Problem Zantema 04 z094

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z094

stdout:

YES(?,O(n^1))

Problem:
f(x1) -> n(c(c(x1)))
c(f(x1)) -> f(c(c(x1)))
c(c(x1)) -> c(x1)
n(s(x1)) -> f(s(s(x1)))
n(f(x1)) -> f(n(x1))

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    f1(19) -> 20*
    s1(17) -> 18*
    s1(18) -> 19*
    n1(7) -> 8*
    c1(5) -> 6*
    c1(6) -> 7*
    c2(22) -> 23*
    c2(31) -> 32*
    c2(21) -> 22*
    f0(1) -> 2*
    n2(23) -> 24*
    n0(1) -> 4*
    c3(33) -> 34*
    c0(1) -> 3*
    s0(1) -> 1*
    1 -> 17,5
    5 -> 31*
    8 -> 2*
    19 -> 21*
    20 -> 4*
    21 -> 33*
    24 -> 20*
    32 -> 7*
    34 -> 23*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z094

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z094

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(x1) -> n(c(c(x1)))
     , c(f(x1)) -> f(c(c(x1)))
     , c(c(x1)) -> c(x1)
     , n(s(x1)) -> f(s(s(x1)))
     , n(f(x1)) -> f(n(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(x1) -> n(c(c(x1)))
          , c(f(x1)) -> f(c(c(x1)))
          , c(c(x1)) -> c(x1)
          , n(s(x1)) -> f(s(s(x1)))
          , n(f(x1)) -> f(n(x1))}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 1
        , n_0(2) -> 1
        , n_1(3) -> 1
        , n_2(7) -> 1
        , c_0(2) -> 1
        , c_1(2) -> 4
        , c_1(4) -> 3
        , c_2(2) -> 3
        , c_2(5) -> 8
        , c_2(8) -> 7
        , c_3(5) -> 7
        , s_0(2) -> 2
        , s_1(2) -> 6
        , s_1(6) -> 5}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z094

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z094

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(x1) -> n(c(c(x1)))
     , c(f(x1)) -> f(c(c(x1)))
     , c(c(x1)) -> c(x1)
     , n(s(x1)) -> f(s(s(x1)))
     , n(f(x1)) -> f(n(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(x1) -> n(c(c(x1)))
          , c(f(x1)) -> f(c(c(x1)))
          , c(c(x1)) -> c(x1)
          , n(s(x1)) -> f(s(s(x1)))
          , n(f(x1)) -> f(n(x1))}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(5) -> 1
        , n_0(2) -> 1
        , n_1(3) -> 1
        , n_2(7) -> 1
        , c_0(2) -> 1
        , c_1(2) -> 4
        , c_1(4) -> 3
        , c_2(2) -> 3
        , c_2(5) -> 8
        , c_2(8) -> 7
        , c_3(5) -> 7
        , s_0(2) -> 2
        , s_1(2) -> 6
        , s_1(6) -> 5}