Problem Strategy outermost added 08 4.17

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 4.17

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    01() -> 5,4
    s1(5) -> 5,4
    g1(2) -> 5*
    g1(1) -> 5*
    f0(1,1,1) -> 3*
    f0(2,2,1) -> 3*
    f0(1,1,2) -> 3*
    f0(2,2,2) -> 3*
    f0(1,2,1) -> 3*
    f0(2,1,1) -> 3*
    f0(1,2,2) -> 3*
    f0(2,1,2) -> 3*
    g0(2) -> 4*
    g0(1) -> 4*
    s0(2) -> 1*
    s0(1) -> 1*
    00() -> 2*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 4.17

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 4.17

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

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

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 4.17

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Strategy outermost added 08 4.17

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

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