77.58/19.68 YES 77.58/19.68 property Termination 77.58/19.68 has value True 77.58/19.68 for SRS ( [a] -> [], [a, a] -> [b, a, b, c], [b] -> [], [c, b] -> [a, c]) 77.58/19.68 reason 77.93/19.69 remap for 4 rules 77.93/19.69 property Termination 77.93/19.69 has value True 77.93/19.69 for SRS ( [0] -> [], [0, 0] -> [1, 0, 1, 2], [1] -> [], [2, 1] -> [0, 2]) 77.93/19.69 reason 77.93/19.69 DP transform 77.93/19.69 property Termination 77.93/19.69 has value True 77.93/19.69 for SRS ( [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2], [0#, 0] |-> [1#, 0, 1, 2], [0#, 0] |-> [0#, 1, 2], [0#, 0] |-> [1#, 2], [0#, 0] |-> [2#], [2#, 1] |-> [0#, 2], [2#, 1] |-> [2#]) 77.93/19.69 reason 77.93/19.69 remap for 10 rules 77.93/19.69 property Termination 77.93/19.69 has value True 77.94/19.70 for SRS ( [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2], [3, 0] |-> [4, 0, 1, 2], [3, 0] |-> [3, 1, 2], [3, 0] |-> [4, 2], [3, 0] |-> [5], [5, 1] |-> [3, 2], [5, 1] |-> [5]) 77.94/19.70 reason 77.94/19.70 weights 77.94/19.70 Map [(3, 1/2), (5, 1/2)] 77.94/19.70 77.94/19.70 property Termination 77.94/19.70 has value True 77.98/19.70 for SRS ( [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2], [3, 0] |-> [3, 1, 2], [3, 0] |-> [5], [5, 1] |-> [3, 2], [5, 1] |-> [5]) 77.98/19.70 reason 77.98/19.70 EDG has 1 SCCs 77.98/19.71 property Termination 77.98/19.71 has value True 77.98/19.71 for SRS ( [3, 0] |-> [3, 1, 2], [3, 0] |-> [5], [5, 1] |-> [5], [5, 1] |-> [3, 2], [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 77.98/19.71 reason 78.04/19.73 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.04/19.73 interpretation 78.04/19.73 0 Wk / 0A - - 1A \ 78.04/19.73 | 3A 0A 3A 4A | 78.04/19.74 | 4A 3A 3A 4A | 78.04/19.74 \ - - - 0A / 78.04/19.74 1 Wk / 0A - - 1A \ 78.04/19.74 | 4A 3A 0A 4A | 78.04/19.74 | 0A 0A 0A 1A | 78.04/19.74 \ - - - 0A / 78.04/19.74 2 Wk / 0A - - 0A \ 78.04/19.74 | - 0A - - | 78.04/19.74 | 1A 0A - 0A | 78.04/19.74 \ - - - 0A / 78.04/19.74 3 Wk / 4A 2A 2A 0A \ 78.04/19.74 | 5A - 1A - | 78.04/19.74 | - 0A 0A 2A | 78.04/19.74 \ - - - 0A / 78.04/19.74 5 Wk / 0A - 4A 1A \ 78.04/19.74 | - 1A 0A - | 78.04/19.74 | 0A - 1A 0A | 78.04/19.74 \ - - - 0A / 78.04/19.74 [3, 0] |-> [3, 1, 2] 78.04/19.75 lhs rhs ge gt 78.04/19.75 Wk / 6A 5A 5A 6A \ Wk / 6A 5A - 6A \ True False 78.04/19.75 | 5A 4A 4A 6A | | 5A 1A - 6A | 78.04/19.75 | 4A 3A 3A 4A | | 4A 3A - 4A | 78.04/19.75 \ - - - 0A / \ - - - 0A / 78.04/19.75 [3, 0] |-> [5] 78.04/19.76 lhs rhs ge gt 78.04/19.76 Wk / 6A 5A 5A 