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


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


YES
**************************************************
summary
**************************************************
SRS with 4 rules on 4 letters       mirror
SRS with 4 rules on 4 letters       tile all, by Config   { method = Forward,width = 2,unlabel = False}
SRS with 32 rules on 16 letters       weights
SRS with 27 rules on 13 letters       unlabel
SRS with 3 rules on 4 letters       DP
SRS with 4 strict rules and 3 weak rules on 7 letters       EDG
SRS with 4 strict rules and 3 weak rules on 7 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = False}
SRS with 3 strict rules and 3 weak rules on 7 letters       EDG
SRS with 3 strict rules and 3 weak rules on 7 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 4, dim = 3, solver = Minisatapi, verbose = False, tracing = False}
SRS with 2 strict rules and 3 weak rules on 7 letters       weights
SRS with 0 strict rules and 3 weak rules on 4 letters       EDG

**************************************************
proof
**************************************************
property Termination
has value Just True
for SRS
  [a, a] -> [b, b] {- Input 0 -}
  [c, c, b] -> [d, c, a] {- Input 1 -}
  [a] -> [d, c, c] {- Input 2 -}
  [c, d] -> [b, c] {- Input 3 -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [a, a] -> [b, b] {- Mirror (Input 0) -}
  [b, c, c] -> [a, c, d] {- Mirror (Input 1) -}
  [a] -> [c, c, d] {- Mirror (Input 2) -}
  [d, c] -> [c, b] {- Mirror (Input 3) -}
reason
  Tiling   { method = Forward, width = 2, state_type = Bit64, map_type = Enum, unlabel = False, print_completion_steps = False, print_tiles = False, verbose = False, tracing = False}
  steps 3
  using 18 tiles
  tile all rules
  steps: 3
  
