Problem Strategy outermost added 08 n001

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 n001

stdout:

YES(?,O(n^1))

Problem:
h(f(f(x))) -> h(f(g(f(x))))
f(g(f(x))) -> f(f(x))

Proof:
Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    h0(1) -> 2*
    f0(1) -> 3*
    g0(1) -> 1*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 n001

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 n001

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:
    {  h(f(f(x))) -> h(f(g(f(x))))
     , f(g(f(x))) -> f(f(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:
         {  h(f(f(x))) -> h(f(g(f(x))))
          , f(g(f(x))) -> f(f(x))}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  h_0(2) -> 1
        , f_0(2) -> 1
        , g_0(2) -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 n001

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 n001

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  h(f(f(x))) -> h(f(g(f(x))))
     , f(g(f(x))) -> f(f(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:
         {  h(f(f(x))) -> h(f(g(f(x))))
          , f(g(f(x))) -> f(f(x))}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  h_0(2) -> 1
        , f_0(2) -> 1
        , g_0(2) -> 2}