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


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YES
**************************************************
summary
**************************************************
SRS with 4 rules on 4 letters       DP
SRS with 6 strict rules and 4 weak rules on 7 letters       weights
SRS with 4 strict rules and 4 weak rules on 6 letters       EDG
SRS with 4 strict rules and 4 weak rules on 6 letters       Matrix   { monotone = Weak, domain = Natural, shape = Full, bits = 5, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
SRS with 2 strict rules and 4 weak rules on 6 letters       EDG
SRS with 2 strict rules and 4 weak rules on 6 letters       Matrix   { monotone = Weak, domain = Natural, shape = Full, bits = 5, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
SRS with 1 strict rules and 4 weak rules on 6 letters       weights
SRS with 0 strict rules and 4 weak rules on 4 letters       EDG

**************************************************
proof
**************************************************
property Termination
has value Just True
for SRS
  [a, d] -> [d, b] {- Input 0 -}
  [a] -> [b, b, b] {- Input 1 -}
  [b, d, b] -> [a, c] {- Input 2 -}
  [c] -> [d] {- Input 3 -}
reason
  DP
   property Termination
has value Just True
for SRS
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
  [a#] |-> [b#] {- DP (Top 2) (Input 1) -}
  [a#] |-> [b#, b] {- DP (Top 1) (Input 1) -}
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [a#, d] |-> [b#] {- DP (Top 1) (Input 0) -}
  [b#, d, b] |-> [a#, c] {- DP (Top 0) (Input 2) -}
  [b#, d, b] |-> [c#] {- DP (Top 1) (Input 2) -}
reason
  (d, 1/2)
  (c, 1/2)
   property Termination
has value Just True
for SRS
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
  [a#] |-> [b#] {- DP (Top 2) (Input 1) -}
  [a#] |-> [b#, b] {- DP (Top 1) (Input 1) -}
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [b#, d, b] |-> [a#, c] {- DP (Top 0) (Input 2) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#] |-> [b#] {- DP (Top 2) (Input 1) -}
  [b#, d, b] |-> [a#, c] {- DP (Top 0) (Input 2) -}
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [a#] |-> [b#, b] {- DP (Top 1) (Input 1) -}
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
reason
  ( a
  , Wk  / 1 3 \
        \ 0 1 / )
  ( d
  , Wk  / 2 0 \
        \ 0 1 / )
  ( b
  , Wk  / 1 1 \
        \ 0 1 / )
  ( c
  , Wk  / 2 0 \
        \ 0 1 / )
  ( a#
  , Wk  / 3 17 \
        \ 0 1  / )
  ( b#
  , Wk  / 3 11 \
        \ 0 1  / )
   property Termination
has value Just True
for SRS
  [b#, d, b] |-> [a#, c] {- DP (Top 0) (Input 2) -}
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [b#, d, b] |-> [a#, c] {- DP (Top 0) (Input 2) -}
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
reason
  ( a
  , Wk  / 1 12 \
        \ 0 1  / )
  ( d
  , Wk  / 5 6 \
        \ 0 1 / )
  ( b
  , Wk  / 1 2 \
        \ 0 1 / )
  ( c
  , Wk  / 5 6 \
        \ 0 1 / )
  ( a#
  , Wk  / 1 17 \
        \ 0 1  / )
  ( b#
  , Wk  / 1 13 \
        \ 0 1  / )
   property Termination
has value Just True
for SRS
  [a#] |-> [b#, b, b] {- DP (Top 0) (Input 1) -}
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
reason
  (a#, 1/1)
   property Termination
has value Just True
for SRS
  [a, d] ->= [d, b] {- DP Nontop (Input 0) -}
  [a] ->= [b, b, b] {- DP Nontop (Input 1) -}
  [b, d, b] ->= [a, c] {- DP Nontop (Input 2) -}
  [c] ->= [d] {- DP Nontop (Input 3) -}
reason
  EDG

**************************************************
skeleton: (4,4)\Deepee(6/4,7)\Weight\EDG(4/4,6)\Matrix{\Natural}{2}\EDG(2/4,6)\Matrix{\Natural}{2}(1/4,6)\Weight(0/4,4)\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)])