Problem ICFP 2010 25192

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	ICFP 2010 25192

stdout:

YES(?,O(n^1))

Problem:
0(x1) -> 1(x1)
4(5(4(5(x1)))) -> 4(4(5(5(x1))))
5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    11(10) -> 11*
    11(8) -> 9*
    00(2) -> 3*
    00(1) -> 3*
    10(2) -> 1*
    10(1) -> 1*
    40(2) -> 4*
    40(1) -> 4*
    50(2) -> 5*
    50(1) -> 5*
    20(2) -> 2*
    20(1) -> 2*
    1 -> 8*
    2 -> 10*
    9 -> 3*
    11 -> 3*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	ICFP 2010 25192

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	ICFP 2010 25192

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:
    {  0(x1) -> 1(x1)
     , 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
     , 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(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:
         {  0(x1) -> 1(x1)
          , 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
          , 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  0_0(2) -> 1
        , 1_0(2) -> 2
        , 1_1(2) -> 1
        , 4_0(2) -> 1
        , 5_0(2) -> 1
        , 2_0(2) -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	ICFP 2010 25192

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	ICFP 2010 25192

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  0(x1) -> 1(x1)
     , 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
     , 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(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:
         {  0(x1) -> 1(x1)
          , 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
          , 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  0_0(2) -> 1
        , 1_0(2) -> 2
        , 1_1(2) -> 1
        , 4_0(2) -> 1
        , 5_0(2) -> 1
        , 2_0(2) -> 2}