**************************************************
Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4)
    , deadline = Just
                     (Time
                          -2040393102)
    }
is false because of
mirror image
  R' = { reverse(l) -> reverse(r) | (l -> r) in R }
    (VAR x1)
    (RULES 0 q0 0 -> q0 0 0 ,
           h q0 0 -> h q0 0 0 ,
           0 q1 1 -> q1 0 1 ,
           h q1 1 -> h q1 0 1 ,
           1 q1 1 -> q1 1 1 ,
           0 q1 0 -> q2 0 0 ,
           h q1 0 -> h q2 0 0 ,
           1 q1 0 -> q2 1 0 ,
           0 q2 1 -> q2 0 1 ,
           h q2 1 -> h q2 0 1 ,
           1 q2 1 -> q2 1 1 ,
           q2 0 -> 1 q3 ,
           q3 1 -> 1 q3 ,
           q3 0 -> 0 q4 ,
           q4 1 -> 1 q4 ,
           0 q4 0 -> q5 0 1 ,
           1 q4 0 -> q5 1 1 ,
           0 q5 1 -> q1 0 0 ,
           h q5 1 -> h q1 0 0 ,
           1 q5 1 -> q1 1 0 ,
           q3 h -> q3 0 h ,
           q4 h -> q4 0 h)
      looping forward closure
      of length 1
      Derivation
          { lhs = [ h , q0 , 0 ] , rhs = [ h , q0 , 0 , 0 ]
          , hash_value = -1037175702 , strict = True
          , steps = [ Step
                          { rule = 1 , position = 0 }
                    ]
          }
      this is closure number 14
MAYBE
**************************************************
summary
 
satisfy: no strategy annotation
  satisfy: no theory annotation
    satisfy: no relative rules
      linear weights (from simplex method)
        direct (half-strict semi-ring) matrix method
        domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
          direct (half-strict semi-ring) matrix method
          domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
            direct (half-strict semi-ring) matrix method
            domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
              direct (half-strict semi-ring) matrix method
              domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                direct (half-strict semi-ring) matrix method
                domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                  direct (half-strict semi-ring) matrix method
                  domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    open: Standard termination
**************************************************
detail
 
Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q0 0 -> 0 0 q1 ,
                      1 q0 h -> 0 0 q1 h ,
                      1 q0 1 -> 0 1 q1 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 h -> 1 0 q5 h ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040389993)
    }

follows by
    satisfy: no strategy annotation
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q0 0 -> 0 0 q1 ,
                      1 q0 h -> 0 0 q1 h ,
                      1 q0 1 -> 0 1 q1 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 h -> 1 0 q5 h ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040389993)
    }

follows by
    satisfy: no theory annotation
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q0 0 -> 0 0 q1 ,
                      1 q0 h -> 0 0 q1 h ,
                      1 q0 1 -> 0 1 q1 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 h -> 1 0 q5 h ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040389993)
    }

follows by
    satisfy: no relative rules
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q0 0 -> 0 0 q1 ,
                      1 q0 h -> 0 0 q1 h ,
                      1 q0 1 -> 0 1 q1 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 h -> 1 0 q5 h ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040389993)
    }

follows by
    linear interpretation (weights, rational numbers):
        listToFM
            [ ( 0 , 0 / 1 ) , ( 1 , 0 / 1 ) , ( h , 0 / 1 ) , ( q0 , 1 / 1 ) , ( q1 , 0 / 1 )
            , ( q2 , 0 / 1 ) , ( q3 , 0 / 1 ) , ( q4 , 0 / 1 ) , ( q5 , 0 / 1 )
            ]
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 h -> 1 0 q5 h ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040394987)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 1 ] , [ -inf , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 2 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ 0 , 0 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ 0 , 0 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        ]
        }
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q2 -> h 0 q2 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040394553)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 4 ] , [ -inf , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 4 , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ 6 , 4 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 4 ] , [ -inf , 0 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 5 ] , [ -inf , 0 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 4 ] , [ -inf , 0 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 4 ] , [ -inf , 0 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 4 ] , [ -inf , 0 ] ]
                          )
                        ]
        }
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q0 -> h 0 q0 ,
                      h q1 -> h 0 q1 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040394178)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ 5 , 1 ] , [ 1 , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 3 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ 1 , 0 ] , [ -inf , 4 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ 3 , -inf ] , [ -inf , 4 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 4 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 4 , 4 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 4 ] ]
                          )
                        ]
        }
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q1 -> h 0 q1 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040393807)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ 2 , 0 ] , [ 2 , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ 4 , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        ]
        }
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4 ,
                      h q5 -> h 0 q5)
    , deadline = Just
                     (Time
                          -2040393447)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ 4 , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ 4 , 0 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 4 ] , [ -inf , 0 ] ]
                          )
                        ]
        }
from

Claim
    { termination = Standard
    , system = (VAR x1)
               (RULES 0 q0 0 -> 0 0 q0 ,
                      0 q0 h -> 0 0 q0 h ,
                      0 q0 1 -> 0 1 q0 ,
                      1 q1 0 -> 1 0 q1 ,
                      1 q1 h -> 1 0 q1 h ,
                      1 q1 1 -> 1 1 q1 ,
                      0 q1 0 -> 0 0 q2 ,
                      0 q1 h -> 0 0 q2 h ,
                      0 q1 1 -> 0 1 q2 ,
                      1 q2 0 -> 1 0 q2 ,
                      1 q2 h -> 1 0 q2 h ,
                      1 q2 1 -> 1 1 q2 ,
                      0 q2 -> q3 1 ,
                      1 q3 -> q3 1 ,
                      0 q3 -> q4 0 ,
                      1 q4 -> q4 1 ,
                      0 q4 0 -> 1 0 q5 ,
                      0 q4 1 -> 1 1 q5 ,
                      1 q5 0 -> 0 0 q1 ,
                      1 q5 h -> 0 0 q1 h ,
                      1 q5 1 -> 0 1 q1 ,
                      h q3 -> h 0 q3 ,
                      h q4 -> h 0 q4)
    , deadline = Just
                     (Time
                          -2040393102)
    }