   property Termination
has value Just True
for SRS
  [[<, b], [b, c], [c, c], [c, a]] -> [ [<, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 0 (Concon 0 (Mirror (Input 1))) -}
  [[<, b], [b, c], [c, c], [c, b]] -> [ [<, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 0 (Concon 1 (Mirror (Input 1))) -}
  [[<, b], [b, c], [c, c], [c, c]] -> [ [<, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 0 (Concon 2 (Mirror (Input 1))) -}
  [[<, b], [b, c], [c, c], [c, d]] -> [ [<, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 0 (Concon 3 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, a]] -> [ [b, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 1 (Concon 0 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, b]] -> [ [b, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 1 (Concon 1 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, c]] -> [ [b, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 1 (Concon 2 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, d]] -> [ [b, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 1 (Concon 3 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, a]] -> [ [c, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 2 (Concon 0 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, b]] -> [ [c, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 2 (Concon 1 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, c]] -> [ [c, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 2 (Concon 2 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, d]] -> [ [c, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 2 (Concon 3 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, a]] -> [ [d, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 3 (Concon 0 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, b]] -> [ [d, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 3 (Concon 1 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, c]] -> [ [d, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 3 (Concon 2 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, d]] -> [ [d, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 3 (Concon 3 (Mirror (Input 1))) -}
  [[<, a], [a, c]] -> [ [<, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 0 (Concon 0 (Mirror (Input 2))) -}
  [[b, a], [a, c]] -> [ [b, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 1 (Concon 0 (Mirror (Input 2))) -}
  [[c, a], [a, c]] -> [ [c, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 2 (Concon 0 (Mirror (Input 2))) -}
  [[d, a], [a, c]] -> [ [d, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 3 (Concon 0 (Mirror (Input 2))) -}
  [[b, d], [d, c], [c, a]] -> [ [b, c] , [c, b] , [ b , a ] ] {- Semlab 0 (Concon 0 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, b]] -> [ [b, c] , [c, b] , [ b , b ] ] {- Semlab 0 (Concon 1 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, c]] -> [ [b, c] , [c, b] , [ b , c ] ] {- Semlab 0 (Concon 2 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, d]] -> [ [b, c] , [c, b] , [ b , d ] ] {- Semlab 0 (Concon 3 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, a]] -> [ [c, c] , [c, b] , [ b , a ] ] {- Semlab 1 (Concon 0 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, b]] -> [ [c, c] , [c, b] , [ b , b ] ] {- Semlab 1 (Concon 1 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, c]] -> [ [c, c] , [c, b] , [ b , c ] ] {- Semlab 1 (Concon 2 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, d]] -> [ [c, c] , [c, b] , [ b , d ] ] {- Semlab 1 (Concon 3 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, a]] -> [ [d, c] , [c, b] , [ b , a ] ] {- Semlab 2 (Concon 0 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, b]] -> [ [d, c] , [c, b] , [ b , b ] ] {- Semlab 2 (Concon 1 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, c]] -> [ [d, c] , [c, b] , [ b , c ] ] {- Semlab 2 (Concon 2 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, d]] -> [ [d, c] , [c, b] , [ b , d ] ] {- Semlab 2 (Concon 3 (Mirror (Input 3))) -}
reason
  ([<, b], 2/1)
  ([<, a], 1/1)
   property Termination
has value Just True
for SRS
  [[b, b], [b, c], [c, c], [c, a]] -> [ [b, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 1 (Concon 0 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, b]] -> [ [b, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 1 (Concon 1 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, c]] -> [ [b, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 1 (Concon 2 (Mirror (Input 1))) -}
  [[b, b], [b, c], [c, c], [c, d]] -> [ [b, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 1 (Concon 3 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, a]] -> [ [c, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 2 (Concon 0 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, b]] -> [ [c, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 2 (Concon 1 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, c]] -> [ [c, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 2 (Concon 2 (Mirror (Input 1))) -}
  [[c, b], [b, c], [c, c], [c, d]] -> [ [c, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 2 (Concon 3 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, a]] -> [ [d, a] , [a, c] , [c, d] , [ d , a ] ] {- Semlab 3 (Concon 0 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, b]] -> [ [d, a] , [a, c] , [c, d] , [ d , b ] ] {- Semlab 3 (Concon 1 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, c]] -> [ [d, a] , [a, c] , [c, d] , [ d , c ] ] {- Semlab 3 (Concon 2 (Mirror (Input 1))) -}
  [[d, b], [b, c], [c, c], [c, d]] -> [ [d, a] , [a, c] , [c, d] , [ d , d ] ] {- Semlab 3 (Concon 3 (Mirror (Input 1))) -}
  [[b, a], [a, c]] -> [ [b, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 1 (Concon 0 (Mirror (Input 2))) -}
  [[c, a], [a, c]] -> [ [c, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 2 (Concon 0 (Mirror (Input 2))) -}
  [[d, a], [a, c]] -> [ [d, c] , [c, c] , [c, d] , [d, c] ] {- Semlab 3 (Concon 0 (Mirror (Input 2))) -}
  [[b, d], [d, c], [c, a]] -> [ [b, c] , [c, b] , [ b , a ] ] {- Semlab 0 (Concon 0 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, b]] -> [ [b, c] , [c, b] , [ b , b ] ] {- Semlab 0 (Concon 1 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, c]] -> [ [b, c] , [c, b] , [ b , c ] ] {- Semlab 0 (Concon 2 (Mirror (Input 3))) -}
  [[b, d], [d, c], [c, d]] -> [ [b, c] , [c, b] , [ b , d ] ] {- Semlab 0 (Concon 3 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, a]] -> [ [c, c] , [c, b] , [ b , a ] ] {- Semlab 1 (Concon 0 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, b]] -> [ [c, c] , [c, b] , [ b , b ] ] {- Semlab 1 (Concon 1 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, c]] -> [ [c, c] , [c, b] , [ b , c ] ] {- Semlab 1 (Concon 2 (Mirror (Input 3))) -}
  [[c, d], [d, c], [c, d]] -> [ [c, c] , [c, b] , [ b , d ] ] {- Semlab 1 (Concon 3 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, a]] -> [ [d, c] , [c, b] , [ b , a ] ] {- Semlab 2 (Concon 0 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, b]] -> [ [d, c] , [c, b] , [ b , b ] ] {- Semlab 2 (Concon 1 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, c]] -> [ [d, c] , [c, b] , [ b , c ] ] {- Semlab 2 (Concon 2 (Mirror (Input 3))) -}
  [[d, d], [d, c], [c, d]] -> [ [d, c] , [c, b] , [ b , d ] ] {- Semlab 2 (Concon 3 (Mirror (Input 3))) -}
reason
  unlabel
   property Termination
has value Just True
for SRS
  [1, 2, 2] -> [0, 2, 3] {- Mirror (Input 1) -}
  [0] -> [2, 2, 3] {- Mirror (Input 2) -}
  [3, 2] -> [2, 1] {- Mirror (Input 3) -}
reason
  DP
   property Termination
has value Just True
for SRS
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
  [0#] |-> [3#] {- DP (Top 2) (Mirror (Input 2)) -}
  [1#, 2, 2] |-> [0#, 2, 3] {- DP (Top 0) (Mirror (Input 1)) -}
  [1#, 2, 2] |-> [3#] {- DP (Top 2) (Mirror (Input 1)) -}
  [3#, 2] |-> [1#] {- DP (Top 1) (Mirror (Input 3)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [0#] |-> [3#] {- DP (Top 2) (Mirror (Input 2)) -}
  [3#, 2] |-> [1#] {- DP (Top 1) (Mirror (Input 3)) -}
  [1#, 2, 2] |-> [3#] {- DP (Top 2) (Mirror (Input 1)) -}
  [1#, 2, 2] |-> [0#, 2, 3] {- DP (Top 0) (Mirror (Input 1)) -}
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
reason
  ( 1
  , Wk  / 0A  0A  3A \
        | -3A -3A 0A |
        \ -3A -3A 0A / )
  ( 2
  , Wk  / 0A  0A 3A \
        | 0A  0A 0A |
        \ -3A 0A 0A / )
  ( 0
  , Wk  / 3A 3A 3A \
        | 0A 0A 0A |
        \ 0A 0A 0A / )
  ( 3
  , Wk  / 0A  0A  0A  \
        | 0A  0A  0A  |
        \ -3A -3A -3A / )
  ( 0#
  , Wk  / 4A 5A 7A \
        | 4A 5A 7A |
        \ 4A 5A 7A / )
  ( 3#
  , Wk  / 4A 5A 7A \
        | 4A 5A 7A |
        \ 4A 5A 7A / )
  ( 1#
  , Wk  / 5A 7A 7A \
        | 5A 7A 7A |
        \ 5A 7A 7A / )
   property Termination
has value Just True
for SRS
  [0#] |-> [3#] {- DP (Top 2) (Mirror (Input 2)) -}
  [3#, 2] |-> [1#] {- DP (Top 1) (Mirror (Input 3)) -}
  [1#, 2, 2] |-> [0#, 2, 3] {- DP (Top 0) (Mirror (Input 1)) -}
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [0#] |-> [3#] {- DP (Top 2) (Mirror (Input 2)) -}
  [3#, 2] |-> [1#] {- DP (Top 1) (Mirror (Input 3)) -}
  [1#, 2, 2] |-> [0#, 2, 3] {- DP (Top 0) (Mirror (Input 1)) -}
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
reason
  ( 1
  , Wk  / 0A  0A  3A \
        | -3A -3A 0A |
        \ -3A -3A 0A / )
  ( 2
  , Wk  / 0A  0A 3A \
        | 0A  0A 0A |
        \ -3A 0A 0A / )
  ( 0
  , Wk  / 3A 3A 3A \
        | 0A 0A 0A |
        \ 0A 0A 0A / )
  ( 3
  , Wk  / 0A  0A  0A  \
        | 0A  0A  0A  |
        \ -3A -3A -3A / )
  ( 0#
  , Wk  / 43A 44A 44A \
        | 43A 44A 44A |
        \ 43A 44A 44A / )
  ( 3#
  , Wk  / 42A 44A 44A \
        | 42A 44A 44A |
        \ 42A 44A 44A / )
  ( 1#
  , Wk  / 41A 43A 44A \
        | 41A 43A 44A |
        \ 41A 43A 44A / )
   property Termination
has value Just True
for SRS
  [0#] |-> [3#] {- DP (Top 2) (Mirror (Input 2)) -}
  [1#, 2, 2] |-> [0#, 2, 3] {- DP (Top 0) (Mirror (Input 1)) -}
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
reason
  (0#, 1/1)
  (1#, 2/1)
   property Termination
has value Just True
for SRS
  [1, 2, 2] ->= [0, 2, 3] {- DP Nontop (Mirror (Input 1)) -}
  [0] ->= [2, 2, 3] {- DP Nontop (Mirror (Input 2)) -}
  [3, 2] ->= [2, 1] {- DP Nontop (Mirror (Input 3)) -}
reason
  EDG

