/export/starexec/sandbox/solver/bin/starexec_run_tc20-rel.sh /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
**************************************************
summary
**************************************************
SRS with 3 strict rules and 2 weak rules on 4 letters       Matrix   { monotone = Strict, domain = Natural, shape = Full, bits = 3, dim = 3, solver = Minisatapi, verbose = False, tracing = False}
SRS with 2 strict rules and 2 weak rules on 4 letters       Matrix   { monotone = Strict, domain = Natural, shape = Full, bits = 3, dim = 3, solver = Minisatapi, verbose = False, tracing = False}
SRS with 1 strict rules and 2 weak rules on 4 letters       tile all, by Config   { method = Overlap,width = 2,unlabel = True}
SRS with 9 strict rules and 4 weak rules on 11 letters       weights
SRS with 6 strict rules and 4 weak rules on 10 letters       remove some, by Config   { method = Overlap,width = 2,unlabel = True}
SRS with 6 strict rules and 2 weak rules on 10 letters       weights
SRS with 4 strict rules and 2 weak rules on 8 letters       Matrix   { monotone = Strict, domain = Natural, shape = Full, bits = 3, dim = 3, solver = Minisatapi, verbose = False, tracing = False}
SRS with 0 strict rules and 2 weak rules on 6 letters       no strict rules

**************************************************
proof
**************************************************
property Termination
has value Just True
for SRS
  [a] -> [b, c] {- Input 0 -}
  [a, b] -> [b, a] {- Input 1 -}
  [a, c] -> [c, a] {- Input 2 -}
  [d, c] ->= [d, a] {- Input 3 -}
  [d, a] ->= [d, c, b] {- Input 4 -}
reason
  ( a
  , St  / 1 0 4 \
        | 1 2 0 |
        \ 0 0 1 / )
  ( b
  , St  / 1 0 0 \
        | 0 0 0 |
        \ 0 0 1 / )
  ( c
  , St  / 1 0 1 \
        | 1 2 3 |
        \ 0 0 1 / )
  ( d
  , St  / 1 1 0 \
        | 0 0 0 |
        \ 0 0 1 / )
   property Termination
has value Just True
for SRS
  [a, b] -> [b, a] {- Input 1 -}
  [a, c] -> [c, a] {- Input 2 -}
  [d, c] ->= [d, a] {- Input 3 -}
  [d, a] ->= [d, c, b] {- Input 4 -}
reason
  ( a
  , St  / 2 0 1 \
        | 0 0 1 |
        \ 0 0 1 / )
  ( b
  , St  / 1 0 0 \
        | 0 0 1 |
        \ 0 0 1 / )
  ( c
  , St  / 2 0 3 \
        | 0 0 0 |
        \ 0 0 1 / )
  ( d
  , St  / 1 2 1 \
        | 2 4 1 |
        \ 0 0 1 / )
   property Termination
has value Just True
for SRS
  [a, b] -> [b, a] {- Input 1 -}
  [d, c] ->= [d, a] {- Input 3 -}
  [d, a] ->= [d, c, b] {- Input 4 -}
reason
  Tiling   { method = Overlap, width = 2, state_type = Bit64, map_type = Enum, unlabel = True, print_completion_steps = False, print_tiles = False, verbose = False, tracing = True}
  steps 1
  using 12 tiles
  tile all rules
  steps: 1
  
   property Termination
has value Just True
for SRS
  [[a, a], [a, b], [b, >]] -> [ [a, b] , [b, a] , [a, >] ] {- Semlab 0 (Concon 0 (Input 1)) -}
  [[a, a], [a, b], [b, a]] -> [ [a, b] , [b, a] , [a, a] ] {- Semlab 0 (Concon 1 (Input 1)) -}
