Problem AG01 innermost 4.37

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.37

stdout:

YES(?,O(n^1))

Problem:
f(c(s(x),y)) -> f(c(x,s(y)))
g(c(x,s(y))) -> g(c(s(x),y))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    g1(9) -> 4*
    c1(7,1) -> 9*
    c1(2,7) -> 8*
    c1(1,7) -> 8*
    c1(7,2) -> 9*
    s1(7) -> 7*
    s1(2) -> 7*
    s1(1) -> 7*
    f1(8) -> 3*
    f0(2) -> 3*
    f0(1) -> 3*
    c0(1,2) -> 1*
    c0(2,1) -> 1*
    c0(1,1) -> 1*
    c0(2,2) -> 1*
    s0(2) -> 2*
    s0(1) -> 2*
    g0(2) -> 4*
    g0(1) -> 4*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.37

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.37

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(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(c(s(x), y))}

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(c(s(x), y)) -> f(c(x, s(y)))
          , g(c(x, s(y))) -> g(c(s(x), y))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(3) -> 1
        , c_0(2, 2) -> 2
        , c_1(2, 4) -> 3
        , c_1(4, 2) -> 5
        , s_0(2) -> 2
        , s_1(2) -> 4
        , s_1(4) -> 4
        , g_0(2) -> 1
        , g_1(5) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.37

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.37

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(c(s(x), y)) -> f(c(x, s(y)))
     , g(c(x, s(y))) -> g(c(s(x), y))}

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(c(s(x), y)) -> f(c(x, s(y)))
          , g(c(x, s(y))) -> g(c(s(x), y))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(3) -> 1
        , c_0(2, 2) -> 2
        , c_1(2, 4) -> 3
        , c_1(4, 2) -> 5
        , s_0(2) -> 2
        , s_1(2) -> 4
        , s_1(4) -> 4
        , g_0(2) -> 1
        , g_1(5) -> 1}