/export/starexec/sandbox2/solver/bin/starexec_run_tc20-std.sh /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
**************************************************
summary
**************************************************
SRS with 9 rules on 6 letters       weights
SRS with 8 rules on 6 letters       mirror
SRS with 8 rules on 6 letters       DP
SRS with 22 strict rules and 8 weak rules on 11 letters       weights
SRS with 14 strict rules and 8 weak rules on 10 letters       EDG
2 sub-proofs
  1 SRS with 2 strict rules and 8 weak rules on 7 letters       mirror
  SRS with 2 strict rules and 8 weak rules on 7 letters       Matrix   { monotone = Strict, domain = Natural, shape = Full, bits = 3, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 2 strict rules and 7 weak rules on 5 letters       mirror
  SRS with 2 strict rules and 7 weak rules on 5 letters       EDG
  SRS with 2 strict rules and 7 weak rules on 5 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 1 strict rules and 7 weak rules on 5 letters       EDG
  SRS with 1 strict rules and 7 weak rules on 5 letters       Matrix   { monotone = Weak, domain = Natural, shape = Full, bits = 5, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 0 strict rules and 7 weak rules on 4 letters       EDG
  
  2 SRS with 12 strict rules and 8 weak rules on 9 letters       mirror
  SRS with 12 strict rules and 8 weak rules on 9 letters       Matrix   { monotone = Strict, domain = Natural, shape = Full, bits = 3, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 12 strict rules and 7 weak rules on 7 letters       mirror
  SRS with 12 strict rules and 7 weak rules on 7 letters       EDG
  SRS with 12 strict rules and 7 weak rules on 7 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 4, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 10 strict rules and 7 weak rules on 7 letters       EDG
  SRS with 10 strict rules and 7 weak rules on 7 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 5, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 7 strict rules and 7 weak rules on 7 letters       weights
  SRS with 4 strict rules and 7 weak rules on 6 letters       EDG
  SRS with 4 strict rules and 7 weak rules on 6 letters       Matrix   { monotone = Weak, domain = Natural, shape = Full, bits = 5, dim = 2, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 3 strict rules and 7 weak rules on 6 letters       EDG
  SRS with 3 strict rules and 7 weak rules on 6 letters       Matrix   { monotone = Weak, domain = Arctic, shape = Full, bits = 3, dim = 4, solver = Minisatapi, verbose = False, tracing = False}
  SRS with 1 strict rules and 7 weak rules on 6 letters       weights
  SRS with 0 strict rules and 7 weak rules on 4 letters       EDG
  
**************************************************
proof
**************************************************
property Termination
has value Just True
for SRS
  [a, b] -> [b, c, a] {- Input 0 -}
  [b, c] -> [c, b, b] {- Input 1 -}
  [a, c] -> [c, a, b] {- Input 2 -}
  [a, a] -> [a, d, d, d] {- Input 3 -}
  [d, a] -> [d, d, c] {- Input 4 -}
  [a, d, d, c] -> [a, a, a, d] {- Input 5 -}
  [e, e, f, f] -> [f, f, f, e, e] {- Input 6 -}
  [e] -> [a] {- Input 7 -}
