Problem Transformed CSR 04 Ex15 Luc06 Z

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5,4}
   transitions:
    g1(64) -> 65*
    g1(56) -> 57*
    g1(58) -> 59*
    a1() -> 52*
    f1(50) -> 51*
    f1(42) -> 43*
    f1(12) -> 13*
    f1(44) -> 45*
    f1(14) -> 15*
    n__g1(34) -> 35*
    n__g1(36) -> 37*
    n__g1(28) -> 29*
    n__g1(13) -> 14*
    n__a1() -> 12*
    n__f1(22) -> 23*
    n__f1(24) -> 25*
    n__f1(16) -> 17*
    n__g2(96) -> 97*
    n__g2(88) -> 89*
    n__g2(90) -> 91*
    n__a2() -> 86*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    n__f2(70) -> 71*
    n__f2(84) -> 85*
    n__f2(76) -> 77*
    n__f2(78) -> 79*
    n__f2(68) -> 69*
    n__f0(2) -> 1*
    n__f0(1) -> 1*
    n__f0(3) -> 1*
    n__a0() -> 2*
    n__g0(2) -> 3*
    n__g0(1) -> 3*
    n__g0(3) -> 3*
    a0() -> 5*
    g0(2) -> 6*
    g0(1) -> 6*
    g0(3) -> 6*
    activate0(2) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,58,44,34,22
    2 -> 7,56,42,36,24
    3 -> 7,64,50,28,16
    12 -> 84,5
    14 -> 76*
    15 -> 45,7,4
    17 -> 4*
    23 -> 4*
    25 -> 4*
    29 -> 6*
    35 -> 6*
    37 -> 6*
    42 -> 68*
    43 -> 7*
    44 -> 70*
    45 -> 7*
    50 -> 78*
    51 -> 7*
    52 -> 7*
    56 -> 88*
    57 -> 7*
    58 -> 90*
    59 -> 7*
    64 -> 96*
    65 -> 7*
    69 -> 43*
    71 -> 45*
    77 -> 15*
    79 -> 51,7
    85 -> 13*
    86 -> 52,7
    89 -> 57*
    91 -> 59,7
    97 -> 65,7
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 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(n__f(n__a())) -> f(n__g(f(n__a())))
     , f(X) -> n__f(X)
     , a() -> n__a()
     , g(X) -> n__g(X)
     , activate(n__f(X)) -> f(X)
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(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(n__f(n__a())) -> f(n__g(f(n__a())))
          , f(X) -> n__f(X)
          , a() -> n__a()
          , g(X) -> n__g(X)
          , activate(n__f(X)) -> f(X)
          , activate(n__a()) -> a()
          , activate(n__g(X)) -> g(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
        , f_1(3) -> 1
        , f_1(5) -> 4
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , n__f_2(3) -> 1
        , n__f_2(5) -> 4
        , n__a_0() -> 1
        , n__a_0() -> 2
        , n__a_1() -> 1
        , n__a_1() -> 5
        , n__a_2() -> 1
        , n__g_0(2) -> 1
        , n__g_0(2) -> 2
        , n__g_1(2) -> 1
        , n__g_1(4) -> 3
        , n__g_2(2) -> 1
        , a_0() -> 1
        , a_1() -> 1
        , g_0(2) -> 1
        , g_1(2) -> 1
        , activate_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 Luc06 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex15 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(n__f(n__a())) -> f(n__g(f(n__a())))
     , f(X) -> n__f(X)
     , a() -> n__a()
     , g(X) -> n__g(X)
     , activate(n__f(X)) -> f(X)
     , activate(n__a()) -> a()
     , activate(n__g(X)) -> g(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(n__f(n__a())) -> f(n__g(f(n__a())))
          , f(X) -> n__f(X)
          , a() -> n__a()
          , g(X) -> n__g(X)
          , activate(n__f(X)) -> f(X)
          , activate(n__a()) -> a()
          , activate(n__g(X)) -> g(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
        , f_1(3) -> 1
        , f_1(5) -> 4
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , n__f_2(3) -> 1
        , n__f_2(5) -> 4
        , n__a_0() -> 1
        , n__a_0() -> 2
        , n__a_1() -> 1
        , n__a_1() -> 5
        , n__a_2() -> 1
        , n__g_0(2) -> 1
        , n__g_0(2) -> 2
        , n__g_1(2) -> 1
        , n__g_1(4) -> 3
        , n__g_2(2) -> 1
        , a_0() -> 1
        , a_1() -> 1
        , g_0(2) -> 1
        , g_1(2) -> 1
        , activate_0(2) -> 1}