/54.35 \ 0 0 0 1 / 215.06/54.35 2 Wk / 1 1 0 1 \ 215.06/54.35 | 0 0 0 0 | 215.06/54.35 | 0 0 0 6 | 215.06/54.35 \ 0 0 0 1 / 215.06/54.35 [2, 1, 0, 0] |-> [2, 1, 0] 216.38/54.74 lhs rhs ge gt 216.38/54.74 Wk / 0 4 4 7 \ Wk / 0 4 4 3 \ True True 216.38/54.74 | 0 0 0 0 | | 0 0 0 0 | 216.38/54.74 | 0 0 0 6 | | 0 0 0 6 | 216.38/54.74 \ 0 0 0 1 / \ 0 0 0 1 / 216.38/54.74 [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0] 216.38/54.74 lhs rhs ge gt 216.38/54.74 Wk / 0 0 0 2 \ Wk / 0 0 0 2 \ True False 216.38/54.74 | 0 0 0 1 | | 0 0 0 1 | 216.38/54.74 | 0 4 4 6 | | 0 4 4 5 | 216.38/54.74 \ 0 0 0 1 / \ 0 0 0 1 / 216.38/54.74 [0, 0, 1, 0] ->= [0, 0, 0] 216.38/54.74 lhs rhs ge gt 216.38/54.74 Wk / 0 0 0 2 \ Wk / 0 0 0 2 \ True False 216.38/54.74 | 0 0 0 1 | | 0 0 0 1 | 216.38/54.74 | 0 4 4 3 | | 0 1 1 2 | 216.38/54.74 \ 0 0 0 1 / \ 0 0 0 1 / 216.38/54.74 [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0] 216.69/54.76 lhs rhs ge gt 216.69/54.76 Wk / 0 0 0 2 \ Wk / 0 0 0 2 \ True False 216.69/54.76 | 0 0 0 1 | | 0 0 0 1 | 216.69/54.76 | 0 1 1 2 | | 0 0 0 2 | 216.69/54.76 \ 0 0 0 1 / \ 0 0 0 1 / 216.69/54.76 property Termination 216.69/54.76 has value True 216.69/54.76 for SRS ( [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 216.69/54.76 reason 216.69/54.76 EDG has 0 SCCs 216.69/54.76 216.69/54.76 property Termination 216.69/54.76 has value True 216.69/54.76 for SRS ( [2, 0, 1, 0] |-> [2, 0], [2, 0, 1, 0] |-> [2, 0, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 216.69/54.76 reason 216.69/54.76 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 216.69/54.76 interpretation 216.69/54.76 0 Wk / 0A - - 1A \ 216.69/54.76 | 2A - 1A 3A | 216.69/54.76 | 3A - 0A - | 216.69/54.76 \ - - - 0A / 216.69/54.76 1 Wk / 0A - - - \ 216.69/54.76 | 0A - - 0A | 216.69/54.76 | - 1A - - | 216.69/54.76 \ - - - 0A / 216.69/54.76 2 Wk / 0A 2A - 6A \ 216.69/54.76 | - - - - | 216.85/54.79 | - - - - | 216.85/54.79 \ - - - 0A / 216.85/54.79 [2, 0, 1, 0] |-> [2, 0] 216.85/54.79 lhs rhs ge gt 216.85/54.79 Wk / 6A - 5A 7A \ Wk / 4A - 3A 6A \ True True 216.85/54.79 | - - - - | | - - - - | 216.85/54.79 | - - - - | | - - - - | 216.85/54.79 \ - - - 0A / \ - - - 0A / 216.85/54.79 [2, 0, 1, 0] |-> [2, 0, 0] 216.85/54.79 lhs rhs ge gt 216.85/54.79 Wk / 6A - 5A 7A \ Wk / 6A - 3A 6A \ True False 216.85/54.79 | - - - - | | - - - - | 216.85/54.79 | - - - - | | - - - - | 216.85/54.79 \ - - - 0A / \ - - - 0A / 216.85/54.79 [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0] 216.85/54.80 lhs rhs ge gt 216.85/54.80 Wk / 0A - - 1A \ Wk / 0A - - 1A \ True False 216.85/54.80 | 6A - 3A 5A | | 4A - 3A 5A | 216.85/54.80 | 5A - 2A 4A | | 3A - 2A 4A | 216.85/54.80 \ - - - 0A / \ - - - 0A / 216.85/54.80 [0, 0, 1, 0] ->= [0, 0, 0] 216.85/54.80 lhs rhs ge gt 216.85/54.80 Wk / 0A - - 1A \ Wk / 0A - - 1A \ True False 216.85/54.80 | 4A - 3A 5A | | 4A - 1A 5A | 216.85/54.80 | 3A - 2A 4A | | 3A - 0A 4A | 216.85/54.80 \ - - - 0A / \ - - - 0A / 216.85/54.80 [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0] 216.85/54.80 lhs rhs ge gt 216.85/54.80 Wk / 0A - - 1A \ Wk / 0A - - 1A \ True False 216.85/54.80 | 4A - 1A 5A | | 4A - - 5A | 216.85/54.80 | 3A - 0A 4A | | 3A - - 4A | 216.85/54.80 \ - - - 0A / \ - - - 0A / 216.85/54.80 property Termination 216.85/54.80 has value True 216.85/54.80 for SRS ( [2, 0, 1, 0] |-> [2, 0, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 216.85/54.80 reason 216.85/54.80 EDG has 1 SCCs 216.85/54.82 property