  [b, d] -> [d, d] {- Input 8 -}
reason
  (e, 1/1)
   property Termination
has value Just True
for SRS
  [a, b] -> [b, c, a] {- Input 0 -}
  [b, c] -> [c, b, b] {- Input 1 -}
  [a, c] -> [c, a, b] {- Input 2 -}
  [a, a] -> [a, d, d, d] {- Input 3 -}
  [d, a] -> [d, d, c] {- Input 4 -}
  [a, d, d, c] -> [a, a, a, d] {- Input 5 -}
  [e, e, f, f] -> [f, f, f, e, e] {- Input 6 -}
  [b, d] -> [d, d] {- Input 8 -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [b, a] -> [a, c, b] {- Mirror (Input 0) -}
  [c, b] -> [b, b, c] {- Mirror (Input 1) -}
  [c, a] -> [b, a, c] {- Mirror (Input 2) -}
  [a, a] -> [d, d, d, a] {- Mirror (Input 3) -}
  [a, d] -> [c, d, d] {- Mirror (Input 4) -}
  [c, d, d, a] -> [d, a, a, a] {- Mirror (Input 5) -}
  [f, f, e, e] -> [e, e, f, f, f] {- Mirror (Input 6) -}
  [d, b] -> [d, d] {- Mirror (Input 8) -}
reason
  DP
   property Termination
has value Just True
for SRS
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [f, f, e, e] ->= [e, e, f, f, f] {- DP Nontop (Mirror (Input 6)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
  [a#, a] |-> [d#, a] {- DP (Top 2) (Mirror (Input 3)) -}
  [a#, a] |-> [d#, d, a] {- DP (Top 1) (Mirror (Input 3)) -}
  [a#, a] |-> [d#, d, d, a] {- DP (Top 0) (Mirror (Input 3)) -}
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [a#, d] |-> [d#, d] {- DP (Top 1) (Mirror (Input 4)) -}
  [b#, a] |-> [a#, c, b] {- DP (Top 0) (Mirror (Input 0)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, a] |-> [a#, c] {- DP (Top 1) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [d#, a, a, a] {- DP (Top 0) (Mirror (Input 5)) -}
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [d#, b] |-> [d#, d] {- DP (Top 0) (Mirror (Input 8)) -}
  [f#, f, e, e] |-> [f#] {- DP (Top 4) (Mirror (Input 6)) -}
  [f#, f, e, e] |-> [f#, f] {- DP (Top 3) (Mirror (Input 6)) -}
  [f#, f, e, e] |-> [f#, f, f] {- DP (Top 2) (Mirror (Input 6)) -}
reason
  (e, 1/2)
  (a#, 1/5)
  (c#, 1/5)
  (b#, 1/5)
   property Termination
has value Just True
for SRS
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [f, f, e, e] ->= [e, e, f, f, f] {- DP Nontop (Mirror (Input 6)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [b#, a] |-> [a#, c, b] {- DP (Top 0) (Mirror (Input 0)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, a] |-> [a#, c] {- DP (Top 1) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [d#, b] |-> [d#, d] {- DP (Top 0) (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [d#, b] |-> [d#, d] {- DP (Top 0) (Mirror (Input 8)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [f, f, e, e] ->= [e, e, f, f, f] {- DP Nontop (Mirror (Input 6)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [b, d#] ->| [d#] {- Mirror (DP (Top 1) (Mirror (Input 8))) -}
  [b, d#] ->| [d, d#] {- Mirror (DP (Top 0) (Mirror (Input 8))) -}
  [a, b] ->= [b, c, a] {- Mirror (DP Nontop (Mirror (Input 0))) -}
  [b, c] ->= [c, b, b] {- Mirror (DP Nontop (Mirror (Input 1))) -}
  [a, c] ->= [c, a, b] {- Mirror (DP Nontop (Mirror (Input 2))) -}
  [a, a] ->= [a, d, d, d] {- Mirror (DP Nontop (Mirror (Input 3))) -}
  [d, a] ->= [d, d, c] {- Mirror (DP Nontop (Mirror (Input 4))) -}
  [a, d, d, c] ->= [a, a, a, d] {- Mirror (DP Nontop (Mirror (Input 5))) -}
