Problem Zantema 04 z013

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z013

stdout:

YES(?,O(n^1))

Problem:
g(c(x1)) -> g(f(c(x1)))
g(f(c(x1))) -> g(f(f(c(x1))))
g(g(x1)) -> g(f(g(x1)))
f(f(g(x1))) -> g(f(x1))

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    g1(6) -> 7*
    f1(5) -> 6*
    c1(4) -> 5*
    g2(20) -> 21*
    g0(1) -> 2*
    f2(19) -> 20*
    f2(18) -> 19*
    c0(1) -> 1*
    c2(17) -> 18*
    f0(1) -> 3*
    1 -> 4*
    4 -> 17*
    7 -> 2*
    21 -> 7,2
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z013

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z013

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:
    {  g(c(x1)) -> g(f(c(x1)))
     , g(f(c(x1))) -> g(f(f(c(x1))))
     , g(g(x1)) -> g(f(g(x1)))
     , f(f(g(x1))) -> g(f(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:
         {  g(c(x1)) -> g(f(c(x1)))
          , g(f(c(x1))) -> g(f(f(c(x1))))
          , g(g(x1)) -> g(f(g(x1)))
          , f(f(g(x1))) -> g(f(x1))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  g_0(2) -> 1
        , g_1(3) -> 1
        , g_2(5) -> 1
        , c_0(2) -> 2
        , c_1(2) -> 4
        , c_2(2) -> 7
        , f_0(2) -> 1
        , f_1(4) -> 3
        , f_2(6) -> 5
        , f_2(7) -> 6}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z013

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z013

stdout:

YES(?,O(n^1))

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

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  g_0(2) -> 1
        , g_1(3) -> 1
        , g_2(5) -> 1
        , c_0(2) -> 2
        , c_1(2) -> 4
        , c_2(2) -> 7
        , f_0(2) -> 1
        , f_1(4) -> 3
        , f_2(6) -> 5
        , f_2(7) -> 6}