Problem Zantema 04 z091

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z091

stdout:

YES(?,O(n^1))

Problem:
r0(0(x1)) -> 0(r0(x1))
r0(1(x1)) -> 1(r0(x1))
r0(m(x1)) -> m(r0(x1))
r1(0(x1)) -> 0(r1(x1))
r1(1(x1)) -> 1(r1(x1))
r1(m(x1)) -> m(r1(x1))
r0(b(x1)) -> qr(0(b(x1)))
r1(b(x1)) -> qr(1(b(x1)))
0(qr(x1)) -> qr(0(x1))
1(qr(x1)) -> qr(1(x1))
m(qr(x1)) -> ql(m(x1))
0(ql(x1)) -> ql(0(x1))
1(ql(x1)) -> ql(1(x1))
b(ql(0(x1))) -> 0(b(r0(x1)))
b(ql(1(x1))) -> 1(b(r1(x1)))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {8,7,6,5,4,3}
   transitions:
    ql1(41) -> 42*
    ql1(43) -> 44*
    ql1(33) -> 34*
    11(25) -> 26*
    11(22) -> 23*
    01(15) -> 16*
    01(12) -> 13*
    m1(35) -> 36*
    m1(32) -> 33*
    qr1(23) -> 24*
    qr1(13) -> 14*
    r00(2) -> 3*
    r00(1) -> 3*
    00(2) -> 5*
    00(1) -> 5*
    10(2) -> 6*
    10(1) -> 6*
    m0(2) -> 7*
    m0(1) -> 7*
    r10(2) -> 4*
    r10(1) -> 4*
    b0(2) -> 8*
    b0(1) -> 8*
    qr0(2) -> 1*
    qr0(1) -> 1*
    ql0(2) -> 2*
    ql0(1) -> 2*
    1 -> 35,25,15
    2 -> 32,22,12
    13 -> 41*
    14 -> 16,13,41,5
    16 -> 13*
    23 -> 43*
    24 -> 26,23,43,6
    26 -> 23*
    34 -> 36,33,7
    36 -> 33*
    42 -> 13,41,5
    44 -> 23,43,6
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z091

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z091

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:
    {  r0(0(x1)) -> 0(r0(x1))
     , r0(1(x1)) -> 1(r0(x1))
     , r0(m(x1)) -> m(r0(x1))
     , r1(0(x1)) -> 0(r1(x1))
     , r1(1(x1)) -> 1(r1(x1))
     , r1(m(x1)) -> m(r1(x1))
     , r0(b(x1)) -> qr(0(b(x1)))
     , r1(b(x1)) -> qr(1(b(x1)))
     , 0(qr(x1)) -> qr(0(x1))
     , 1(qr(x1)) -> qr(1(x1))
     , m(qr(x1)) -> ql(m(x1))
     , 0(ql(x1)) -> ql(0(x1))
     , 1(ql(x1)) -> ql(1(x1))
     , b(ql(0(x1))) -> 0(b(r0(x1)))
     , b(ql(1(x1))) -> 1(b(r1(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:
         {  r0(0(x1)) -> 0(r0(x1))
          , r0(1(x1)) -> 1(r0(x1))
          , r0(m(x1)) -> m(r0(x1))
          , r1(0(x1)) -> 0(r1(x1))
          , r1(1(x1)) -> 1(r1(x1))
          , r1(m(x1)) -> m(r1(x1))
          , r0(b(x1)) -> qr(0(b(x1)))
          , r1(b(x1)) -> qr(1(b(x1)))
          , 0(qr(x1)) -> qr(0(x1))
          , 1(qr(x1)) -> qr(1(x1))
          , m(qr(x1)) -> ql(m(x1))
          , 0(ql(x1)) -> ql(0(x1))
          , 1(ql(x1)) -> ql(1(x1))
          , b(ql(0(x1))) -> 0(b(r0(x1)))
          , b(ql(1(x1))) -> 1(b(r1(x1)))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  r0_0(2) -> 1
        , 0_0(2) -> 1
        , 0_1(2) -> 3
        , 1_0(2) -> 1
        , 1_1(2) -> 3
        , m_0(2) -> 1
        , m_1(2) -> 4
        , r1_0(2) -> 1
        , b_0(2) -> 1
        , qr_0(2) -> 2
        , qr_1(3) -> 1
        , qr_1(3) -> 3
        , ql_0(2) -> 2
        , ql_1(3) -> 1
        , ql_1(3) -> 3
        , ql_1(4) -> 1
        , ql_1(4) -> 4}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z091

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z091

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  r0(0(x1)) -> 0(r0(x1))
     , r0(1(x1)) -> 1(r0(x1))
     , r0(m(x1)) -> m(r0(x1))
     , r1(0(x1)) -> 0(r1(x1))
     , r1(1(x1)) -> 1(r1(x1))
     , r1(m(x1)) -> m(r1(x1))
     , r0(b(x1)) -> qr(0(b(x1)))
     , r1(b(x1)) -> qr(1(b(x1)))
     , 0(qr(x1)) -> qr(0(x1))
     , 1(qr(x1)) -> qr(1(x1))
     , m(qr(x1)) -> ql(m(x1))
     , 0(ql(x1)) -> ql(0(x1))
     , 1(ql(x1)) -> ql(1(x1))
     , b(ql(0(x1))) -> 0(b(r0(x1)))
     , b(ql(1(x1))) -> 1(b(r1(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:
         {  r0(0(x1)) -> 0(r0(x1))
          , r0(1(x1)) -> 1(r0(x1))
          , r0(m(x1)) -> m(r0(x1))
          , r1(0(x1)) -> 0(r1(x1))
          , r1(1(x1)) -> 1(r1(x1))
          , r1(m(x1)) -> m(r1(x1))
          , r0(b(x1)) -> qr(0(b(x1)))
          , r1(b(x1)) -> qr(1(b(x1)))
          , 0(qr(x1)) -> qr(0(x1))
          , 1(qr(x1)) -> qr(1(x1))
          , m(qr(x1)) -> ql(m(x1))
          , 0(ql(x1)) -> ql(0(x1))
          , 1(ql(x1)) -> ql(1(x1))
          , b(ql(0(x1))) -> 0(b(r0(x1)))
          , b(ql(1(x1))) -> 1(b(r1(x1)))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  r0_0(2) -> 1
        , 0_0(2) -> 1
        , 0_1(2) -> 3
        , 1_0(2) -> 1
        , 1_1(2) -> 3
        , m_0(2) -> 1
        , m_1(2) -> 4
        , r1_0(2) -> 1
        , b_0(2) -> 1
        , qr_0(2) -> 2
        , qr_1(3) -> 1
        , qr_1(3) -> 3
        , ql_0(2) -> 2
        , ql_1(3) -> 1
        , ql_1(3) -> 3
        , ql_1(4) -> 1
        , ql_1(4) -> 4}