  [e, e, f, f] ->= [f, f, f, e, e] {- Mirror (DP Nontop (Mirror (Input 6))) -}
  [b, d] ->= [d, d] {- Mirror (DP Nontop (Mirror (Input 8))) -}
reason
  ( b
  , St  / 1 0 \
        \ 0 1 / )
  ( a
  , St  / 1 0 \
        \ 0 1 / )
  ( c
  , St  / 1 0 \
        \ 0 1 / )
  ( d
  , St  / 1 0 \
        \ 0 1 / )
  ( f
  , St  / 1 1 \
        \ 0 1 / )
  ( e
  , St  / 2 0 \
        \ 0 1 / )
  ( d#
  , St  / 1 0 \
        \ 0 1 / )
   property Termination
has value Just True
for SRS
  [b, d#] ->| [d#] {- Mirror (DP (Top 1) (Mirror (Input 8))) -}
  [b, d#] ->| [d, d#] {- Mirror (DP (Top 0) (Mirror (Input 8))) -}
  [a, b] ->= [b, c, a] {- Mirror (DP Nontop (Mirror (Input 0))) -}
  [b, c] ->= [c, b, b] {- Mirror (DP Nontop (Mirror (Input 1))) -}
  [a, c] ->= [c, a, b] {- Mirror (DP Nontop (Mirror (Input 2))) -}
  [a, a] ->= [a, d, d, d] {- Mirror (DP Nontop (Mirror (Input 3))) -}
  [d, a] ->= [d, d, c] {- Mirror (DP Nontop (Mirror (Input 4))) -}
  [a, d, d, c] ->= [a, a, a, d] {- Mirror (DP Nontop (Mirror (Input 5))) -}
  [b, d] ->= [d, d] {- Mirror (DP Nontop (Mirror (Input 8))) -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [d#, b] |-> [d#, d] {- DP (Top 0) (Mirror (Input 8)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [d#, b] |-> [d#, d] {- DP (Top 0) (Mirror (Input 8)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 0A 0A \
        \ 0A 0A / )
  ( a
  , Wk  / 0A 0A \
        \ 0A 0A / )
  ( c
  , Wk  / 0A  0A \
        \ -2A 0A / )
  ( d
  , Wk  / 0A  0A  \
        \ -2A -2A / )
  ( d#
  , Wk  / 17A 18A \
        \ 17A 18A / )
   property Termination
has value Just True
for SRS
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [d#, b] |-> [d#] {- DP (Top 1) (Mirror (Input 8)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 1 7 \
        \ 0 1 / )
  ( a
  , Wk  / 0 4 \
        \ 0 1 / )
  ( c
  , Wk  / 3 0 \
        \ 0 1 / )
  ( d
  , Wk  / 0 1 \
        \ 0 1 / )
  ( d#
  , Wk  / 4 2 \
        \ 0 1 / )
   property Termination
has value Just True
for SRS
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG

property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [a#, c, b] {- DP (Top 0) (Mirror (Input 0)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [c#, a] |-> [a#, c] {- DP (Top 1) (Mirror (Input 2)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [f, f, e, e] ->= [e, e, f, f, f] {- DP Nontop (Mirror (Input 6)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [d, a#] ->| [d, d, c#] {- Mirror (DP (Top 0) (Mirror (Input 4))) -}
  [a, d, d, c#] ->| [a, a, a#] {- Mirror (DP (Top 1) (Mirror (Input 5))) -}
  [a, d, d, c#] ->| [a, a#] {- Mirror (DP (Top 2) (Mirror (Input 5))) -}
  [b, c#] ->| [c#] {- Mirror (DP (Top 2) (Mirror (Input 1))) -}
  [b, c#] ->| [c, b#] {- Mirror (DP (Top 1) (Mirror (Input 1))) -}
  [a, b#] ->| [b, c#] {- Mirror (DP (Top 1) (Mirror (Input 0))) -}
  [b, c#] ->| [c, b, b#] {- Mirror (DP (Top 0) (Mirror (Input 1))) -}
  [a, b#] ->| [b#] {- Mirror (DP (Top 2) (Mirror (Input 0))) -}
  [a, b#] ->| [b, c, a#] {- Mirror (DP (Top 0) (Mirror (Input 0))) -}
  [a, c#] ->| [c#] {- Mirror (DP (Top 2) (Mirror (Input 2))) -}
  [a, c#] ->| [c, a, b#] {- Mirror (DP (Top 0) (Mirror (Input 2))) -}