6A \ Wk / 0A - 4A 1A \ True True 78.04/19.76 | 5A 4A 4A 6A | | - 1A 0A - | 78.04/19.76 | 4A 3A 3A 4A | | 0A - 1A 0A | 78.04/19.76 \ - - - 0A / \ - - - 0A / 78.04/19.76 [5, 1] |-> [5] 78.04/19.76 lhs rhs ge gt 78.04/19.76 Wk / 4A 4A 4A 5A \ Wk / 0A - 4A 1A \ True False 78.04/19.76 | 5A 4A 1A 5A | | - 1A 0A - | 78.04/19.76 | 1A 1A 1A 2A | | 0A - 1A 0A | 78.04/19.76 \ - - - 0A / \ - - - 0A / 78.04/19.76 [5, 1] |-> [3, 2] 78.04/19.77 lhs rhs ge gt 78.04/19.77 Wk / 4A 4A 4A 5A \ Wk / 4A 2A - 4A \ True False 78.04/19.77 | 5A 4A 1A 5A | | 5A 1A - 5A | 78.04/19.77 | 1A 1A 1A 2A | | 1A 0A - 2A | 78.04/19.77 \ - - - 0A / \ - - - 0A / 78.04/19.77 [0] ->= [] 78.04/19.77 lhs rhs ge gt 78.04/19.77 Wk / 0A - - 1A \ Wk / 0A - - - \ True False 78.04/19.77 | 3A 0A 3A 4A | | - 0A - - | 78.04/19.77 | 4A 3A 3A 4A | | - - 0A - | 78.04/19.77 \ - - - 0A / \ - - - 0A / 78.04/19.78 [0, 0] ->= [1, 0, 1, 2] 78.04/19.78 lhs rhs ge gt 78.04/19.78 Wk / 0A - - 1A \ Wk / 0A - - 1A \ True False 78.04/19.78 | 7A 6A 6A 7A | | 7A 6A - 7A | 78.04/19.78 | 7A 6A 6A 7A | | 7A 6A - 7A | 78.04/19.78 \ - - - 0A / \ - - - 0A / 78.04/19.78 [1] ->= [] 78.04/19.79 lhs rhs ge gt 78.04/19.79 Wk / 0A - - 1A \ Wk / 0A - - - \ True False 78.04/19.79 | 4A 3A 0A 4A | | - 0A - - | 78.04/19.79 | 0A 0A 0A 1A | | - - 0A - | 78.04/19.79 \ - - - 0A / \ - - - 0A / 78.04/19.79 [2, 1] ->= [0, 2] 78.04/19.79 lhs rhs ge gt 78.04/19.79 Wk / 0A - - 1A \ Wk / 0A - - 1A \ True False 78.04/19.79 | 4A 3A 0A 4A | | 4A 3A - 4A | 78.04/19.79 | 4A 3A 0A 4A | | 4A 3A - 4A | 78.04/19.79 \ - - - 0A / \ - - - 0A / 78.04/19.79 property Termination 78.04/19.79 has value True 78.04/19.79 for SRS ( [3, 0] |-> [3, 1, 2], [5, 1] |-> [5], [5, 1] |-> [3, 2], [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.04/19.79 reason 78.04/19.79 weights 78.04/19.79 Map [(5, 1/1)] 78.04/19.79 78.04/19.79 property Termination 78.04/19.79 has value True 78.04/19.80 for SRS ( [3, 0] |-> [3, 1, 2], [5, 1] |-> [5], [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.04/19.80 reason 78.04/19.80 EDG has 2 SCCs 78.04/19.80 property Termination 78.04/19.80 has value True 78.04/19.80 for SRS ( [3, 0] |-> [3, 1, 2], [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.04/19.80 reason 78.04/19.80 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.04/19.80 interpretation 78.04/19.80 0 Wk / 2A 5A 3A 5A \ 78.04/19.80 | - 0A - 1A | 78.04/19.80 | 1A 1A 0A 2A | 78.04/19.80 \ - - - 0A / 78.04/19.80 1 Wk / 0A - - 3A \ 78.04/19.80 | - 0A - 1A | 78.04/19.80 | - 4A 2A 4A | 78.04/19.80 \ - - - 0A / 78.04/19.80 2 Wk / - - 1A 0A \ 78.04/19.80 | - 0A - 0A | 78.04/19.80 | - - 0A 1A | 78.04/19.80 \ - - - 0A / 78.04/19.80 3 Wk / 0A 2A - - \ 78.04/19.80 | 2A 4A 0A 6A | 78.04/19.80 | - - - - | 78.04/19.80 \ - - - 0A / 78.04/19.81 [3, 0] |-> [3, 1, 2] 78.04/19.81 lhs rhs ge gt 78.04/19.81 Wk / 2A 5A 3A 5A \ Wk / - 2A 1A 3A \ True True 78.04/19.81 | 4A 7A 5A 7A | | - 4A 3A 6A | 78.04/19.81 | - - - - | | - - - - | 78.04/19.81 \ - - - 0A / \ - - - 0A / 78.04/19.81 [0] ->= [] 78.04/19.81 lhs rhs ge gt 78.04/19.81 Wk / 2A 5A 3A 5A \ Wk / 0A - - - \ True False 78.04/19.81 | - 0A - 1A | | - 0A - - | 78.04/19.81 | 1A 1A 0A 2A | | - - 0A - | 78.04/19.81 \ - - - 0A / \ - - - 0A / 78.04/19.81 [0, 0] ->= [1, 0, 1, 2] 78.04/19.81 lhs rhs ge gt 78.04/19.81 Wk / 4A 7A 5A 7A \ Wk / - 7A 5A 7A \ True False 78.04/19.81 | - 0A - 1A | | - 0A - 1A | 78.04/19.81 | 3A 6A 4A 6A | | - 6A 4A 6A | 78.04/19.81 \ - - - 0A / \ - - - 0A / 78.04/19.81 [1] ->= [] 78.04/19.81 lhs rhs ge gt 78.04/19.81 Wk / 0A - - 3A \ Wk / 0A - - - \ True False 78.04/19.81 | - 0A - 1A | | - 0A - - | 78.04/19.81 | - 4A 2A 4A | | - - 0A - | 78.04/19.81 \ - - - 0A / \ - - - 0A / 78.04/19.81 [2, 1] ->= [0, 2] 78.04/19.81 lhs rhs ge gt 78.04/19.81 Wk / - 5A 3A 5A \ Wk / - 5A 3A 5A \ True False 78.04/19.81 | - 0A - 1A | | - 0A - 1A | 78.04/19.81 | - 4A 2A 4A | | - 1A 2A 2A | 78.04/19.81 \ - - - 0A / \ - - - 0A / 78.04/19.81 property Termination 78.04/19.81 has value True 78.04/19.81 for SRS ( [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.04/19.81 reason 78.04/19.81 EDG has 0 SCCs 78.04/19.81 78.04/19.81 property Termination 78.04/19.81 has value True 78.04/19.81 for SRS ( [5, 1] |-> [5], [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.04/19.81 reason 78.41/19.83 Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.41/19.83 interpretation 78.41/19.83 0 Wk / 3A 3A 3A 3A \ 78.41/19.83 | 3A 0A - - | 78.41/19.83 | 3A 1A 2A 2A | 78.41/19.83 \ - - - 0A / 78.41/19.83 1 Wk / 0A 0A 0A - \ 78.41/19.83 | - 3A - 3A | 78.41/19.83 | - 0A 2A - | 78.41/19.83 \ - - - 0A / 78.41/19.83 2 Wk / - 0A - 0A \ 78.41/19.83 | - 0A - 0A | 78.41/19.83 | - 0A - 0A | 78.41/19.83 \ - - - 0A / 78.41/19.83 5 Wk / - 0A - 2A \ 78.41/19.83 | - - - - | 78.41/19.83 | - - - - | 78.41/19.83 \ - - - 0A / 78.41/19.83 [5, 1] |-> [5] 78.41/19.83 lhs rhs ge gt 78.41/19.83 Wk / - 3A - 3A \ Wk / - 0A - 2A \ True True 78.41/19.83 | - - - - | | - - - - | 78.41/19.83 | - - - - | | - - - - | 78.41/19.83 \ - - - 0A / \ - - - 0A / 78.41/19.83 [0] ->= [] 