  [[a, a], [a, b], [b, b]] -> [ [a, b] , [b, a] , [a, b] ] {- Semlab 0 (Concon 2 (Input 1)) -}
  [[b, a], [a, b], [b, >]] -> [ [b, b] , [b, a] , [a, >] ] {- Semlab 1 (Concon 0 (Input 1)) -}
  [[b, a], [a, b], [b, a]] -> [ [b, b] , [b, a] , [a, a] ] {- Semlab 1 (Concon 1 (Input 1)) -}
  [[b, a], [a, b], [b, b]] -> [ [b, b] , [b, a] , [a, b] ] {- Semlab 1 (Concon 2 (Input 1)) -}
  [[d, a], [a, b], [b, >]] -> [ [d, b] , [b, a] , [a, >] ] {- Semlab 2 (Concon 0 (Input 1)) -}
  [[d, a], [a, b], [b, a]] -> [ [d, b] , [b, a] , [a, a] ] {- Semlab 2 (Concon 1 (Input 1)) -}
  [[d, a], [a, b], [b, b]] -> [ [d, b] , [b, a] , [a, b] ] {- Semlab 2 (Concon 2 (Input 1)) -}
  [[<, d], [d, c], [c, b]] ->= [ [<, d] , [d, a] , [a, b] ] {- Semlab 0 (Concon 0 (Input 3)) -}
  [[<, d], [d, a], [a, >]] ->= [ [<, d] , [d, c] , [c, b] , [b, >] ] {- Semlab 0 (Concon 0 (Input 4)) -}
  [[<, d], [d, a], [a, a]] ->= [ [<, d] , [d, c] , [c, b] , [b, a] ] {- Semlab 0 (Concon 1 (Input 4)) -}
  [[<, d], [d, a], [a, b]] ->= [ [<, d] , [d, c] , [c, b] , [b, b] ] {- Semlab 0 (Concon 2 (Input 4)) -}
reason
  ([d, a], 1/3)
  ([d, c], 1/3)
   property Termination
has value Just True
for SRS
  [[a, a], [a, b], [b, >]] -> [ [a, b] , [b, a] , [a, >] ] {- Semlab 0 (Concon 0 (Input 1)) -}
  [[a, a], [a, b], [b, a]] -> [ [a, b] , [b, a] , [a, a] ] {- Semlab 0 (Concon 1 (Input 1)) -}
  [[a, a], [a, b], [b, b]] -> [ [a, b] , [b, a] , [a, b] ] {- Semlab 0 (Concon 2 (Input 1)) -}
  [[b, a], [a, b], [b, >]] -> [ [b, b] , [b, a] , [a, >] ] {- Semlab 1 (Concon 0 (Input 1)) -}
  [[b, a], [a, b], [b, a]] -> [ [b, b] , [b, a] , [a, a] ] {- Semlab 1 (Concon 1 (Input 1)) -}
  [[b, a], [a, b], [b, b]] -> [ [b, b] , [b, a] , [a, b] ] {- Semlab 1 (Concon 2 (Input 1)) -}
  [[<, d], [d, c], [c, b]] ->= [ [<, d] , [d, a] , [a, b] ] {- Semlab 0 (Concon 0 (Input 3)) -}
  [[<, d], [d, a], [a, >]] ->= [ [<, d] , [d, c] , [c, b] , [b, >] ] {- Semlab 0 (Concon 0 (Input 4)) -}
  [[<, d], [d, a], [a, a]] ->= [ [<, d] , [d, c] , [c, b] , [b, a] ] {- Semlab 0 (Concon 1 (Input 4)) -}
  [[<, d], [d, a], [a, b]] ->= [ [<, d] , [d, c] , [c, b] , [b, b] ] {- Semlab 0 (Concon 2 (Input 4)) -}
reason
  Tiling   { method = Overlap, width = 2, state_type = Bit64, map_type = Enum, unlabel = True, print_completion_steps = False, print_tiles = False, verbose = False, tracing = True}
  steps 1
  using 28 tiles
  remove some unmatched rules
  steps: 1
  
   property Termination
has value Just True
for SRS
  [[a, a], [a, b], [b, >]] -> [ [a, b] , [b, a] , [a, >] ] {- Semlab 0 (Concon 0 (Input 1)) -}
  [[a, a], [a, b], [b, a]] -> [ [a, b] , [b, a] , [a, a] ] {- Semlab 0 (Concon 1 (Input 1)) -}
  [[a, a], [a, b], [b, b]] -> [ [a, b] , [b, a] , [a, b] ] {- Semlab 0 (Concon 2 (Input 1)) -}
  [[b, a], [a, b], [b, >]] -> [ [b, b] , [b, a] , [a, >] ] {- Semlab 1 (Concon 0 (Input 1)) -}
  [[b, a], [a, b], [b, a]] -> [ [b, b] , [b, a] , [a, a] ] {- Semlab 1 (Concon 1 (Input 1)) -}
  [[b, a], [a, b], [b, b]] -> [ [b, b] , [b, a] , [a, b] ] {- Semlab 1 (Concon 2 (Input 1)) -}
