Problem Waldmann 07 size12 size-12-alpha-3-num-174

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-174

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(8) -> 9*
    a1(5) -> 6*
    a1(7) -> 8*
    a1(4) -> 5*
    c1(6) -> 7*
    b2(26) -> 27*
    a0(1) -> 2*
    a2(25) -> 26*
    a2(22) -> 23*
    a2(23) -> 24*
    b0(1) -> 1*
    c2(24) -> 25*
    c0(1) -> 3*
    1 -> 4,2
    4 -> 5*
    5 -> 6*
    7 -> 8*
    8 -> 22*
    9 -> 5,2
    22 -> 23*
    23 -> 24*
    25 -> 26*
    27 -> 6*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-174

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-174

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

Proof Output:
  'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with perSymbol-enrichment and initial automaton 'match''
     ----------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  a(x1) -> x1
          , a(b(x1)) -> b(a(c(a(a(x1)))))
          , c(c(c(x1))) -> b(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(2) -> 6
        , a_1(2) -> 7
        , a_1(5) -> 4
        , a_1(5) -> 10
        , a_1(5) -> 11
        , a_1(7) -> 6
        , a_2(4) -> 10
        , a_2(4) -> 11
        , a_2(9) -> 8
        , a_2(11) -> 10
        , b_0(2) -> 1
        , b_0(2) -> 2
        , b_0(2) -> 6
        , b_0(2) -> 7
        , b_1(4) -> 1
        , b_1(4) -> 6
        , b_1(4) -> 7
        , b_2(8) -> 6
        , c_0(2) -> 3
        , c_1(6) -> 4
        , c_1(6) -> 5
        , c_1(6) -> 10
        , c_1(6) -> 11
        , c_2(10) -> 8
        , c_2(10) -> 9}

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-174

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-174

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(b(x1)) -> b(a(c(a(a(x1)))))
     , c(c(c(x1))) -> b(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(b(x1)) -> b(a(c(a(a(x1)))))
          , c(c(c(x1))) -> b(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(2) -> 5
        , a_1(2) -> 6
        , a_1(4) -> 3
        , a_1(4) -> 9
        , a_1(4) -> 10
        , a_1(6) -> 5
        , a_2(3) -> 9
        , a_2(3) -> 10
        , a_2(8) -> 7
        , a_2(10) -> 9
        , b_0(2) -> 1
        , b_0(2) -> 2
        , b_0(2) -> 5
        , b_0(2) -> 6
        , b_1(3) -> 1
        , b_1(3) -> 5
        , b_1(3) -> 6
        , b_2(7) -> 5
        , c_0(2) -> 1
        , c_1(5) -> 3
        , c_1(5) -> 4
        , c_1(5) -> 9
        , c_1(5) -> 10
        , c_2(9) -> 7
        , c_2(9) -> 8}