Problem Transformed CSR 04 Ex18 Luc06 FR

Tool CaT

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

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    a1() -> 35*
    f1(25) -> 26*
    activate1(27) -> 28*
    activate1(24) -> 25*
    activate1(33) -> 34*
    n__a1() -> 19*
    n__f1(17) -> 18*
    n__f1(9) -> 10*
    n__f1(11) -> 12*
    n__a2() -> 41*
    n__f2(37) -> 38*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    f2(47) -> 48*
    a0() -> 5*
    g2(46) -> 47*
    g0(2) -> 1*
    g0(1) -> 1*
    g0(3) -> 1*
    n__f3(51) -> 52*
    n__f0(2) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    n__a0() -> 3*
    activate0(2) -> 6*
    activate0(1) -> 6*
    activate0(3) -> 6*
    1 -> 6,27,11
    2 -> 6,24,17
    3 -> 6,33,9
    10 -> 4*
    12 -> 4*
    18 -> 4*
    19 -> 5*
    24 -> 25*
    25 -> 37*
    26 -> 25,6
    27 -> 28,25
    28 -> 25*
    33 -> 34*
    34 -> 25*
    35 -> 34,25,6
    38 -> 46,26,6
    41 -> 35,6
    47 -> 51*
    48 -> 26,25,6,37
    52 -> 48,26
  problem:

  Qed

Tool IRC1

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

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 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(f(a())) -> f(g(n__f(n__a())))
     , f(X) -> n__f(X)
     , a() -> n__a()
     , activate(n__f(X)) -> f(activate(X))
     , activate(n__a()) -> a()
     , 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(n__a())))
          , f(X) -> n__f(X)
          , a() -> n__a()
          , activate(n__f(X)) -> f(activate(X))
          , activate(n__a()) -> a()
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(3) -> 1
        , f_1(3) -> 3
        , f_2(4) -> 1
        , f_2(4) -> 3
        , a_0() -> 1
        , a_1() -> 1
        , a_1() -> 3
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 3
        , g_2(1) -> 4
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 3
        , n__f_1(2) -> 1
        , n__f_2(3) -> 1
        , n__f_2(3) -> 3
        , n__f_3(4) -> 1
        , n__f_3(4) -> 3
        , n__a_0() -> 1
        , n__a_0() -> 2
        , n__a_0() -> 3
        , n__a_1() -> 1
        , n__a_2() -> 1
        , n__a_2() -> 3
        , activate_0(2) -> 1
        , activate_1(2) -> 3}

Tool RC1

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

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 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(f(a())) -> f(g(n__f(n__a())))
     , f(X) -> n__f(X)
     , a() -> n__a()
     , activate(n__f(X)) -> f(activate(X))
     , activate(n__a()) -> a()
     , 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(n__a())))
          , f(X) -> n__f(X)
          , a() -> n__a()
          , activate(n__f(X)) -> f(activate(X))
          , activate(n__a()) -> a()
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(3) -> 1
        , f_1(3) -> 3
        , f_2(4) -> 1
        , f_2(4) -> 3
        , a_0() -> 1
        , a_1() -> 1
        , a_1() -> 3
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 3
        , g_2(1) -> 4
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 3
        , n__f_1(2) -> 1
        , n__f_2(3) -> 1
        , n__f_2(3) -> 3
        , n__f_3(4) -> 1
        , n__f_3(4) -> 3
        , n__a_0() -> 1
        , n__a_0() -> 2
        , n__a_0() -> 3
        , n__a_1() -> 1
        , n__a_2() -> 1
        , n__a_2() -> 3
        , activate_0(2) -> 1
        , activate_1(2) -> 3}