78.41/19.83 lhs rhs ge gt 78.41/19.83 Wk / 3A 3A 3A 3A \ Wk / 0A - - - \ True False 78.41/19.83 | 3A 0A - - | | - 0A - - | 78.41/19.83 | 3A 1A 2A 2A | | - - 0A - | 78.41/19.83 \ - - - 0A / \ - - - 0A / 78.41/19.83 [0, 0] ->= [1, 0, 1, 2] 78.41/19.83 lhs rhs ge gt 78.41/19.83 Wk / 6A 6A 6A 6A \ Wk / - 6A - 6A \ True False 78.41/19.83 | 6A 6A 6A 6A | | - 6A - 6A | 78.41/19.83 | 6A 6A 6A 6A | | - 6A - 6A | 78.41/19.83 \ - - - 0A / \ - - - 0A / 78.41/19.83 [1] ->= [] 78.41/19.83 lhs rhs ge gt 78.41/19.83 Wk / 0A 0A 0A - \ Wk / 0A - - - \ True False 78.41/19.83 | - 3A - 3A | | - 0A - - | 78.41/19.83 | - 0A 2A - | | - - 0A - | 78.41/19.83 \ - - - 0A / \ - - - 0A / 78.41/19.83 [2, 1] ->= [0, 2] 78.41/19.83 lhs rhs ge gt 78.41/19.83 Wk / - 3A - 3A \ Wk / - 3A - 3A \ True False 78.41/19.83 | - 3A - 3A | | - 3A - 3A | 78.41/19.83 | - 3A - 3A | | - 3A - 3A | 78.41/19.83 \ - - - 0A / \ - - - 0A / 78.41/19.83 property Termination 78.41/19.83 has value True 78.41/19.84 for SRS ( [0] ->= [], [0, 0] ->= [1, 0, 1, 2], [1] ->= [], [2, 1] ->= [0, 2]) 78.41/19.84 reason 78.41/19.84 EDG has 0 SCCs 78.41/19.84 78.41/19.84 ************************************************** 78.41/19.84 summary 78.41/19.84 ************************************************** 78.41/19.84 SRS with 4 rules on 3 letters Remap { tracing = False} 78.41/19.84 SRS with 4 rules on 3 letters DP transform 78.41/19.84 SRS with 10 rules on 6 letters Remap { tracing = False} 78.41/19.84 SRS with 10 rules on 6 letters weights 78.41/19.84 SRS with 8 rules on 5 letters EDG 78.41/19.84 SRS with 8 rules on 5 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.41/19.84 SRS with 7 rules on 5 letters weights 78.41/19.84 SRS with 6 rules on 5 letters EDG 78.41/19.84 2 sub-proofs 78.41/19.84 1 SRS with 5 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.41/19.84 SRS with 4 rules on 3 letters EDG 78.41/19.84 78.41/19.84 2 SRS with 5 rules on 4 letters Matrix { monotone = Weak, domain = Arctic, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False} 78.41/19.84 SRS with 4 rules on 3 letters EDG 78.41/19.84 78.41/19.84 ************************************************** 78.41/19.84 (4, 3)\Deepee(10, 6)\Weight(8, 5)\Matrix{\Arctic}{4}(7, 5)\Weight(6, 5)\EDG[(5, 4)\Matrix{\Arctic}{4}(4, 3)\EDG[],(5, 4)\Matrix{\Arctic}{4}(4, 3)\EDG[]] 78.41/19.84 ************************************************** 78.41/19.87 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]} 78.41/19.87 in Apply (Worker Remap) (First_Of ([ yeah] <> noh)) 78.71/19.96 EOF