/export/starexec/sandbox/solver/bin/starexec_run_tc21-9.sh /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
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summary
**************************************************
SRS with 3 rules on 3 letters       DP
SRS with 4 strict rules and 3 weak rules on 5 letters       weights
SRS with 2 strict rules and 3 weak rules on 4 letters       EDG
SRS with 2 strict rules and 3 weak rules on 4 letters       tile all, by Config   { method = Overlap,width = 2,unlabel = True}
SRS with 4 strict rules and 22 weak rules on 16 letters       weights
SRS with 0 strict rules and 12 weak rules on 10 letters       no strict rules

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proof
**************************************************
property Termination
has value Just True
for SRS
  [a, b] -> [] {- Input 0 -}
  [a, c] -> [c, c] {- Input 1 -}
  [b, c] -> [a, b, a, b] {- Input 2 -}
reason
  DP
   property Termination
has value Just True
for SRS
  [a, b] ->= [] {- DP Nontop (Input 0) -}
  [a, c] ->= [c, c] {- DP Nontop (Input 1) -}
  [b, c] ->= [a, b, a, b] {- DP Nontop (Input 2) -}
  [b#, c] |-> [a#, b] {- DP (Top 2) (Input 2) -}
  [b#, c] |-> [a#, b, a, b] {- DP (Top 0) (Input 2) -}
  [b#, c] |-> [b#] {- DP (Top 3) (Input 2) -}
  [b#, c] |-> [b#, a, b] {- DP (Top 1) (Input 2) -}
reason
  (b#, 2/1)
   property Termination
has value Just True
for SRS
  [a, b] ->= [] {- DP Nontop (Input 0) -}
  [a, c] ->= [c, c] {- DP Nontop (Input 1) -}
  [b, c] ->= [a, b, a, b] {- DP Nontop (Input 2) -}
  [b#, c] |-> [b#] {- DP (Top 3) (Input 2) -}
  [b#, c] |-> [b#, a, b] {- DP (Top 1) (Input 2) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [b#, c] |-> [b#] {- DP (Top 3) (Input 2) -}
  [b#, c] |-> [b#, a, b] {- DP (Top 1) (Input 2) -}
  [a, b] ->= [] {- DP Nontop (Input 0) -}
  [a, c] ->= [c, c] {- DP Nontop (Input 1) -}
  [b, c] ->= [a, b, a, b] {- DP Nontop (Input 2) -}
reason
  Tiling   { method = Overlap, width = 2, state_type = Bit64, map_type = Enum, unlabel = True, print_completion_steps = False, print_tiles = False, max_num_tiles = Just 1000, max_num_rules = Just 100000, verbose = False, tracing = False}
  steps 2
  using 16 tiles
  tile all rules
  steps: 2
  
   property Termination
has value Just True
for SRS
  [[<, b#], [b#, c], [c, >]] |-> [ [<, b#] , [ b# , > ] ] {- Semlab 0 (Concon 0 (DP (Top 3) (Input 2))) -}
  [[<, b#], [b#, c], [c, c]] |-> [ [<, b#] , [ b# , c ] ] {- Semlab 0 (Concon 1 (DP (Top 3) (Input 2))) -}
  [[<, b#], [b#, c], [c, >]] |-> [ [<, b#] , [b#, a] , [a, b] , [ b , > ] ] {- Semlab 0 (Concon 0 (DP (Top 1) (Input 2))) -}
  [[<, b#], [b#, c], [c, c]] |-> [ [<, b#] , [b#, a] , [a, b] , [ b , c ] ] {- Semlab 0 (Concon 1 (DP (Top 1) (Input 2))) -}
  [[<, a], [a, b], [b, >]] ->= [ [ < , > ] ] {- Semlab 0 (Concon 0 (DP Nontop (Input 0))) -}
  [[<, a], [a, b], [b, a]] ->= [ [ < , a ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 0))) -}
  [[<, a], [a, b], [b, c]] ->= [ [ < , c ] ] {- Semlab 0 (Concon 2 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, >]] ->= [ [ a , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, a]] ->= [ [ a , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, c]] ->= [ [ a , c ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, >]] ->= [ [ b , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, a]] ->= [ [ b , a ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, c]] ->= [ [ b , c ] ] {- Semlab 2 (Concon 2 (DP Nontop (Input 0))) -}
  [[b#, a], [a, b], [b, >]] ->= [ [ b# , > ] ] {- Semlab 3 (Concon 0 (DP Nontop (Input 0))) -}
  [[b#, a], [a, b], [b, a]] ->= [ [ b# , a ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 0))) -}
  [[b#, a], [a, b], [b, c]] ->= [ [ b# , c ] ] {- Semlab 3 (Concon 2 (DP Nontop (Input 0))) -}
  [[<, a], [a, c], [c, >]] ->= [ [<, c] , [c, c] , [ c , > ] ] {- Semlab 0 (Concon 0 (DP Nontop (Input 1))) -}
  [[<, a], [a, c], [c, c]] ->= [ [<, c] , [c, c] , [ c , c ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 1))) -}
  [[a, a], [a, c], [c, >]] ->= [ [a, c] , [c, c] , [ c , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 1))) -}
  [[a, a], [a, c], [c, c]] ->= [ [a, c] , [c, c] , [ c , c ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 1))) -}
  [[b, a], [a, c], [c, >]] ->= [ [b, c] , [c, c] , [ c , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 1))) -}
  [[b, a], [a, c], [c, c]] ->= [ [b, c] , [c, c] , [ c , c ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 1))) -}
  [[b#, a], [a, c], [c, >]] ->= [ [b#, c] , [c, c] , [ c , > ] ] {- Semlab 3 (Concon 0 (DP Nontop (Input 1))) -}
  [[b#, a], [a, c], [c, c]] ->= [ [b#, c] , [c, c] , [ c , c ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 1))) -}
  [[a, b], [b, c], [c, >]] ->= [ [a, a] , [a, b] , [b, a] , [a, b] , [ b , > ] ] {- Semlab 0 (Concon 0 (DP Nontop (Input 2))) -}
  [[a, b], [b, c], [c, c]] ->= [ [a, a] , [a, b] , [b, a] , [a, b] , [ b , c ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 2))) -}
reason
  ([b#, c], 1/1)
  ([c, >], 4/1)
  ([c, c], 2/1)
  ([b#, a], 2/1)
  ([b, >], 1/1)
  ([<, a], 4/1)
  ([a, a], 2/1)
  ([a, c], 2/1)
   property Termination
has value Just True
for SRS
  [[<, a], [a, b], [b, a]] ->= [ [ < , a ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, a]] ->= [ [ a , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, c]] ->= [ [ a , c ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, >]] ->= [ [ b , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, a]] ->= [ [ b , a ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 0))) -}
  [[b, a], [a, b], [b, c]] ->= [ [ b , c ] ] {- Semlab 2 (Concon 2 (DP Nontop (Input 0))) -}
  [[b#, a], [a, b], [b, a]] ->= [ [ b# , a ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, c], [c, >]] ->= [ [a, c] , [c, c] , [ c , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 1))) -}
  [[a, a], [a, c], [c, c]] ->= [ [a, c] , [c, c] , [ c , c ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 1))) -}
  [[b, a], [a, c], [c, >]] ->= [ [b, c] , [c, c] , [ c , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 1))) -}
  [[b, a], [a, c], [c, c]] ->= [ [b, c] , [c, c] , [ c , c ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 1))) -}
  [[a, b], [b, c], [c, c]] ->= [ [a, a] , [a, b] , [b, a] , [a, b] , [ b , c ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 2))) -}
reason
  no strict rules

