Problem Transformed CSR 04 Ex18 Luc06 Z

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 Z

stdout:

YES(?,O(n^1))

Problem:
f(f(a())) -> f(g(n__f(a())))
f(X) -> n__f(X)
activate(n__f(X)) -> f(X)
activate(X) -> X

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f1(24) -> 25*
    f1(26) -> 27*
    f1(18) -> 19*
    n__f1(10) -> 11*
    n__f1(16) -> 17*
    n__f1(8) -> 9*
    n__f2(30) -> 31*
    n__f2(36) -> 37*
    n__f2(38) -> 39*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    a0() -> 1*
    g0(2) -> 2*
    g0(1) -> 2*
    g0(3) -> 2*
    n__f0(2) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    activate0(2) -> 5*
    activate0(1) -> 5*
    activate0(3) -> 5*
    1 -> 5,24,10
    2 -> 5,18,16
    3 -> 5,26,8
    9 -> 4*
    11 -> 4*
    17 -> 4*
    18 -> 36*
    19 -> 5*
    24 -> 38*
    25 -> 5*
    26 -> 30*
    27 -> 5*
    31 -> 27*
    37 -> 19,5
    39 -> 25,5
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 Z

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(f(a())) -> f(g(n__f(a())))
     , f(X) -> n__f(X)
     , activate(n__f(X)) -> f(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(f(a())) -> f(g(n__f(a())))
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(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(2) -> 1
        , a_0() -> 1
        , a_0() -> 2
        , g_0(2) -> 1
        , g_0(2) -> 2
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , activate_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 Z

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(f(a())) -> f(g(n__f(a())))
     , f(X) -> n__f(X)
     , activate(n__f(X)) -> f(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(f(a())) -> f(g(n__f(a())))
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(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(2) -> 1
        , a_0() -> 1
        , a_0() -> 2
        , g_0(2) -> 1
        , g_0(2) -> 2
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , activate_0(2) -> 1}