Problem Rubio 04 p266

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Rubio 04 p266

stdout:

YES(?,O(n^1))

Problem:
f(f(X)) -> f(a(b(f(X))))
f(a(g(X))) -> b(X)
b(X) -> a(X)

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    a1(19) -> 20*
    a1(13) -> 14*
    b1(5) -> 6*
    b1(11) -> 12*
    a2(27) -> 28*
    a2(21) -> 22*
    f0(2) -> 3*
    f0(1) -> 3*
    a0(2) -> 1*
    a0(1) -> 1*
    b0(2) -> 4*
    b0(1) -> 4*
    g0(2) -> 2*
    g0(1) -> 2*
    1 -> 13,11
    2 -> 19,5
    5 -> 27*
    6 -> 3*
    11 -> 21*
    12 -> 3*
    14 -> 4*
    20 -> 4*
    22 -> 12*
    28 -> 6,3
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Rubio 04 p266

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Rubio 04 p266

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)) -> f(a(b(f(X))))
     , f(a(g(X))) -> b(X)
     , b(X) -> a(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)) -> f(a(b(f(X))))
          , f(a(g(X))) -> b(X)
          , b(X) -> a(X)}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , a_0(2) -> 2
        , a_1(2) -> 1
        , a_2(2) -> 1
        , b_0(2) -> 1
        , b_1(2) -> 1
        , g_0(2) -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Rubio 04 p266

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Rubio 04 p266

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)) -> f(a(b(f(X))))
     , f(a(g(X))) -> b(X)
     , b(X) -> a(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)) -> f(a(b(f(X))))
          , f(a(g(X))) -> b(X)
          , b(X) -> a(X)}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , a_0(2) -> 2
        , a_1(2) -> 1
        , a_2(2) -> 1
        , b_0(2) -> 1
        , b_1(2) -> 1
        , g_0(2) -> 2}