Problem Zantema 08 ex8

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 ex8

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    f1(5) -> 6*
    f1(4) -> 5*
    f0(1) -> 2*
    g0(1) -> 3*
    f40() -> 1*
    1 -> 4*
    4 -> 6,3
    6 -> 3*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 ex8

stdout:

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

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 ex8

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(g(x)) -> g(g(x))
     , g(x) -> f(f(x))
     , f(f(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(g(x)) -> g(g(x))
          , g(x) -> f(f(x))
          , f(f(x)) -> x}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 3
        , f_1(3) -> 1
        , g_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 ex8

stdout:

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

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 ex8

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(g(x)) -> g(g(x))
     , g(x) -> f(f(x))
     , f(f(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(g(x)) -> g(g(x))
          , g(x) -> f(f(x))
          , f(f(x)) -> x}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 3
        , f_1(3) -> 1
        , g_0(2) -> 1}