**************************************************
skeleton: (3,3)\Deepee(4/3,5)\Weight\EDG(2/3,4)\TileAllROC{2}(4/22,16)\Weight(0/12,10)[]
**************************************************
let {}
in let {trac ?= False;loop_cap = 1;match_cap = 2;tile_cap = 3;matrix_cap = 4;mo = Pre (Or_Else Count (IfSizeLeq 100000 (Simplex Sparse) Fail));wop = Or_Else (Worker (Weight {modus = mo})) Pass;weighted = \ m -> And_Then m wop;done = Worker No_Strict_Rules;dont = \ p -> Fail;tiling = \ m w -> On tile_cap (weighted (And_Then (Worker (Tiling {method = m,width = w,map_type = Enum,max_num_tiles = Just 1000,max_num_rules = Just 100000})) (Worker Remap)));tile_roc = Tree_Search_Preemptive 0 done let {ws = [ 2, 4, 8, 12]}in (for ws (\ w -> tiling Overlap w)) <> [ Worker Unlabel];mb = \ size -> On match_cap (Apply (Worker (Matchbound {method = RFC,max_size = Just size})) done);mbs = \ size -> First_Of [ mb size, Apply (Worker Mirror) (mb size)];tile_rfc = Tree_Search_Preemptive 0 done let {ws = [ 2, 4, 8, 12]}in (for ws (\ w -> tiling Forward w)) <> ((for ws (\ w -> tiling Backward w)) <> [ Worker Unlabel]);solver = Minisatapi;qpi = \ dim bits -> On matrix_cap (weighted (Worker (QPI {tracing = trac,dim = dim,bits = bits,solver = solver})));qpis = Seq [ Timeout 10 (qpi 2 3), Timeout 30 (qpi 4 3), Timeout 50 (qpi 6 3), qpi 8 3];kbo = \ b -> On matrix_cap (weighted (Worker (KBO {bits = b,solver = solver})));matrix = \ dom dim bits -> On matrix_cap (weighted (Worker (Matrix {monotone = Weak,domain = dom,dim = dim,bits = bits,encoding = Ersatz_Binary,tracing = trac,verbose = True,solver = solver})));arctics = Seq [ Timeout 10 (matrix Arctic 2 16), Timeout 30 (matrix Arctic 4 8), Timeout 50 (matrix Arctic 6 4), matrix Arctic 8 2];naturals = Seq [ Timeout 10 (matrix Natural 2 4), Timeout 30 (matrix Natural 4 3), Timeout 50 (matrix Natural 6 2), matrix Natural 8 1];remove = First_Of [ qpis, arctics, naturals, As_Transformer tile_roc];remove_wop = And_Then wop (Or_Else (As_Transformer (Worker No_Strict_Rules)) remove);deepee = Apply (And_Then (Worker DP) (Worker Remap)) (Apply wop (Branch (Worker (EDG {tracing = False,usable = True})) remove_wop));when_small = \ m -> Apply (Worker (SizeAtmost 1000)) m;yeah = First_Of [ when_small (First_Of [ deepee, Apply (Worker Mirror) deepee]), tile_rfc, mbs 100000];noh_for = \ side -> Worker (Simple (Config {closure = side,max_closure_width = Nothing,intermediates = All,priority = Linear [ ( 1, Log2 Steps), ( -1, Width_lhs), ( -2, Log2 Width_rhs)]}));noh = First_Of [ On loop_cap (noh_for Forward), On loop_cap (noh_for Backward), On loop_cap (Worker Transport)]}
  in Apply (Worker Remap) (Apply wop (Seq [ Worker KKST01, First_Of [ yeah, noh]]))
**************************************************
statistics on proof search (nodes types that (together) took more than 1.000000000000)
**************************************************

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