follows by
    Matrix_Interpretation
        { dimension = 2 , domain = "Matrix.MaxPlus.MaxPlus"
        , method = Method
                       { select = mkSet [ 1 , 2 ] , letter_form = DR
                       , difference_form = Positive_Or_Both_Zero
                       }
        , mapping = listToFM
                        [ ( 0
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ 0 , 0 ] ]
                          )
                        , ( 1
                          , Matrix ( 2 , 2 )
                                [ [ -inf , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( h
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q0
                          , Matrix ( 2 , 2 )
                                [ [ 2 , 0 ] , [ -inf , 0 ] ]
                          )
                        , ( q1
                          , Matrix ( 2 , 2 )
                                [ [ 0 , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( q2
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ -inf , 0 ] ]
                          )
                        , ( q3
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q4
                          , Matrix ( 2 , 2 )
                                [ [ -inf , -inf ] , [ 0 , 0 ] ]
                          )
                        , ( q5
                          , Matrix ( 2 , 2 )
                                [ [ 0 , 0 ] , [ -inf , 0 ] ]
                          )
                        ]
        }
from

Open
    (Claim
         { termination = Standard
         , system = (VAR x1)
                    (RULES 0 q0 0 -> 0 0 q0 ,
                           0 q0 h -> 0 0 q0 h ,
                           1 q1 0 -> 1 0 q1 ,
                           1 q1 h -> 1 0 q1 h ,
                           1 q1 1 -> 1 1 q1 ,
                           0 q1 0 -> 0 0 q2 ,
                           0 q1 h -> 0 0 q2 h ,
                           0 q1 1 -> 0 1 q2 ,
                           1 q2 0 -> 1 0 q2 ,
                           1 q2 h -> 1 0 q2 h ,
                           1 q2 1 -> 1 1 q2 ,
                           0 q2 -> q3 1 ,
                           1 q3 -> q3 1 ,
                           0 q3 -> q4 0 ,
                           1 q4 -> q4 1 ,
                           0 q4 0 -> 1 0 q5 ,
                           0 q4 1 -> 1 1 q5 ,
                           1 q5 0 -> 0 0 q1 ,
                           1 q5 h -> 0 0 q1 h ,
                           1 q5 1 -> 0 1 q1 ,
                           h q3 -> h 0 q3 ,
                           h q4 -> h 0 q4)
         , deadline = Just
                          (Time
                               -2040393102)
         })
**************************************************
MAYBE
**************************************************
summary
 
satisfy: no strategy annotation
  satisfy: no theory annotation
    satisfy: no relative rules
      linear weights (from simplex method)
        direct (half-strict semi-ring) matrix method
        domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
          direct (half-strict semi-ring) matrix method
          domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
            direct (half-strict semi-ring) matrix method
            domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
              direct (half-strict semi-ring) matrix method
              domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                direct (half-strict semi-ring) matrix method
                domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                  direct (half-strict semi-ring) matrix method
                  domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    open: Standard termination
**************************************************
**************************************************
statistics:
total atomic proof attempts
    number = 33, total = 49
    maximal = [ Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040393505
                    , end = Time
                                -2040392547
                    , duration = 9 , success = False
                    }
              ]
successful atomic proof attempts
    number = 14, total = 21
    maximal = [ Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040394101
                    , end = Time
                                -2040393509
                    , duration = 5 , success = True
                    }
              , Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040395987
                    , end = Time
                                -2040395554
                    , duration = 4 , success = True
                    }
              , Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040394447
                    , end = Time
                                -2040394102
                    , duration = 3 , success = True
                    }
              , Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040395178
                    , end = Time
                                -2040394812
                    , duration = 3 , success = True
                    }
              , Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040394807
                    , end = Time
                                -2040394452
                    , duration = 3 , success = True
                    }
              , Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040395553
                    , end = Time
                                -2040395180
                    , duration = 3 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392502
                    , end = Time
                                -2040392494
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392539
                    , end = Time
                                -2040392530
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392532
                    , end = Time
                                -2040392516
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392541
                    , end = Time
                                -2040392540
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392514
                    , end = Time
                                -2040392503
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392544
                    , end = Time
                                -2040392534
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040395991
                    , end = Time
                                -2040395991
                    , duration = 0 , success = True
                    }
              , Log
                    { what = simplex
                    , start = Time
                                  -2040392529
                    , end = Time
                                -2040392519
                    , duration = 0 , success = True
                    }
              ]
failed atomic proof attempts
    number = 19, total = 28
    maximal = [ Log
                    { what = direct (half-strict semi-ring) matrix method
                             domain: Matrix.MaxPlus.MaxPlus, dimension: 2, unknowns <= 7, intermediates <= 15
                    , start = Time
                                  -2040393505
                    , end = Time
                                -2040392547
                    , duration = 9 , 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/tmpongfjx/matchbox-2007-06-01/minisat --timeout-command=/tmp/tmpongfjx/matchbox-2007-06-01/timeout --tmpdir=tmp --timeout=60 /tmp/tmp.Vg3YzfYs9B/a.srs
started        : Thu Jan 26 12:27:57 CET 2012
finished       : Thu Jan 26 12:28:37 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: 40 secs