Problem Transformed CSR 04 Ex23 Luc06 FR

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {8,7,6,5}
   transitions:
    a1() -> 65*
    g1(63) -> 64*
    activate1(55) -> 56*
    activate1(57) -> 58*
    activate1(49) -> 50*
    activate1(46) -> 47*
    f1(47) -> 48*
    n__a1() -> 41*
    n__g1(25) -> 26*
    n__g1(39) -> 40*
    n__g1(31) -> 32*
    n__g1(33) -> 34*
    n__f1(15) -> 16*
    n__f1(17) -> 18*
    n__f1(9) -> 10*
    n__f1(23) -> 24*
    n__a2() -> 76*
    n__g2(73) -> 74*
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    n__f2(69) -> 70*
    a0() -> 7*
    c2(79) -> 80*
    c0(2) -> 1*
    c0(4) -> 1*
    c0(1) -> 1*
    c0(3) -> 1*
    n__f0(2) -> 2*
    n__f0(4) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    n__g0(2) -> 3*
    n__g0(4) -> 3*
    n__g0(1) -> 3*
    n__g0(3) -> 3*
    n__a0() -> 4*
    g0(2) -> 6*
    g0(4) -> 6*
    g0(1) -> 6*
    g0(3) -> 6*
    activate0(2) -> 8*
    activate0(4) -> 8*
    activate0(1) -> 8*
    activate0(3) -> 8*
    1 -> 8,55,31,15
    2 -> 8,46,39,23
    3 -> 8,57,25,9
    4 -> 8,49,33,17
    10 -> 5*
    16 -> 5*
    18 -> 5*
    24 -> 5*
    26 -> 6*
    32 -> 6*
    34 -> 6*
    40 -> 6*
    41 -> 7*
    46 -> 47*
    47 -> 69,63
    48 -> 47,63,8
    49 -> 50,47
    50 -> 47*
    55 -> 56,47
    56 -> 47*
    57 -> 58*
    58 -> 47*
    63 -> 73*
    64 -> 58,47,63,8
    65 -> 50,47,63,8
    70 -> 79,48,8
    74 -> 64,8
    76 -> 65,8
    80 -> 48,8,47,73
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 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())) -> c(n__f(n__g(n__f(n__a()))))
     , f(X) -> n__f(X)
     , g(X) -> n__g(X)
     , a() -> n__a()
     , activate(n__f(X)) -> f(activate(X))
     , activate(n__g(X)) -> g(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())) -> c(n__f(n__g(n__f(n__a()))))
          , f(X) -> n__f(X)
          , g(X) -> n__g(X)
          , a() -> n__a()
          , activate(n__f(X)) -> f(activate(X))
          , activate(n__g(X)) -> g(activate(X))
          , activate(n__a()) -> a()
          , 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(3) -> 1
        , f_1(3) -> 3
        , a_0() -> 1
        , a_1() -> 1
        , a_1() -> 3
        , c_0(2) -> 1
        , c_0(2) -> 2
        , c_0(2) -> 3
        , c_2(4) -> 1
        , c_2(4) -> 3
        , 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_2(5) -> 4
        , n__g_0(2) -> 1
        , n__g_0(2) -> 2
        , n__g_0(2) -> 3
        , n__g_1(2) -> 1
        , n__g_2(1) -> 5
        , n__g_2(3) -> 1
        , n__g_2(3) -> 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
        , g_0(2) -> 1
        , g_1(3) -> 1
        , g_1(3) -> 3
        , activate_0(2) -> 1
        , activate_1(2) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 FR

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 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())) -> c(n__f(n__g(n__f(n__a()))))
     , f(X) -> n__f(X)
     , g(X) -> n__g(X)
     , a() -> n__a()
     , activate(n__f(X)) -> f(activate(X))
     , activate(n__g(X)) -> g(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())) -> c(n__f(n__g(n__f(n__a()))))
          , f(X) -> n__f(X)
          , g(X) -> n__g(X)
          , a() -> n__a()
          , activate(n__f(X)) -> f(activate(X))
          , activate(n__g(X)) -> g(activate(X))
          , activate(n__a()) -> a()
          , 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(3) -> 1
        , f_1(3) -> 3
        , a_0() -> 1
        , a_1() -> 1
        , a_1() -> 3
        , c_0(2) -> 1
        , c_0(2) -> 2
        , c_0(2) -> 3
        , c_2(4) -> 1
        , c_2(4) -> 3
        , 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_2(5) -> 4
        , n__g_0(2) -> 1
        , n__g_0(2) -> 2
        , n__g_0(2) -> 3
        , n__g_1(2) -> 1
        , n__g_2(1) -> 5
        , n__g_2(3) -> 1
        , n__g_2(3) -> 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
        , g_0(2) -> 1
        , g_1(3) -> 1
        , g_1(3) -> 3
        , activate_0(2) -> 1
        , activate_1(2) -> 3}