Problem Waldmann 07 size12 size-12-alpha-3-num-30

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-30

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(11) -> 12*
    a1(13) -> 14*
    c1(10) -> 11*
    c1(12) -> 13*
    b1(7) -> 8*
    b1(8) -> 9*
    b2(27) -> 28*
    b2(24) -> 25*
    b2(26) -> 27*
    b2(23) -> 24*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 10,7,2
    9 -> 2*
    10 -> 13,23,14,2
    11 -> 26,12
    13 -> 23,14
    14 -> 2*
    25 -> 14*
    28 -> 12*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-30

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-30

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

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(4) -> 1
        , a_1(6) -> 5
        , b_0(2) -> 1
        , b_0(2) -> 2
        , b_0(2) -> 4
        , b_1(2) -> 3
        , b_1(3) -> 1
        , b_2(4) -> 7
        , b_2(6) -> 8
        , b_2(7) -> 1
        , b_2(8) -> 5
        , c_0(2) -> 1
        , c_1(2) -> 5
        , c_1(2) -> 6
        , c_1(5) -> 1
        , c_1(5) -> 4}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-30

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-30

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

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(4) -> 1
        , a_1(6) -> 5
        , b_0(2) -> 1
        , b_0(2) -> 2
        , b_0(2) -> 4
        , b_1(2) -> 3
        , b_1(3) -> 1
        , b_2(4) -> 7
        , b_2(6) -> 8
        , b_2(7) -> 1
        , b_2(8) -> 5
        , c_0(2) -> 1
        , c_1(2) -> 5
        , c_1(2) -> 6
        , c_1(5) -> 1
        , c_1(5) -> 4}