Problem Zantema 04 z124

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z124

stdout:

YES(?,O(n^1))

Problem:
q0(a(x1)) -> x(q1(x1))
q1(a(x1)) -> a(q1(x1))
q1(y(x1)) -> y(q1(x1))
a(q1(b(x1))) -> q2(a(y(x1)))
a(q2(a(x1))) -> q2(a(a(x1)))
a(q2(y(x1))) -> q2(a(y(x1)))
y(q1(b(x1))) -> q2(y(y(x1)))
y(q2(a(x1))) -> q2(y(a(x1)))
y(q2(y(x1))) -> q2(y(y(x1)))
q2(x(x1)) -> x(q0(x1))
q0(y(x1)) -> y(q3(x1))
q3(y(x1)) -> y(q3(x1))
q3(bl(x1)) -> bl(q4(x1))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {10,9,8,7,6,5}
   transitions:
    bl1(33) -> 34*
    q41(35) -> 36*
    q41(32) -> 33*
    q41(41) -> 42*
    q41(43) -> 44*
    x1(15) -> 16*
    q01(25) -> 26*
    q01(17) -> 18*
    q01(14) -> 15*
    q01(23) -> 24*
    q00(2) -> 5*
    q00(4) -> 5*
    q00(1) -> 5*
    q00(3) -> 5*
    a0(2) -> 7*
    a0(4) -> 7*
    a0(1) -> 7*
    a0(3) -> 7*
    x0(2) -> 1*
    x0(4) -> 1*
    x0(1) -> 1*
    x0(3) -> 1*
    q10(2) -> 6*
    q10(4) -> 6*
    q10(1) -> 6*
    q10(3) -> 6*
    y0(2) -> 8*
    y0(4) -> 8*
    y0(1) -> 8*
    y0(3) -> 8*
    b0(2) -> 2*
    b0(4) -> 2*
    b0(1) -> 2*
    b0(3) -> 2*
    q20(2) -> 9*
    q20(4) -> 9*
    q20(1) -> 9*
    q20(3) -> 9*
    q30(2) -> 10*
    q30(4) -> 10*
    q30(1) -> 10*
    q30(3) -> 10*
    bl0(2) -> 3*
    bl0(4) -> 3*
    bl0(1) -> 3*
    bl0(3) -> 3*
    q40(2) -> 4*
    q40(4) -> 4*
    q40(1) -> 4*
    q40(3) -> 4*
    1 -> 41,23
    2 -> 32,14
    3 -> 43,25
    4 -> 35,17
    16 -> 9*
    18 -> 15*
    24 -> 15*
    26 -> 15*
    34 -> 10*
    36 -> 33*
    42 -> 33*
    44 -> 33*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z124

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z124

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:
    {  q0(a(x1)) -> x(q1(x1))
     , q1(a(x1)) -> a(q1(x1))
     , q1(y(x1)) -> y(q1(x1))
     , a(q1(b(x1))) -> q2(a(y(x1)))
     , a(q2(a(x1))) -> q2(a(a(x1)))
     , a(q2(y(x1))) -> q2(a(y(x1)))
     , y(q1(b(x1))) -> q2(y(y(x1)))
     , y(q2(a(x1))) -> q2(y(a(x1)))
     , y(q2(y(x1))) -> q2(y(y(x1)))
     , q2(x(x1)) -> x(q0(x1))
     , q0(y(x1)) -> y(q3(x1))
     , q3(y(x1)) -> y(q3(x1))
     , q3(bl(x1)) -> bl(q4(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:
         {  q0(a(x1)) -> x(q1(x1))
          , q1(a(x1)) -> a(q1(x1))
          , q1(y(x1)) -> y(q1(x1))
          , a(q1(b(x1))) -> q2(a(y(x1)))
          , a(q2(a(x1))) -> q2(a(a(x1)))
          , a(q2(y(x1))) -> q2(a(y(x1)))
          , y(q1(b(x1))) -> q2(y(y(x1)))
          , y(q2(a(x1))) -> q2(y(a(x1)))
          , y(q2(y(x1))) -> q2(y(y(x1)))
          , q2(x(x1)) -> x(q0(x1))
          , q0(y(x1)) -> y(q3(x1))
          , q3(y(x1)) -> y(q3(x1))
          , q3(bl(x1)) -> bl(q4(x1))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  q0_0(2) -> 1
        , q0_1(2) -> 3
        , a_0(2) -> 1
        , x_0(2) -> 2
        , x_1(3) -> 1
        , q1_0(2) -> 1
        , y_0(2) -> 1
        , b_0(2) -> 2
        , q2_0(2) -> 1
        , q3_0(2) -> 1
        , bl_0(2) -> 2
        , bl_1(4) -> 1
        , q4_0(2) -> 2
        , q4_1(2) -> 4}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z124

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z124

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  q0(a(x1)) -> x(q1(x1))
     , q1(a(x1)) -> a(q1(x1))
     , q1(y(x1)) -> y(q1(x1))
     , a(q1(b(x1))) -> q2(a(y(x1)))
     , a(q2(a(x1))) -> q2(a(a(x1)))
     , a(q2(y(x1))) -> q2(a(y(x1)))
     , y(q1(b(x1))) -> q2(y(y(x1)))
     , y(q2(a(x1))) -> q2(y(a(x1)))
     , y(q2(y(x1))) -> q2(y(y(x1)))
     , q2(x(x1)) -> x(q0(x1))
     , q0(y(x1)) -> y(q3(x1))
     , q3(y(x1)) -> y(q3(x1))
     , q3(bl(x1)) -> bl(q4(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:
         {  q0(a(x1)) -> x(q1(x1))
          , q1(a(x1)) -> a(q1(x1))
          , q1(y(x1)) -> y(q1(x1))
          , a(q1(b(x1))) -> q2(a(y(x1)))
          , a(q2(a(x1))) -> q2(a(a(x1)))
          , a(q2(y(x1))) -> q2(a(y(x1)))
          , y(q1(b(x1))) -> q2(y(y(x1)))
          , y(q2(a(x1))) -> q2(y(a(x1)))
          , y(q2(y(x1))) -> q2(y(y(x1)))
          , q2(x(x1)) -> x(q0(x1))
          , q0(y(x1)) -> y(q3(x1))
          , q3(y(x1)) -> y(q3(x1))
          , q3(bl(x1)) -> bl(q4(x1))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  q0_0(2) -> 1
        , q0_1(2) -> 3
        , a_0(2) -> 1
        , x_0(2) -> 2
        , x_1(3) -> 1
        , q1_0(2) -> 1
        , y_0(2) -> 1
        , b_0(2) -> 2
        , q2_0(2) -> 1
        , q3_0(2) -> 1
        , bl_0(2) -> 2
        , bl_1(4) -> 1
        , q4_0(2) -> 2
        , q4_1(2) -> 4}