Problem Zantema 06 while2

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 while2

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    a1(30) -> 31*
    a1(9) -> 10*
    a1(36) -> 37*
    f1(10) -> 11*
    b1(22) -> 23*
    b1(7) -> 8*
    b1(28) -> 29*
    b1(8) -> 9*
    c1(20) -> 21*
    c1(6) -> 7*
    d2(44) -> 45*
    d2(46) -> 47*
    d2(38) -> 39*
    a0(2) -> 3*
    a0(1) -> 3*
    b0(2) -> 4*
    b0(1) -> 4*
    d0(2) -> 5*
    d0(1) -> 5*
    c0(2) -> 1*
    c0(1) -> 1*
    f0(2) -> 2*
    f0(1) -> 2*
    1 -> 36,28,20
    2 -> 30,22,6
    8 -> 46*
    11 -> 39,45,10,5
    21 -> 7*
    22 -> 38*
    23 -> 9*
    28 -> 44*
    29 -> 9*
    31 -> 3*
    37 -> 31,3
    39 -> 10*
    45 -> 10*
    47 -> 10*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 while2

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 while2

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(b(x1)) -> d(x1)
     , b(a(x1)) -> a(b(x1))
     , d(c(x1)) -> f(a(b(b(c(x1)))))
     , d(f(x1)) -> f(a(b(x1)))
     , a(f(x1)) -> a(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(b(x1)) -> d(x1)
          , b(a(x1)) -> a(b(x1))
          , d(c(x1)) -> f(a(b(b(c(x1)))))
          , d(f(x1)) -> f(a(b(x1)))
          , a(f(x1)) -> a(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) -> 1
        , a_1(4) -> 3
        , b_0(2) -> 1
        , b_1(2) -> 4
        , b_1(5) -> 4
        , b_1(6) -> 5
        , d_0(2) -> 1
        , d_2(2) -> 3
        , d_2(5) -> 3
        , c_0(2) -> 2
        , c_1(2) -> 6
        , f_0(2) -> 2
        , f_1(3) -> 1
        , f_1(3) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 while2

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 while2

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(b(x1)) -> d(x1)
     , b(a(x1)) -> a(b(x1))
     , d(c(x1)) -> f(a(b(b(c(x1)))))
     , d(f(x1)) -> f(a(b(x1)))
     , a(f(x1)) -> a(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(b(x1)) -> d(x1)
          , b(a(x1)) -> a(b(x1))
          , d(c(x1)) -> f(a(b(b(c(x1)))))
          , d(f(x1)) -> f(a(b(x1)))
          , a(f(x1)) -> a(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) -> 1
        , a_1(4) -> 3
        , b_0(2) -> 1
        , b_1(2) -> 4
        , b_1(5) -> 4
        , b_1(6) -> 5
        , d_0(2) -> 1
        , d_2(2) -> 3
        , d_2(5) -> 3
        , c_0(2) -> 2
        , c_1(2) -> 6
        , f_0(2) -> 2
        , f_1(3) -> 1
        , f_1(3) -> 3}