  [a, c#] ->| [c, a#] {- Mirror (DP (Top 1) (Mirror (Input 2))) -}
  [a, b] ->= [b, c, a] {- Mirror (DP Nontop (Mirror (Input 0))) -}
  [b, c] ->= [c, b, b] {- Mirror (DP Nontop (Mirror (Input 1))) -}
  [a, c] ->= [c, a, b] {- Mirror (DP Nontop (Mirror (Input 2))) -}
  [a, a] ->= [a, d, d, d] {- Mirror (DP Nontop (Mirror (Input 3))) -}
  [d, a] ->= [d, d, c] {- Mirror (DP Nontop (Mirror (Input 4))) -}
  [a, d, d, c] ->= [a, a, a, d] {- Mirror (DP Nontop (Mirror (Input 5))) -}
  [e, e, f, f] ->= [f, f, f, e, e] {- Mirror (DP Nontop (Mirror (Input 6))) -}
  [b, d] ->= [d, d] {- Mirror (DP Nontop (Mirror (Input 8))) -}
reason
  ( b
  , St  / 1 0 \
        \ 0 1 / )
  ( a
  , St  / 1 0 \
        \ 0 1 / )
  ( c
  , St  / 1 0 \
        \ 0 1 / )
  ( d
  , St  / 1 0 \
        \ 0 1 / )
  ( f
  , St  / 1 1 \
        \ 0 1 / )
  ( e
  , St  / 2 0 \
        \ 0 1 / )
  ( a#
  , St  / 1 0 \
        \ 0 1 / )
  ( c#
  , St  / 1 0 \
        \ 0 1 / )
  ( b#
  , St  / 1 0 \
        \ 0 1 / )
   property Termination
has value Just True
for SRS
  [d, a#] ->| [d, d, c#] {- Mirror (DP (Top 0) (Mirror (Input 4))) -}
  [a, d, d, c#] ->| [a, a, a#] {- Mirror (DP (Top 1) (Mirror (Input 5))) -}
  [a, d, d, c#] ->| [a, a#] {- Mirror (DP (Top 2) (Mirror (Input 5))) -}
  [b, c#] ->| [c#] {- Mirror (DP (Top 2) (Mirror (Input 1))) -}
  [b, c#] ->| [c, b#] {- Mirror (DP (Top 1) (Mirror (Input 1))) -}
  [a, b#] ->| [b, c#] {- Mirror (DP (Top 1) (Mirror (Input 0))) -}
  [b, c#] ->| [c, b, b#] {- Mirror (DP (Top 0) (Mirror (Input 1))) -}
  [a, b#] ->| [b#] {- Mirror (DP (Top 2) (Mirror (Input 0))) -}
  [a, b#] ->| [b, c, a#] {- Mirror (DP (Top 0) (Mirror (Input 0))) -}
  [a, c#] ->| [c#] {- Mirror (DP (Top 2) (Mirror (Input 2))) -}
  [a, c#] ->| [c, a, b#] {- Mirror (DP (Top 0) (Mirror (Input 2))) -}
  [a, c#] ->| [c, a#] {- Mirror (DP (Top 1) (Mirror (Input 2))) -}
  [a, b] ->= [b, c, a] {- Mirror (DP Nontop (Mirror (Input 0))) -}
  [b, c] ->= [c, b, b] {- Mirror (DP Nontop (Mirror (Input 1))) -}
  [a, c] ->= [c, a, b] {- Mirror (DP Nontop (Mirror (Input 2))) -}
  [a, a] ->= [a, d, d, d] {- Mirror (DP Nontop (Mirror (Input 3))) -}
  [d, a] ->= [d, d, c] {- Mirror (DP Nontop (Mirror (Input 4))) -}
  [a, d, d, c] ->= [a, a, a, d] {- Mirror (DP Nontop (Mirror (Input 5))) -}
  [b, d] ->= [d, d] {- Mirror (DP Nontop (Mirror (Input 8))) -}
reason
  mirror
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [a#, c, b] {- DP (Top 0) (Mirror (Input 0)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [c#, a] |-> [a#, c] {- DP (Top 1) (Mirror (Input 2)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, a] |-> [a#, c] {- DP (Top 1) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [b#, a] |-> [a#, c, b] {- DP (Top 0) (Mirror (Input 0)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 0A 0A \
        \ 0A 0A / )
  ( a
  , Wk  / 0A 0A \
        \ 0A 0A / )
  ( c
  , Wk  / 0A 0A \
        \ 0A 0A / )
  ( d
  , Wk  / 0A  0A  \
        \ -2A -2A / )
  ( a#
  , Wk  / 19A 19A \
        \ 19A 19A / )
  ( c#
  , Wk  / 19A 20A \
        \ 19A 20A / )
  ( b#
  , Wk  / 18A 20A \
        \ 18A 20A / )
