/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES




The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

r is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
s is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
u is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
t is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 13-rule system
{ r r -> s r ,
  r s -> s r ,
  r b -> u s b ,
  r u -> u r ,
  s u -> u s ,
  n u -> u n ,
  t r u -> t c r ,
  t s u -> t c r ,
  c u -> u c ,
  c s -> s c ,
  c r -> r c ,
  c n -> n c ,
  c n -> n }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

r is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
s is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
u is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
t is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ r s -> s r ,
  r b -> u s b ,
  r u -> u r ,
  s u -> u s ,
  n u -> u n ,
  t s u -> t c r ,
  c u -> u c ,
  c s -> s c ,
  c r -> r c ,
  c n -> n c ,
  c n -> n }


The system was reversed.

Remains to prove termination of the 11-rule system
{ s r -> r s ,
  b r -> b s u ,
  u r -> r u ,
  u s -> s u ,
  u n -> n u ,
  u s t -> r c t ,
  u c -> c u ,
  s c -> c s ,
  r c -> c r ,
  n c -> c n ,
  n c -> n }


The dependency pairs transformation was applied.

Remains to prove termination of the 27-rule system
{ (s,true) (r,false) -> (r,true) (s,false) ,
  (s,true) (r,false) -> (s,true) ,
  (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (b,true) (r,false) -> (s,true) (u,false) ,
  (b,true) (r,false) -> (u,true) ,
  (u,true) (r,false) -> (r,true) (u,false) ,
  (u,true) (r,false) -> (u,true) ,
  (u,true) (s,false) -> (s,true) (u,false) ,
  (u,true) (s,false) -> (u,true) ,
  (u,true) (n,false) -> (n,true) (u,false) ,
  (u,true) (n,false) -> (u,true) ,
  (u,true) (s,false) (t,false) -> (r,true) (c,false) (t,false) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }




The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 25-rule system
{ (s,true) (r,false) -> (r,true) (s,false) ,
  (s,true) (r,false) -> (s,true) ,
  (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (u,true) (r,false) -> (r,true) (u,false) ,
  (u,true) (r,false) -> (u,true) ,
  (u,true) (s,false) -> (s,true) (u,false) ,
  (u,true) (s,false) -> (u,true) ,
  (u,true) (n,false) -> (n,true) (u,false) ,
  (u,true) (n,false) -> (u,true) ,
  (u,true) (s,false) (t,false) -> (r,true) (c,false) (t,false) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 21-rule system
{ (s,true) (r,false) -> (r,true) (s,false) ,
  (s,true) (r,false) -> (s,true) ,
  (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (u,true) (r,false) -> (u,true) ,
  (u,true) (s,false) -> (u,true) ,
  (u,true) (n,false) -> (u,true) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 20-rule system
{ (s,true) (r,false) -> (s,true) ,
  (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (u,true) (r,false) -> (u,true) ,
  (u,true) (s,false) -> (u,true) ,
  (u,true) (n,false) -> (u,true) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 19-rule system
{ (s,true) (r,false) -> (s,true) ,
  (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (u,true) (r,false) -> (u,true) ,
  (u,true) (s,false) -> (u,true) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 16-rule system
{ (b,true) (r,false) -> (b,true) (s,false) (u,false) ,
  (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

(s,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(r,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
(r,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(s,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
(b,true) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(u,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
(u,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(n,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(n,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(t,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
(c,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 15-rule system
{ (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (b,false) (r,false) ->= (b,false) (s,false) (u,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

(s,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(r,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
(r,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(s,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
(b,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(u,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
(u,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(n,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(n,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(t,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
(c,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 14-rule system
{ (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (s,false) (t,false) ->= (r,false) (c,false) (t,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 13-rule system
{ (u,true) (c,false) -> (u,true) ,
  (s,true) (c,false) -> (s,true) ,
  (r,true) (c,false) -> (r,true) ,
  (n,true) (c,false) -> (n,true) ,
  (s,false) (r,false) ->= (r,false) (s,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) ,
  (n,false) (c,false) ->= (n,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(s,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(u,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(n,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ (s,false) (r,false) ->= (r,false) (s,false) ,
  (u,false) (r,false) ->= (r,false) (u,false) ,
  (u,false) (s,false) ->= (s,false) (u,false) ,
  (u,false) (n,false) ->= (n,false) (u,false) ,
  (u,false) (c,false) ->= (c,false) (u,false) ,
  (s,false) (c,false) ->= (c,false) (s,false) ,
  (r,false) (c,false) ->= (c,false) (r,false) ,
  (n,false) (c,false) ->= (c,false) (n,false) }


The system is trivially terminating.