**************************************************
Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES a -> ,
                      a a -> b b c ,
                      b -> ,
                      c b -> b a c)
    , deadline = Just
                     (Time
                          -2040245610)
    }
is false because of
admits a looping transport system
    notation: http://dfa.imn.htwk-leipzig.de/matchbox/methods/loop.pdf
pivot p = [ b , b ]
block alphabet Gamma = [ [ b ] , [ c ] ]
forall g in Gamma: g p ->^* p phi(g)  where
    phi = listToFM
              [ ( [ b ] , [ [ b ] ] ) , ( [ c ] , [ [ b ] , [ c ] , [ c ] ] ) ]
        phi ([ b ]) = [ [ b ] ]
            because of Derivation
                           { lhs = [ b ] , rhs = [ b ] , hash_value = -165547832
                           , strict = False , steps = [ ]
                           }
        phi ([ c ]) = [ [ b ] , [ c ] , [ c ] ]
            because of Derivation
                           { lhs = [ c , b , b ] , rhs = [ b , b , b , c , c ]
                           , hash_value = -847960582 , strict = True
                           , steps = [ Step
                                           { rule = 3 , position = 0 }
                                     , Step
                                           { rule = 3 , position = 2 }
                                     , Step
                                           { rule = 2 , position = 2 }
                                     , Step
                                           { rule = 1 , position = 1 }
                                     ]
                           }
start s = [ c ]
exponent k = 5
phi^k(s)  contains  s (.. p ..)^k
this implies  there is a loop starting at  s p^k
**************************************************
statistics:
total atomic proof attempts
    number = 8, total = 5
    maximal = [ Log
                    { what = rfc match bounds (classical)
                    , start = Time
                                  -2040251565
                    , end = Time
                                -2040251062
                    , duration = 5 , success = False
                    }
              ]
successful atomic proof attempts
    number = 1, total = 0
    maximal = [ Log
                    { what = simplex
                    , start = Time
                                  -2040251566
                    , end = Time
                                -2040251566
                    , duration = 0 , success = True
                    }
              ]
failed atomic proof attempts
    number = 7, total = 5
    maximal = [ Log
                    { what = rfc match bounds (classical)
                    , start = Time
                                  -2040251565
                    , end = Time
                                -2040251062
                    , duration = 5 , success = False
                    }
              ]
**************************************************
matchbox general information (including details on proof methods):
http://dfa.imn.htwk-leipzig.de/matchbox/

this matchbox implementation uses the SAT solver
MiniSat by Niklas Een and Niklas Sörensson
http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/

matchbox process information
arguments      : --solver=/tmp/tmp2xV4B8/matchbox-2007-06-01/minisat --timeout-command=/tmp/tmp2xV4B8/matchbox-2007-06-01/timeout --tmpdir=tmp --timeout=60 /tmp/tmp.yB4nB2T0yv/a.srs
started        : Thu Jan 26 12:52:01 CET 2012
finished       : Thu Jan 26 12:52:07 CET 2012
run system     : Linux uc01-11 2.6.32-5-amd64 #1 SMP Wed Jan 12 03:40:32 UTC 2011 x86_64
release date   : Fri Jun 1 17:36:44 CEST 2007
build date     : Fri Jun 1 17:36:44 CEST 2007
build system   : Linux dfa 2.6.8-2-k7 #1 Tue Aug 16 14:00:15 UTC 2005 i686 GNU/Linux

used clock time: 6 secs