Problem Transformed CSR 04 Ex23 Luc06 GM

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 GM

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    f1(55) -> 56*
    f1(12) -> 13*
    f1(69) -> 70*
    f1(14) -> 15*
    f1(61) -> 62*
    f1(63) -> 64*
    g1(53) -> 54*
    g1(13) -> 14*
    mark1(25) -> 26*
    mark1(27) -> 28*
    mark1(17) -> 18*
    mark1(33) -> 34*
    c1(45) -> 46*
    c1(15) -> 16*
    c1(47) -> 48*
    c1(37) -> 38*
    c1(39) -> 40*
    a1() -> 12*
    a__f1(18) -> 19*
    f2(75) -> 76*
    f2(77) -> 78*
    f2(71) -> 72*
    a__f0(2) -> 5*
    a__f0(4) -> 5*
    a__f0(1) -> 5*
    a__f0(3) -> 5*
    c2(78) -> 79*
    f0(2) -> 1*
    f0(4) -> 1*
    f0(1) -> 1*
    f0(3) -> 1*
    g2(76) -> 77*
    a0() -> 2*
    a2() -> 75*
    c0(2) -> 3*
    c0(4) -> 3*
    c0(1) -> 3*
    c0(3) -> 3*
    g0(2) -> 4*
    g0(4) -> 4*
    g0(1) -> 4*
    g0(3) -> 4*
    mark0(2) -> 6*
    mark0(4) -> 6*
    mark0(1) -> 6*
    mark0(3) -> 6*
    1 -> 61,45,27
    2 -> 69,37,17
    3 -> 55,47,33
    4 -> 63,39,25
    12 -> 18,53,6
    16 -> 5*
    18 -> 71,53
    19 -> 28,18,53,6
    26 -> 18*
    28 -> 18*
    34 -> 18*
    38 -> 34,18,53,6
    40 -> 34,18,53,6
    46 -> 34,18,53,6
    48 -> 34,18,53,6
    54 -> 26,18,53,6
    56 -> 5*
    62 -> 5*
    64 -> 5*
    70 -> 5*
    72 -> 19,6
    79 -> 19,28,6,18,71
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 GM

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 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())) -> c(f(g(f(a()))))
     , mark(f(X)) -> a__f(mark(X))
     , mark(a()) -> a()
     , mark(c(X)) -> c(X)
     , mark(g(X)) -> g(mark(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())) -> c(f(g(f(a()))))
          , mark(f(X)) -> a__f(mark(X))
          , mark(a()) -> a()
          , mark(c(X)) -> c(X)
          , mark(g(X)) -> g(mark(X))
          , a__f(X) -> f(X)}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a__f_0(2) -> 1
        , a__f_1(7) -> 1
        , a__f_1(7) -> 7
        , f_0(2) -> 2
        , f_1(2) -> 1
        , f_1(4) -> 3
        , f_1(6) -> 5
        , f_2(7) -> 1
        , f_2(7) -> 7
        , f_2(9) -> 8
        , f_2(11) -> 10
        , a_0() -> 2
        , a_1() -> 1
        , a_1() -> 6
        , a_1() -> 7
        , a_2() -> 11
        , c_0(2) -> 2
        , c_1(2) -> 1
        , c_1(2) -> 7
        , c_1(3) -> 1
        , c_2(8) -> 1
        , c_2(8) -> 7
        , g_0(2) -> 2
        , g_1(5) -> 4
        , g_1(7) -> 1
        , g_1(7) -> 7
        , g_2(10) -> 9
        , mark_0(2) -> 1
        , mark_1(2) -> 7}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 Luc06 GM

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex23 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())) -> c(f(g(f(a()))))
     , mark(f(X)) -> a__f(mark(X))
     , mark(a()) -> a()
     , mark(c(X)) -> c(X)
     , mark(g(X)) -> g(mark(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())) -> c(f(g(f(a()))))
          , mark(f(X)) -> a__f(mark(X))
          , mark(a()) -> a()
          , mark(c(X)) -> c(X)
          , mark(g(X)) -> g(mark(X))
          , a__f(X) -> f(X)}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a__f_0(2) -> 1
        , a__f_1(7) -> 1
        , a__f_1(7) -> 7
        , f_0(2) -> 2
        , f_1(2) -> 1
        , f_1(4) -> 3
        , f_1(6) -> 5
        , f_2(7) -> 1
        , f_2(7) -> 7
        , f_2(9) -> 8
        , f_2(11) -> 10
        , a_0() -> 2
        , a_1() -> 1
        , a_1() -> 6
        , a_1() -> 7
        , a_2() -> 11
        , c_0(2) -> 2
        , c_1(2) -> 1
        , c_1(2) -> 7
        , c_1(3) -> 1
        , c_2(8) -> 1
        , c_2(8) -> 7
        , g_0(2) -> 2
        , g_1(5) -> 4
        , g_1(7) -> 1
        , g_1(7) -> 7
        , g_2(10) -> 9
        , mark_0(2) -> 1
        , mark_1(2) -> 7}