Problem Transformed CSR 04 Ex18 Luc06 GM

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^1))

Problem:
a__f(f(a())) -> a__f(g(f(a())))
mark(f(X)) -> a__f(mark(X))
mark(a()) -> a()
mark(g(X)) -> g(X)
a__f(X) -> f(X)

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f1(40) -> 41*
    f1(46) -> 47*
    f1(6) -> 7*
    f1(48) -> 49*
    g1(30) -> 31*
    g1(32) -> 33*
    g1(7) -> 8*
    g1(38) -> 39*
    a1() -> 6*
    a__f1(18) -> 19*
    a__f1(8) -> 9*
    mark1(20) -> 21*
    mark1(17) -> 18*
    mark1(26) -> 27*
    f2(60) -> 61*
    f2(52) -> 53*
    f2(58) -> 59*
    a__f0(2) -> 4*
    a__f0(1) -> 4*
    a__f0(3) -> 4*
    a__f2(62) -> 63*
    f0(2) -> 1*
    f0(1) -> 1*
    f0(3) -> 1*
    g2(61) -> 62*
    a0() -> 2*
    a2() -> 60*
    g0(2) -> 3*
    g0(1) -> 3*
    g0(3) -> 3*
    f3(70) -> 71*
    mark0(2) -> 5*
    mark0(1) -> 5*
    mark0(3) -> 5*
    1 -> 46,32,20
    2 -> 48,30,17
    3 -> 40,38,26
    6 -> 18,5
    8 -> 58*
    9 -> 4*
    18 -> 52*
    19 -> 21,18,5
    21 -> 18*
    27 -> 18*
    31 -> 27,18,5
    33 -> 27,18,5
    39 -> 27,18,5
    41 -> 4*
    47 -> 4*
    49 -> 4*
    53 -> 19,5
    59 -> 9,4
    62 -> 70*
    63 -> 19,21,5,18,52
    71 -> 63,19
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 GM

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:
    {  a__f(f(a())) -> a__f(g(f(a())))
     , mark(f(X)) -> a__f(mark(X))
     , mark(a()) -> a()
     , mark(g(X)) -> g(X)
     , a__f(X) -> f(X)}

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:
         {  a__f(f(a())) -> a__f(g(f(a())))
          , mark(f(X)) -> a__f(mark(X))
          , mark(a()) -> a()
          , mark(g(X)) -> g(X)
          , a__f(X) -> f(X)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  a__f_0(2) -> 1
        , a__f_1(3) -> 1
        , a__f_1(3) -> 3
        , a__f_2(6) -> 1
        , a__f_2(6) -> 3
        , f_0(2) -> 2
        , f_1(2) -> 1
        , f_1(5) -> 4
        , f_2(3) -> 1
        , f_2(3) -> 3
        , f_2(8) -> 7
        , f_3(6) -> 1
        , f_3(6) -> 3
        , a_0() -> 2
        , a_1() -> 1
        , a_1() -> 3
        , a_1() -> 5
        , a_2() -> 8
        , g_0(2) -> 2
        , g_1(2) -> 1
        , g_1(2) -> 3
        , g_1(4) -> 3
        , g_2(7) -> 6
        , mark_0(2) -> 1
        , mark_1(2) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex18 Luc06 GM

stdout:

YES(?,O(n^1))

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

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:
         {  a__f(f(a())) -> a__f(g(f(a())))
          , mark(f(X)) -> a__f(mark(X))
          , mark(a()) -> a()
          , mark(g(X)) -> g(X)
          , a__f(X) -> f(X)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  a__f_0(2) -> 1
        , a__f_1(3) -> 1
        , a__f_1(3) -> 3
        , a__f_2(6) -> 1
        , a__f_2(6) -> 3
        , f_0(2) -> 2
        , f_1(2) -> 1
        , f_1(5) -> 4
        , f_2(3) -> 1
        , f_2(3) -> 3
        , f_2(8) -> 7
        , f_3(6) -> 1
        , f_3(6) -> 3
        , a_0() -> 2
        , a_1() -> 1
        , a_1() -> 3
        , a_1() -> 5
        , a_2() -> 8
        , g_0(2) -> 2
        , g_1(2) -> 1
        , g_1(2) -> 3
        , g_1(4) -> 3
        , g_2(7) -> 6
        , mark_0(2) -> 1
        , mark_1(2) -> 3}