Problem Strategy outermost added 08 jwno9

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 jwno9

stdout:

YES(?,O(n^1))

Problem:
f(x,f(a(),y)) -> f(a(),f(f(f(a(),a()),y),x))

Proof:
Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {2}
   transitions:
    f0(1,1) -> 2*
    a0() -> 1*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 jwno9

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 jwno9

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(x, f(a(), y)) -> f(a(), f(f(f(a(), a()), y), 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(x, f(a(), y)) -> f(a(), f(f(f(a(), a()), y), x))}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  f_0(2, 2) -> 1
        , a_0() -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 jwno9

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 jwno9

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(x, f(a(), y)) -> f(a(), f(f(f(a(), a()), y), 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(x, f(a(), y)) -> f(a(), f(f(f(a(), a()), y), x))}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  f_0(2, 2) -> 1
        , a_0() -> 2}