Problem Waldmann 07 size12 size-12-alpha-3-num-113

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-113

stdout:

YES(?,O(n^1))

Problem:
a(x1) -> x1
a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
c(a(x1)) -> x1

Proof:
Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 2*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-113

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-113

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:
    {  a(x1) -> x1
     , a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
     , c(a(x1)) -> x1}

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:
         {  a(x1) -> x1
          , a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
          , c(a(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , b_0(2) -> 1
        , b_0(2) -> 2
        , c_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-113

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-113

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a(x1) -> x1
     , a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
     , c(a(x1)) -> x1}

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:
         {  a(x1) -> x1
          , a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
          , c(a(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 0.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , b_0(2) -> 1
        , b_0(2) -> 2
        , c_0(2) -> 1}