Problem Zantema 04 z076

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z076

stdout:

YES(?,O(n^1))

Problem:
f(s(x1)) -> s(s(f(p(s(x1)))))
f(0(x1)) -> 0(x1)
p(s(x1)) -> x1

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    01(27) -> 28*
    01(21) -> 22*
    s1(5) -> 6*
    s1(19) -> 20*
    s1(9) -> 10*
    s1(8) -> 9*
    f1(7) -> 8*
    p1(6) -> 7*
    f0(2) -> 3*
    f0(1) -> 3*
    s0(2) -> 1*
    s0(1) -> 1*
    p0(2) -> 4*
    p0(1) -> 4*
    00(2) -> 2*
    00(1) -> 2*
    1 -> 4,27,19
    2 -> 4,21,5
    5 -> 7*
    10 -> 8,3
    19 -> 7*
    20 -> 6*
    22 -> 8,3
    28 -> 8,3
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z076

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z076

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:
    {  f(s(x1)) -> s(s(f(p(s(x1)))))
     , f(0(x1)) -> 0(x1)
     , p(s(x1)) -> 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:
         {  f(s(x1)) -> s(s(f(p(s(x1)))))
          , f(0(x1)) -> 0(x1)
          , p(s(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 4
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 5
        , s_1(2) -> 6
        , s_1(3) -> 1
        , s_1(3) -> 4
        , s_1(4) -> 3
        , p_0(2) -> 1
        , p_1(6) -> 5
        , 0_0(2) -> 1
        , 0_0(2) -> 2
        , 0_0(2) -> 5
        , 0_1(2) -> 1
        , 0_1(2) -> 4}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z076

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z076

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(s(x1)) -> s(s(f(p(s(x1)))))
     , f(0(x1)) -> 0(x1)
     , p(s(x1)) -> 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:
         {  f(s(x1)) -> s(s(f(p(s(x1)))))
          , f(0(x1)) -> 0(x1)
          , p(s(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 4
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 5
        , s_1(2) -> 6
        , s_1(3) -> 1
        , s_1(3) -> 4
        , s_1(4) -> 3
        , p_0(2) -> 1
        , p_1(6) -> 5
        , 0_0(2) -> 1
        , 0_0(2) -> 2
        , 0_0(2) -> 5
        , 0_1(2) -> 1
        , 0_1(2) -> 4}