Problem Waldmann 07 size12 size-12-alpha-3-num-248

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-248

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(7) -> 8*
    c1(6) -> 7*
    a1(5) -> 6*
    a1(4) -> 5*
    b2(17) -> 18*
    a0(1) -> 2*
    c2(16) -> 17*
    b0(1) -> 1*
    a2(15) -> 16*
    a2(14) -> 15*
    c0(1) -> 3*
    1 -> 4,2
    4 -> 5*
    5 -> 6*
    7 -> 14*
    8 -> 5,2
    14 -> 15*
    15 -> 16*
    18 -> 6*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-248

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-248

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(c(a(a(x1))))
     , c(c(c(x1))) -> a(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:    innermost runtime-complexity with respect to
       Rules:
         {  a(x1) -> x1
          , a(b(x1)) -> b(c(a(a(x1))))
          , c(c(c(x1))) -> a(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) -> 4
        , a_1(2) -> 5
        , a_1(5) -> 4
        , a_2(3) -> 7
        , a_2(3) -> 8
        , a_2(8) -> 7
        , b_0(2) -> 1
        , b_0(2) -> 2
        , b_0(2) -> 4
        , b_0(2) -> 5
        , b_1(3) -> 1
        , b_1(3) -> 4
        , b_1(3) -> 5
        , b_2(6) -> 4
        , c_0(2) -> 1
        , c_1(4) -> 3
        , c_1(4) -> 7
        , c_1(4) -> 8
        , c_2(7) -> 6}

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-248

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 07 size12 size-12-alpha-3-num-248

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