Problem Zantema 04 z107

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z107

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(11) -> 12*
    d1(9) -> 10*
    d1(8) -> 9*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 1*
    1 -> 11,8
    10 -> 3*
    12 -> 4*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z107

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z107

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

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 1
        , b_0(2) -> 1
        , c_0(2) -> 1
        , d_0(2) -> 2
        , d_1(2) -> 3
        , d_1(3) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z107

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z107

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

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 1
        , b_0(2) -> 1
        , c_0(2) -> 1
        , d_0(2) -> 2
        , d_1(2) -> 3
        , d_1(3) -> 1}