Problem AG01 innermost 4.20a

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^1))

Problem:
f(f(x)) -> f(x)
f(s(x)) -> f(x)
g(s(0())) -> g(f(s(0())))

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    g1(15) -> 16*
    f1(5) -> 6*
    f1(14) -> 15*
    f1(11) -> 12*
    s1(13) -> 14*
    01() -> 13*
    f2(23) -> 24*
    f0(2) -> 3*
    f0(1) -> 3*
    s0(2) -> 1*
    s0(1) -> 1*
    g0(2) -> 4*
    g0(1) -> 4*
    00() -> 2*
    1 -> 11*
    2 -> 5*
    6 -> 12,3
    12 -> 3*
    13 -> 23*
    16 -> 4*
    24 -> 15*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

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(f(x)) -> f(x)
     , f(s(x)) -> f(x)
     , g(s(0())) -> g(f(s(0())))}

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(f(x)) -> f(x)
          , f(s(x)) -> f(x)
          , g(s(0())) -> g(f(s(0())))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_1(4) -> 3
        , f_2(5) -> 3
        , s_0(2) -> 2
        , s_1(5) -> 4
        , g_0(2) -> 1
        , g_1(3) -> 1
        , 0_0() -> 2
        , 0_1() -> 5}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

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(f(x)) -> f(x)
     , f(s(x)) -> f(x)
     , g(s(0())) -> g(f(s(0())))}

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(f(x)) -> f(x)
          , f(s(x)) -> f(x)
          , g(s(0())) -> g(f(s(0())))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_1(4) -> 3
        , f_2(5) -> 3
        , s_0(2) -> 2
        , s_1(5) -> 4
        , g_0(2) -> 1
        , g_1(3) -> 1
        , 0_0() -> 2
        , 0_1() -> 5}