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [b#, a] |-> [c#, b] {- DP (Top 1) (Mirror (Input 0)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [b#, a] |-> [b#] {- DP (Top 2) (Mirror (Input 0)) -}
  [c#, a] |-> [c#] {- DP (Top 2) (Mirror (Input 2)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 0A -  \
        \ -  0A / )
  ( a
  , Wk  / 4A 22A \
        \ -  0A  / )
  ( c
  , Wk  / 0A 16A \
        \ -  0A  / )
  ( d
  , Wk  / - 0A \
        \ - 0A / )
  ( a#
  , Wk  / - 23A \
        \ - 0A  / )
  ( c#
  , Wk  / 4A 23A \
        \ -  0A  / )
  ( b#
  , Wk  / 4A 4A \
        \ -  0A / )
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, c] {- DP (Top 1) (Mirror (Input 1)) -}
  [c#, b] |-> [b#, b, c] {- DP (Top 0) (Mirror (Input 1)) -}
  [c#, a] |-> [b#, a, c] {- DP (Top 0) (Mirror (Input 2)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  (a#, 1/3)
  (c#, 1/3)
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, b] |-> [c#] {- DP (Top 2) (Mirror (Input 1)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 1 8 \
        \ 0 1 / )
  ( a
  , Wk  / 0 10 \
        \ 0 1  / )
  ( c
  , Wk  / 3 1 \
        \ 0 1 / )
  ( d
  , Wk  / 0 3 \
        \ 0 1 / )
  ( a#
  , Wk  / 0 20 \
        \ 0 1  / )
  ( c#
  , Wk  / 2 14 \
        \ 0 1  / )
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [c#, d, d, a] |-> [a#, a, a] {- DP (Top 1) (Mirror (Input 5)) -}
  [c#, d, d, a] |-> [a#, a] {- DP (Top 2) (Mirror (Input 5)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  ( b
  , Wk  / 0A -  0A 0A \
        | -  0A -  -  |
        | -  -  0A -  |
        \ -  -  -  0A / )
  ( a
  , Wk  / 0A -  0A 0A \
        | 3A 0A 3A 3A |
        | 0A -  0A 0A |
        \ -  -  -  0A / )
  ( c
  , Wk  / 0A - -  -  \
        | -  - 3A -  |
        | 0A - -  -  |
        \ -  - -  0A / )
  ( d
  , Wk  / - 1A 0A 0A \
        | - -  -  -  |
        | - 1A -  0A |
        \ - -  -  0A / )
  ( a#
  , Wk  / 0A - 1A 1A \
        | -  - -  -  |
        | -  - -  -  |
        \ -  - -  0A / )
  ( c#
  , Wk  / 1A 5A 0A 1A \
        | -  -  -  -  |
        | -  -  -  -  |
        \ -  -  -  0A / )
   property Termination
has value Just True
for SRS
  [a#, d] |-> [c#, d, d] {- DP (Top 0) (Mirror (Input 4)) -}
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  (a#, 1/1)
   property Termination
has value Just True
for SRS
  [b, a] ->= [a, c, b] {- DP Nontop (Mirror (Input 0)) -}
  [c, b] ->= [b, b, c] {- DP Nontop (Mirror (Input 1)) -}
  [c, a] ->= [b, a, c] {- DP Nontop (Mirror (Input 2)) -}
  [a, a] ->= [d, d, d, a] {- DP Nontop (Mirror (Input 3)) -}
  [a, d] ->= [c, d, d] {- DP Nontop (Mirror (Input 4)) -}
  [c, d, d, a] ->= [d, a, a, a] {- DP Nontop (Mirror (Input 5)) -}
  [d, b] ->= [d, d] {- DP Nontop (Mirror (Input 8)) -}
reason
  EDG

**************************************************
skeleton: (9,6)\Weight\Mirror(8,6)\Deepee(22/8,11)\Weight(14/8,10)\EDG[\Mirror(2/8,7)\Matrix{\Natural}{2}(2/7,5)\Mirror\EDG(2/7,5)\Matrix{\Arctic}{2}\EDG(1/7,5)\Matrix{\Natural}{2}(0/7,4)\EDG[],\Mirror(12/8,9)\Matrix{\Natural}{2}(12/7,7)\Mirror\EDG(12/7,7)\Matrix{\Arctic}{2}\EDG(10/7,7)\Matrix{\Arctic}{2}(7/7,7)\Weight\EDG(4/7,6)\Matrix{\Natural}{2}\EDG(3/7,6)\Matrix{\Arctic}{4}(1/7,6)\Weight(0/7,4)\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)])