Problem Transformed CSR 04 Ex25 Luc06 Z

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 Z

stdout:

YES(?,O(n^1))

Problem:
f(f(X)) -> c(n__f(g(n__f(X))))
c(X) -> d(activate(X))
h(X) -> c(n__d(X))
f(X) -> n__f(X)
d(X) -> n__d(X)
activate(n__f(X)) -> f(X)
activate(n__d(X)) -> d(X)
activate(X) -> X

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {8,7,6,5,4}
   transitions:
    d1(65) -> 66*
    d1(10) -> 11*
    d1(71) -> 72*
    d1(63) -> 64*
    f1(55) -> 56*
    f1(57) -> 58*
    f1(49) -> 50*
    n__d1(35) -> 36*
    n__d1(29) -> 30*
    n__d1(26) -> 27*
    n__f1(45) -> 46*
    n__f1(37) -> 38*
    n__f1(43) -> 44*
    c1(27) -> 28*
    activate1(17) -> 18*
    activate1(19) -> 20*
    activate1(9) -> 10*
    n__d2(97) -> 98*
    n__d2(99) -> 100*
    n__d2(91) -> 92*
    n__d2(105) -> 106*
    n__f2(89) -> 90*
    n__f2(81) -> 82*
    n__f2(83) -> 84*
    d2(77) -> 78*
    d2(119) -> 120*
    d2(111) -> 112*
    d2(113) -> 114*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    activate2(76) -> 77*
    c0(2) -> 5*
    c0(1) -> 5*
    c0(3) -> 5*
    n__d3(107) -> 108*
    n__d3(131) -> 132*
    n__d3(123) -> 124*
    n__d3(125) -> 126*
    n__f0(2) -> 1*
    n__f0(1) -> 1*
    n__f0(3) -> 1*
    g0(2) -> 2*
    g0(1) -> 2*
    g0(3) -> 2*
    d0(2) -> 7*
    d0(1) -> 7*
    d0(3) -> 7*
    activate0(2) -> 8*
    activate0(1) -> 8*
    activate0(3) -> 8*
    h0(2) -> 6*
    h0(1) -> 6*
    h0(3) -> 6*
    n__d0(2) -> 3*
    n__d0(1) -> 3*
    n__d0(3) -> 3*
    1 -> 8,65,55,43,29,17
    2 -> 8,63,49,45,35,19
    3 -> 8,71,57,37,26,9
    9 -> 10*
    10 -> 91*
    11 -> 5*
    17 -> 18,10
    18 -> 10*
    19 -> 20*
    20 -> 10*
    26 -> 119*
    27 -> 76,7
    28 -> 6*
    29 -> 113*
    30 -> 27*
    35 -> 111*
    36 -> 27*
    38 -> 4*
    44 -> 4*
    46 -> 4*
    49 -> 83*
    50 -> 18,10,8
    55 -> 89*
    56 -> 18,10,8
    57 -> 81*
    58 -> 18,10,8
    63 -> 99*
    64 -> 10,8
    65 -> 105*
    66 -> 10,8
    71 -> 97*
    72 -> 10,8
    76 -> 77*
    77 -> 107*
    78 -> 28,6
    82 -> 58*
    84 -> 50,8
    90 -> 56,8
    92 -> 11*
    98 -> 72*
    100 -> 64,8
    106 -> 66,8
    108 -> 78,28
    111 -> 123*
    112 -> 77*
    113 -> 125*
    114 -> 77*
    119 -> 131*
    120 -> 77*
    124 -> 112*
    126 -> 114,77,107
    132 -> 120,77,107
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 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(X)) -> c(n__f(g(n__f(X))))
     , c(X) -> d(activate(X))
     , h(X) -> c(n__d(X))
     , f(X) -> n__f(X)
     , d(X) -> n__d(X)
     , activate(n__f(X)) -> f(X)
     , activate(n__d(X)) -> d(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(X)) -> c(n__f(g(n__f(X))))
          , c(X) -> d(activate(X))
          , h(X) -> c(n__d(X))
          , f(X) -> n__f(X)
          , d(X) -> n__d(X)
          , activate(n__f(X)) -> f(X)
          , activate(n__d(X)) -> d(X)
          , 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(2) -> 1
        , f_1(2) -> 3
        , c_0(2) -> 1
        , c_1(4) -> 1
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 3
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , n__f_2(2) -> 3
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 3
        , d_0(2) -> 1
        , d_1(2) -> 1
        , d_1(2) -> 3
        , d_1(3) -> 1
        , d_2(2) -> 5
        , d_2(5) -> 1
        , activate_0(2) -> 1
        , activate_1(2) -> 3
        , activate_2(4) -> 5
        , h_0(2) -> 1
        , n__d_0(2) -> 1
        , n__d_0(2) -> 2
        , n__d_0(2) -> 3
        , n__d_1(2) -> 1
        , n__d_1(2) -> 4
        , n__d_1(2) -> 5
        , n__d_2(2) -> 1
        , n__d_2(2) -> 3
        , n__d_2(3) -> 1
        , n__d_3(2) -> 5
        , n__d_3(5) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 Luc06 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex25 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(X)) -> c(n__f(g(n__f(X))))
     , c(X) -> d(activate(X))
     , h(X) -> c(n__d(X))
     , f(X) -> n__f(X)
     , d(X) -> n__d(X)
     , activate(n__f(X)) -> f(X)
     , activate(n__d(X)) -> d(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(X)) -> c(n__f(g(n__f(X))))
          , c(X) -> d(activate(X))
          , h(X) -> c(n__d(X))
          , f(X) -> n__f(X)
          , d(X) -> n__d(X)
          , activate(n__f(X)) -> f(X)
          , activate(n__d(X)) -> d(X)
          , 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(2) -> 1
        , f_1(2) -> 3
        , c_0(2) -> 1
        , c_1(4) -> 1
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_0(2) -> 3
        , n__f_1(2) -> 1
        , n__f_2(2) -> 1
        , n__f_2(2) -> 3
        , g_0(2) -> 1
        , g_0(2) -> 2
        , g_0(2) -> 3
        , d_0(2) -> 1
        , d_1(2) -> 1
        , d_1(2) -> 3
        , d_1(3) -> 1
        , d_2(2) -> 5
        , d_2(5) -> 1
        , activate_0(2) -> 1
        , activate_1(2) -> 3
        , activate_2(4) -> 5
        , h_0(2) -> 1
        , n__d_0(2) -> 1
        , n__d_0(2) -> 2
        , n__d_0(2) -> 3
        , n__d_1(2) -> 1
        , n__d_1(2) -> 4
        , n__d_1(2) -> 5
        , n__d_2(2) -> 1
        , n__d_2(2) -> 3
        , n__d_2(3) -> 1
        , n__d_3(2) -> 5
        , n__d_3(5) -> 1}