Problem ICFP 2010 230948

Tool CaT

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 230948

stdout:

YES(?,O(n^1))

Problem:
 0(x1) -> 1(x1)
 0(0(x1)) -> 0(x1)
 3(4(5(x1))) -> 4(3(5(x1)))
 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(
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                                                                    2
                                                                    (
                                                                    2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 ->
 1(0(1(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(
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                                                                    0(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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                                                                    1
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                                                                    0(0(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 ->
 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(
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                                                                    2
                                                                    (
                                                                    2
                                                                    (
                                                                    2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    41(21) -> 22*
    31(20) -> 21*
    51(29) -> 30*
    51(19) -> 20*
    51(31) -> 32*
    11(17) -> 18*
    11(9) -> 10*
    11(11) -> 12*
    00(2) -> 4*
    00(1) -> 4*
    00(3) -> 4*
    10(2) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    30(2) -> 5*
    30(1) -> 5*
    30(3) -> 5*
    40(2) -> 2*
    40(1) -> 2*
    40(3) -> 2*
    50(2) -> 3*
    50(1) -> 3*
    50(3) -> 3*
    20(2) -> 6*
    20(1) -> 6*
    20(3) -> 6*
    1 -> 29,11
    2 -> 19,17
    3 -> 31,9
    10 -> 4*
    12 -> 4*
    18 -> 4*
    22 -> 5*
    30 -> 20*
    32 -> 20*
  problem:
   
  Qed

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputICFP 2010 230948

stdout:

MAYBE

Tool IRC2

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 230948

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)
     , 0(0(x1)) -> 0(x1)
     , 3(4(5(x1))) -> 4(3(5(x1)))
     , 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
       ->
       1(0(1(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
     , 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
       ->
       2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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)
          , 0(0(x1)) -> 0(x1)
          , 3(4(5(x1))) -> 4(3(5(x1)))
          , 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
            ->
            1(0(1(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
          , 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
            ->
            2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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
        , 3_0(2) -> 1
        , 3_1(4) -> 3
        , 4_0(2) -> 2
        , 4_1(3) -> 1
        , 5_0(2) -> 2
        , 5_1(2) -> 4
        , 2_0(2) -> 1}

Tool RC1

Execution TimeUnknown
Answer
MAYBE
InputICFP 2010 230948

stdout:

MAYBE

Tool RC2

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 230948

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)
     , 0(0(x1)) -> 0(x1)
     , 3(4(5(x1))) -> 4(3(5(x1)))
     , 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
       ->
       1(0(1(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
     , 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
       ->
       2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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)
          , 0(0(x1)) -> 0(x1)
          , 3(4(5(x1))) -> 4(3(5(x1)))
          , 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
            ->
            1(0(1(1(1(0(1(0(1(1(1(0(1(1(0(0(0(1(0(1(1(1(1(1(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(1(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
          , 0(0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(1(0(1(1(0(0(1(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(1(1(0(1(1(0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
            ->
            2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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
        , 3_0(2) -> 1
        , 3_1(4) -> 3
        , 4_0(2) -> 2
        , 4_1(3) -> 1
        , 5_0(2) -> 2
        , 5_1(2) -> 4
        , 2_0(2) -> 1}