**************************************************
skeleton: \Mirror(4,4)\TileAllRFC{2}(32,16)\Weight(27,13)\Unlabel(3,4)\Deepee\EDG(4/3,7)\Matrix{\Arctic}{3}\EDG(3/3,7)\Matrix{\Arctic}{3}(2/3,7)\Weight(0/3,4)\EDG[]
**************************************************
let {}
in let {trac = False;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,unlabel = False})) (Worker Remap));when_small = \ m -> And_Then (Worker (SizeAtmost 1000)) m;when_medium = \ m -> And_Then (Worker (SizeAtmost 10000)) m;solver = Minisatapi;qpi = \ dim bits -> weighted (when_small (Worker (QPI {tracing = trac,dim = dim,bits = bits,solver = solver})));matrix = \ dom dim bits -> weighted (when_small (Worker (Matrix {monotone = Weak,domain = dom,dim = dim,bits = bits,tracing = trac,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]] <> ([ Seq [ matrix Arctic 2 5, matrix Arctic 3 4, matrix Arctic 4 3], Seq [ matrix Natural 2 5, matrix Natural 3 4, matrix Natural 4 3]] <> [ kbo 1, And_Then (Worker Mirror) (And_Then (kbo 1) (Worker Mirror))])));dp = As_Transformer (Apply (And_Then (Worker (DP {tracing = True})) (Worker Remap)) (Apply wop (Branch (Worker (EDG {tracing = True})) remove)));noh = [ Worker (Enumerate {closure = Forward}), 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, tiling Forward 2, And_Then (Worker Mirror) (tiling Forward 2)] <> [ Worker (Unlabel {verbose = True})])}
  in Apply (Worker Remap) (Seq [ Worker KKST01, First_Of ([ yeah] <> noh)])