Problem Zantema 06 01

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 01

stdout:

YES(?,O(n^1))

Problem:
a(b(x1)) -> b(r(x1))
r(a(x1)) -> d(r(x1))
r(x1) -> d(x1)
d(a(x1)) -> a(a(d(x1)))
d(x1) -> a(x1)

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(17) -> 18*
    d1(11) -> 12*
    b1(9) -> 10*
    r1(8) -> 9*
    a2(25) -> 26*
    a0(1) -> 2*
    d2(19) -> 20*
    b0(1) -> 1*
    a3(29) -> 30*
    r0(1) -> 3*
    d0(1) -> 4*
    1 -> 17,11,8
    8 -> 19*
    10 -> 30,20,26,12,18,4,2
    11 -> 25*
    12 -> 3*
    18 -> 4*
    19 -> 29*
    20 -> 9*
    26 -> 12,3
    30 -> 20,9
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 01

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 01

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)) -> b(r(x1))
     , r(a(x1)) -> d(r(x1))
     , r(x1) -> d(x1)
     , d(a(x1)) -> a(a(d(x1)))
     , d(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)) -> b(r(x1))
          , r(a(x1)) -> d(r(x1))
          , r(x1) -> d(x1)
          , d(a(x1)) -> a(a(d(x1)))
          , d(x1) -> a(x1)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 1
        , a_2(2) -> 1
        , a_3(2) -> 3
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 3
        , r_0(2) -> 1
        , r_1(2) -> 3
        , d_0(2) -> 1
        , d_1(2) -> 1
        , d_2(2) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 01

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 01

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)) -> b(r(x1))
     , r(a(x1)) -> d(r(x1))
     , r(x1) -> d(x1)
     , d(a(x1)) -> a(a(d(x1)))
     , d(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)) -> b(r(x1))
          , r(a(x1)) -> d(r(x1))
          , r(x1) -> d(x1)
          , d(a(x1)) -> a(a(d(x1)))
          , d(x1) -> a(x1)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 1
        , a_2(2) -> 1
        , a_3(2) -> 3
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 3
        , r_0(2) -> 1
        , r_1(2) -> 3
        , d_0(2) -> 1
        , d_1(2) -> 1
        , d_2(2) -> 3}