Problem Waldmann 06 jwmatchb1

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 06 jwmatchb1

stdout:

YES(?,O(n^1))

Problem:
h(f(x,y)) -> f(y,f(h(h(x)),a()))

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    f1(16,4) -> 17*
    f1(6,4) -> 7*
    f1(2,7) -> 19,5,3
    f1(2,17) -> 19,5,3
    f1(1,7) -> 19,5,3
    f1(1,17) -> 19,5,3
    h1(15) -> 16*
    h1(5) -> 6*
    h1(2) -> 15*
    h1(1) -> 5*
    a1() -> 4*
    f2(17,21) -> 20,6
    f2(7,21) -> 20,6
    f2(20,18) -> 21*
    h0(2) -> 3*
    h0(1) -> 3*
    h2(2) -> 19*
    h2(19) -> 20*
    h2(1) -> 19*
    f0(1,2) -> 1*
    f0(2,1) -> 1*
    f0(1,1) -> 1*
    f0(2,2) -> 1*
    a2() -> 18*
    a0() -> 2*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 06 jwmatchb1

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 06 jwmatchb1

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: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}

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: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  h_0(2) -> 1
        , h_1(2) -> 6
        , h_1(6) -> 4
        , h_2(2) -> 10
        , h_2(10) -> 8
        , f_0(2, 2) -> 2
        , f_1(2, 3) -> 1
        , f_1(2, 3) -> 6
        , f_1(2, 3) -> 10
        , f_1(4, 5) -> 3
        , f_2(3, 7) -> 4
        , f_2(3, 7) -> 8
        , f_2(8, 9) -> 7
        , a_0() -> 2
        , a_1() -> 5
        , a_2() -> 9}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 06 jwmatchb1

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Waldmann 06 jwmatchb1

stdout:

YES(?,O(n^1))

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

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: {h(f(x, y)) -> f(y, f(h(h(x)), a()))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  h_0(2) -> 1
        , h_1(2) -> 6
        , h_1(6) -> 4
        , h_2(2) -> 10
        , h_2(10) -> 8
        , f_0(2, 2) -> 2
        , f_1(2, 3) -> 1
        , f_1(2, 3) -> 6
        , f_1(2, 3) -> 10
        , f_1(4, 5) -> 3
        , f_2(3, 7) -> 4
        , f_2(3, 7) -> 8
        , f_2(8, 9) -> 7
        , a_0() -> 2
        , a_1() -> 5
        , a_2() -> 9}