  [[<, d], [d, c], [c, b]] ->= [ [<, d] , [d, a] , [a, b] ] {- Semlab 0 (Concon 0 (Input 3)) -}
  [[<, d], [d, a], [a, b]] ->= [ [<, d] , [d, c] , [c, b] , [b, b] ] {- Semlab 0 (Concon 2 (Input 4)) -}
reason
  ([b, >], 2/1)
   property Termination
has value Just True
for SRS
  [[a, a], [a, b], [b, a]] -> [ [a, b] , [b, a] , [a, a] ] {- Semlab 0 (Concon 1 (Input 1)) -}
  [[a, a], [a, b], [b, b]] -> [ [a, b] , [b, a] , [a, b] ] {- Semlab 0 (Concon 2 (Input 1)) -}
  [[b, a], [a, b], [b, a]] -> [ [b, b] , [b, a] , [a, a] ] {- Semlab 1 (Concon 1 (Input 1)) -}
  [[b, a], [a, b], [b, b]] -> [ [b, b] , [b, a] , [a, b] ] {- Semlab 1 (Concon 2 (Input 1)) -}
  [[<, d], [d, c], [c, b]] ->= [ [<, d] , [d, a] , [a, b] ] {- Semlab 0 (Concon 0 (Input 3)) -}
  [[<, d], [d, a], [a, b]] ->= [ [<, d] , [d, c] , [c, b] , [b, b] ] {- Semlab 0 (Concon 2 (Input 4)) -}
reason
  ( [a, a]
  , St  / 2 2 0 \
        | 1 1 0 |
        \ 0 0 1 / )
  ( [a, b]
  , St  / 1 0 0 \
        | 0 1 0 |
        \ 0 0 1 / )
  ( [b, a]
  , St  / 2 2 2 \
        | 1 1 0 |
        \ 0 0 1 / )
  ( [b, b]
  , St  / 1 0 0 \
        | 0 1 2 |
        \ 0 0 1 / )
  ( [<, d]
  , St  / 1 1 6 \
        | 0 0 0 |
        \ 0 0 1 / )
  ( [d, c]
  , St  / 1 0 0 \
        | 1 0 1 |
        \ 0 0 1 / )
  ( [c, b]
  , St  / 1 0 0 \
        | 0 0 0 |
        \ 0 0 1 / )
  ( [d, a]
  , St  / 1 0 0 \
        | 1 0 1 |
        \ 0 0 1 / )
   property Termination
has value Just True
for SRS
  [[<, d], [d, c], [c, b]] ->= [ [<, d] , [d, a] , [a, b] ] {- Semlab 0 (Concon 0 (Input 3)) -}
  [[<, d], [d, a], [a, b]] ->= [ [<, d] , [d, c] , [c, b] , [b, b] ] {- Semlab 0 (Concon 2 (Input 4)) -}
reason
  no strict rules

**************************************************
skeleton: (3/2,4)\Matrix{\Natural}{3}(2/2,4)\Matrix{\Natural}{3}(1/2,4)\TileAllROC{2}(9/4,11)\Weight(6/4,10)\TileRemoveROC{2}(6/2,10)\Weight(4/2,8)\Matrix{\Natural}{3}(0/2,6)[]
**************************************************
let {}
in let {done = Worker No_Strict_Rules;mo = Pre (Or_Else Count (IfSizeLeq 100000 GLPK Fail));wop = Or_Else (Worker (Weight {modus = mo})) Pass;weighted = \ m -> And_Then m wop;when_small = \ m -> And_Then (Worker (SizeAtmost 100)) m;when_medium = \ m -> And_Then (Worker (SizeAtmost 10000)) m;tiling = \ m w -> weighted (And_Then (Worker (Tiling {method = m,width = w,tracing = True})) (Worker Remap));matrix = \ mo dom dim bits -> when_small (weighted (Worker (Matrix {monotone = mo,domain = dom,dim = dim,bits = bits,shape = Corner})));kbo = \ b -> when_medium (weighted (Worker (KBO {bits = b,solver = Minisatapi})));yeah = Apply wop (Tree_Search_Preemptive 0 done ([ ] <> ([ kbo 1, And_Then (Worker Mirror) (kbo 1)] <> ((for [ 3, 4] (\ d -> matrix Strict Natural d 3)) <> (for [ 2, 3, 5] (\ w -> tiling Overlap w))))));noh = [ Timeout 5 (Worker (Enumerate {closure = Forward})), Timeout 5 (Worker (Enumerate {closure = Backward}))]}
  in Apply (Worker Remap) (First_Of ([ yeah] <> noh))