Problem Zantema 04 z008

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z008

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    s1(8) -> 9*
    a1(7) -> 8*
    a0(1) -> 2*
    s0(1) -> 1*
    b0(1) -> 3*
    1 -> 7*
    9 -> 8,2
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z008

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z008

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(s(x1)) -> s(a(x1))
     , b(a(b(s(x1)))) -> a(b(s(a(x1))))
     , b(a(b(b(x1)))) -> a(b(a(b(x1))))
     , a(b(a(a(x1)))) -> b(a(b(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(s(x1)) -> s(a(x1))
          , b(a(b(s(x1)))) -> a(b(s(a(x1))))
          , b(a(b(b(x1)))) -> a(b(a(b(x1))))
          , a(b(a(a(x1)))) -> b(a(b(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) -> 3
        , s_0(2) -> 2
        , s_1(3) -> 1
        , s_1(3) -> 3
        , b_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z008

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z008

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(s(x1)) -> s(a(x1))
     , b(a(b(s(x1)))) -> a(b(s(a(x1))))
     , b(a(b(b(x1)))) -> a(b(a(b(x1))))
     , a(b(a(a(x1)))) -> b(a(b(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(s(x1)) -> s(a(x1))
          , b(a(b(s(x1)))) -> a(b(s(a(x1))))
          , b(a(b(b(x1)))) -> a(b(a(b(x1))))
          , a(b(a(a(x1)))) -> b(a(b(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) -> 3
        , s_0(2) -> 2
        , s_1(3) -> 1
        , s_1(3) -> 3
        , b_0(2) -> 1}