Problem Transformed CSR 04 ExConc Zan97 FR

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

stdout:

YES(?,O(n^1))

Problem:
f(X) -> g(n__h(n__f(X)))
h(X) -> n__h(X)
f(X) -> n__f(X)
activate(n__h(X)) -> h(activate(X))
activate(n__f(X)) -> f(activate(X))
activate(X) -> X

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    f1(51) -> 52*
    activate1(45) -> 46*
    activate1(35) -> 36*
    activate1(43) -> 44*
    h1(36) -> 37*
    n__f1(15) -> 16*
    n__f1(21) -> 22*
    n__f1(11) -> 12*
    n__h1(12) -> 13*
    n__h1(29) -> 30*
    n__h1(31) -> 32*
    n__h1(23) -> 24*
    g1(13) -> 14*
    n__f2(57) -> 58*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    n__h2(63) -> 64*
    n__h2(58) -> 59*
    g0(2) -> 1*
    g0(1) -> 1*
    g0(3) -> 1*
    g2(59) -> 60*
    n__h0(2) -> 2*
    n__h0(1) -> 2*
    n__h0(3) -> 2*
    n__f0(2) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    h0(2) -> 5*
    h0(1) -> 5*
    h0(3) -> 5*
    activate0(2) -> 6*
    activate0(1) -> 6*
    activate0(3) -> 6*
    1 -> 6,43,29,15
    2 -> 6,35,31,21
    3 -> 6,45,23,11
    12 -> 4*
    14 -> 4*
    16 -> 12*
    22 -> 12*
    24 -> 5*
    30 -> 5*
    32 -> 5*
    35 -> 36*
    36 -> 63,51
    37 -> 36,51,6
    43 -> 44*
    44 -> 36*
    45 -> 46,36
    46 -> 36*
    51 -> 57*
    52 -> 46,36,51,6
    58 -> 52,6
    60 -> 52,6
    64 -> 37,6
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> X}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  f(X) -> g(n__h(n__f(X)))
          , h(X) -> n__h(X)
          , f(X) -> n__f(X)
          , activate(n__h(X)) -> h(activate(X))
          , activate(n__f(X)) -> f(activate(X))
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 1
        , f_1(5) -> 5
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 5
        , g_1(3) -> 1
        , g_2(6) -> 1
        , g_2(6) -> 5
        , n__h_0(2) -> 1
        , n__h_0(2) -> 2
        , n__h_0(2) -> 5
        , n__h_1(2) -> 1
        , n__h_1(4) -> 3
        , n__h_2(5) -> 1
        , n__h_2(5) -> 5
        , n__h_2(7) -> 6
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 5
        , n__f_1(2) -> 1
        , n__f_1(2) -> 4
        , n__f_2(5) -> 1
        , n__f_2(5) -> 5
        , n__f_2(5) -> 7
        , h_0(2) -> 1
        , h_1(5) -> 1
        , h_1(5) -> 5
        , activate_0(2) -> 1
        , activate_1(2) -> 5}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> X}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  f(X) -> g(n__h(n__f(X)))
          , h(X) -> n__h(X)
          , f(X) -> n__f(X)
          , activate(n__h(X)) -> h(activate(X))
          , activate(n__f(X)) -> f(activate(X))
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 1
        , f_1(5) -> 5
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 5
        , g_1(3) -> 1
        , g_2(6) -> 1
        , g_2(6) -> 5
        , n__h_0(2) -> 1
        , n__h_0(2) -> 2
        , n__h_0(2) -> 5
        , n__h_1(2) -> 1
        , n__h_1(4) -> 3
        , n__h_2(5) -> 1
        , n__h_2(5) -> 5
        , n__h_2(7) -> 6
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 5
        , n__f_1(2) -> 1
        , n__f_1(2) -> 4
        , n__f_2(5) -> 1
        , n__f_2(5) -> 5
        , n__f_2(5) -> 7
        , h_0(2) -> 1
        , h_1(5) -> 1
        , h_1(5) -> 5
        , activate_0(2) -> 1
        , activate_1(2) -> 5}