Termination 216.85/54.82 has value True 216.85/54.82 for SRS ( [2, 0, 1, 0] |-> [2, 0, 0], [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 216.85/54.82 reason 216.85/54.82 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 216.85/54.82 interpretation 216.85/54.82 0 Wk / 0A 0A 1A 3A \ 216.85/54.82 | 0A 0A 3A 4A | 216.85/54.82 | - - 0A 3A | 216.85/54.82 \ - - - 0A / 216.85/54.82 1 Wk / - - - 0A \ 216.85/54.82 | 3A - - - | 216.85/54.82 | 0A - - 1A | 216.85/54.82 \ - - - 0A / 216.85/54.82 2 Wk / 1A - 1A 6A \ 216.85/54.82 | - - - - | 216.85/54.82 | - - - - | 216.85/54.82 \ - - - 0A / 216.85/54.82 [2, 0, 1, 0] |-> [2, 0, 0] 216.85/54.82 lhs rhs ge gt 216.85/54.82 Wk / 4A 4A 5A 7A \ Wk / 1A 1A 4A 6A \ True True 216.85/54.82 | - - - - | | - - - - | 216.85/54.82 | - - - - | | - - - - | 216.85/54.82 \ - - - 0A / \ - - - 0A / 216.85/54.82 [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0] 216.85/54.84 lhs rhs ge gt 216.85/54.84 Wk / 3A 3A 6A 7A \ Wk / 3A 3A 4A 6A \ True False 216.85/54.84 | 3A 3A 6A 7A | | 3A 3A 4A 6A | 216.85/54.84 | 0A 0A 3A 4A | | 0A 0A 1A 3A | 216.85/54.84 \ - - - 0A / \ - - - 0A / 216.85/54.84 [0, 0, 1, 0] ->= [0, 0, 0] 216.85/54.84 lhs rhs ge gt 216.85/54.84 Wk / 3A 3A 4A 6A \ Wk / 0A 0A 3A 6A \ True False 216.85/54.84 | 3A 3A 4A 6A | | 0A 0A 3A 6A | 216.85/54.84 | 0A 0A 1A 3A | | - - 0A 3A | 216.85/54.84 \ - - - 0A / \ - - - 0A / 216.85/54.84 [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0] 217.10/54.86 lhs rhs ge gt 217.10/54.86 Wk / 0A 0A 3A 6A \ Wk / - - - 6A \ True False 217.10/54.86 | 0A 0A 3A 6A | | - - - 6A | 217.10/54.86 | - - 0A 3A | | - - - 3A | 217.10/54.86 \ - - - 0A / \ - - - 0A / 217.10/54.86 property Termination 217.10/54.86 has value True 217.10/54.86 for SRS ( [0, 1, 0, 0] ->= [0, 0, 0, 0, 1, 0], [0, 0, 1, 0] ->= [0, 0, 0], [0, 0, 0] ->= [0, 1, 0, 1, 1, 0, 0]) 217.10/54.86 reason 217.10/54.86 EDG has 0 SCCs 217.10/54.86 217.10/54.86 ************************************************** 217.10/54.86 summary 217.10/54.86 ************************************************** 217.10/54.86 SRS with 3 rules on 2 letters Remap { tracing = False} 217.10/54.86 SRS with 3 rules on 2 letters reverse each lhs and rhs 217.10/54.86 SRS with 3 rules on 2 letters DP transform 217.10/54.86 SRS with 11 rules on 3 letters Remap { tracing = False} 217.10/54.86 SRS with 11 rules on 3 letters EDG 217.10/54.86 SRS with 9 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = True} 217.10/54.86 SRS with 6 rules on 3 letters EDG 217.10/54.86 2 sub-proofs 217.10/54.86 1 SRS with 4 rules on 3 letters Matrix { monotone = Weak, domain = Natural, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 217.10/54.86 SRS with 3 rules on 2 letters EDG 217.10/54.86 217.10/54.86 2 SRS with 5 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 217.10/54.86 SRS with 4 rules on 3 letters EDG 217.10/54.86 SRS with 4 rules on 3 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 217.10/54.86 SRS with 3 rules on 2 letters EDG 217.10/54.86 217.10/54.86 ************************************************** 217.19/54.88 (3, 2)\Deepee(11, 3)\EDG(9, 3)\Matrix{\Arctic}{2}(6, 3)\EDG[(4, 3)\Matrix{\Natural}{4}(3, 2)\EDG[],(5, 3)\Matrix{\Arctic}{4}(4, 3)\Matrix{\Arctic}{4}(3, 2)\EDG[]] 217.19/54.88 ************************************************** 217.83/55.05 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]} 217.83/55.05 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 219.83/55.54 EOF