**************************************************
Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES a -> ,
                      a a b -> c a ,
                      a c -> c b a a)
    , deadline = Just
                     (Time
                          -2040336310)
    }
is false because of
mirror image
  R' = { reverse(l) -> reverse(r) | (l -> r) in R }
    (VAR x1)
    (RULES a -> ,
           b a a -> a c ,
           c a -> a a b c)
      admits a looping transport system
          notation: http://dfa.imn.htwk-leipzig.de/matchbox/methods/loop.pdf
      pivot p = [ a , a ]
      block alphabet Gamma = [ [ a , a ] , [ a , c ] , [ b , c ] , [ c ]
                             , [ c , b ]
                             ]
      forall g in Gamma: g p ->^* p phi(g)  where
          phi = listToFM
                    [ ( [ a , a ] , [ ] )
                    , ( [ a , c ] , [ [ a , a ] , [ c , b ] , [ c ] ] )
                    , ( [ b , c ] , [ [ b , c ] , [ c , b ] , [ c ] ] )
                    , ( [ c ] , [ [ a , c ] , [ b , c ] ] )
                    , ( [ c , b ] , [ [ b , c ] , [ c ] ] )
                    ]
              phi ([ a , a ]) = [ ]
                  because of Derivation
                                 { lhs = [ a , a , a , a ] , rhs = [ a , a ]
                                 , hash_value = -213036735 , strict = True
                                 , steps = [ Step
                                                 { rule = 0 , position = 0 }
                                           , Step
                                                 { rule = 0 , position = 0 }
                                           ]
                                 }
              phi ([ a , c ]) = [ [ a , a ] , [ c , b ] , [ c ] ]
                  because of Derivation
                                 { lhs = [ a , c , a , a ] , rhs = [ a , a , a , a , c , b , c ]
                                 , hash_value = -1769603782 , strict = True
                                 , steps = [ Step
                                                 { rule = 2 , position = 1 }
                                           , Step
                                                 { rule = 2 , position = 4 }
                                           , Step
                                                 { rule = 1 , position = 3 }
                                           ]
                                 }
              phi ([ b , c ]) = [ [ b , c ] , [ c , b ] , [ c ] ]
                  because of Derivation
                                 { lhs = [ b , c , a , a ] , rhs = [ a , a , b , c , c , b , c ]
                                 , hash_value = -26344444 , strict = True
                                 , steps = [ Step
                                                 { rule = 2 , position = 1 }
                                           , Step
                                                 { rule = 2 , position = 4 }
                                           , Step
                                                 { rule = 1 , position = 0 }
                                           , Step
                                                 { rule = 0 , position = 0 }
                                           , Step
                                                 { rule = 1 , position = 1 }
                                           , Step
                                                 { rule = 2 , position = 0 }
                                           ]
                                 }
              phi ([ c ]) = [ [ a , c ] , [ b , c ] ]
                  because of Derivation
                                 { lhs = [ c , a , a ] , rhs = [ a , a , a , c , b , c ]
                                 , hash_value = 1058579968 , strict = True
                                 , steps = [ Step
                                                 { rule = 2 , position = 0 }
                                           , Step
                                                 { rule = 2 , position = 3 }
                                           , Step
                                                 { rule = 1 , position = 2 }
                                           ]
                                 }
              phi ([ c , b ]) = [ [ b , c ] , [ c ] ]
                  because of Derivation
                                 { lhs = [ c , b , a , a ] , rhs = [ a , a , b , c , c ]
                                 , hash_value = 1142084671 , strict = True
                                 , steps = [ Step
                                                 { rule = 1 , position = 1 }
                                           , Step
                                                 { rule = 2 , position = 0 }
                                           ]
                                 }
      start s = [ a , c ]
      exponent k = 6
      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
                                  -2040342262
                    , end = Time
                                -2040341758
                    , duration = 5 , success = False
                    }
              ]
successful atomic proof attempts
    number = 1, total = 0
    maximal = [ Log
                    { what = simplex
                    , start = Time
                                  -2040342262
                    , end = Time
                                -2040342262
                    , duration = 0 , success = True
                    }
              ]
failed atomic proof attempts
    number = 7, total = 5
    maximal = [ Log
                    { what = rfc match bounds (classical)
                    , start = Time
                                  -2040342262
                    , end = Time
                                -2040341758
                    , 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/tmpHtlhcd/matchbox-2007-06-01/minisat --timeout-command=/tmp/tmpHtlhcd/matchbox-2007-06-01/timeout --tmpdir=tmp --timeout=60 /tmp/tmp.jIvpTUCYgm/a.srs
started        : Thu Jan 26 12:37:08 CET 2012
finished       : Thu Jan 26 12:37:14 CET 2012
run system     : Linux uc01-02 2.6.32-5-amd64 #1 SMP Tue Jun 14 09:42:28 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