Problem Zantema 04 z082

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z082

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(5) -> 6*
    a1(7) -> 8*
    a1(6) -> 7*
    a0(1) -> 2*
    c0(1) -> 1*
    b0(1) -> 4*
    d0(1) -> 3*
    1 -> 5*
    8 -> 4*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z082

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z082

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(c(a(x1))) -> c(a(c(x1)))
     , a(a(b(x1))) -> a(d(b(x1)))
     , a(b(x1)) -> b(a(a(x1)))
     , d(d(x1)) -> a(d(b(x1)))
     , b(b(x1)) -> b(c(x1))
     , a(d(c(x1))) -> c(a(x1))
     , b(c(x1)) -> a(a(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(c(a(x1))) -> c(a(c(x1)))
          , a(a(b(x1))) -> a(d(b(x1)))
          , a(b(x1)) -> b(a(a(x1)))
          , d(d(x1)) -> a(d(b(x1)))
          , b(b(x1)) -> b(c(x1))
          , a(d(c(x1))) -> c(a(x1))
          , b(c(x1)) -> a(a(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) -> 4
        , a_1(3) -> 1
        , a_1(4) -> 3
        , c_0(2) -> 2
        , b_0(2) -> 1
        , d_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z082

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z082

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(c(a(x1))) -> c(a(c(x1)))
     , a(a(b(x1))) -> a(d(b(x1)))
     , a(b(x1)) -> b(a(a(x1)))
     , d(d(x1)) -> a(d(b(x1)))
     , b(b(x1)) -> b(c(x1))
     , a(d(c(x1))) -> c(a(x1))
     , b(c(x1)) -> a(a(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(c(a(x1))) -> c(a(c(x1)))
          , a(a(b(x1))) -> a(d(b(x1)))
          , a(b(x1)) -> b(a(a(x1)))
          , d(d(x1)) -> a(d(b(x1)))
          , b(b(x1)) -> b(c(x1))
          , a(d(c(x1))) -> c(a(x1))
          , b(c(x1)) -> a(a(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) -> 4
        , a_1(3) -> 1
        , a_1(4) -> 3
        , c_0(2) -> 2
        , b_0(2) -> 1
        , d_0(2) -> 1}