Problem Secret 06 SRS aprove00

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 SRS aprove00

stdout:

YES(?,O(n^1))

Problem:
a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1))))))))))
b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1))))))))))))
c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1)))))))))
p(p(s(x1))) -> p(x1)
p(s(x1)) -> x1

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    p1(60) -> 61*
    p1(35) -> 36*
    p1(30) -> 31*
    p1(20) -> 21*
    p1(62) -> 63*
    p1(34) -> 35*
    p1(19) -> 20*
    p1(28) -> 29*
    p1(23) -> 24*
    s1(25) -> 26*
    s1(37) -> 38*
    s1(32) -> 33*
    s1(22) -> 23*
    s1(17) -> 18*
    s1(59) -> 60*
    s1(29) -> 30*
    s1(24) -> 25*
    s1(61) -> 62*
    s1(36) -> 37*
    s1(26) -> 27*
    s1(38) -> 39*
    s1(33) -> 34*
    s1(18) -> 19*
    a1(58) -> 59*
    c1(31) -> 32*
    b1(21) -> 22*
    p2(66) -> 67*
    p2(68) -> 69*
    a0(1) -> 2*
    s0(1) -> 1*
    p0(1) -> 5*
    b0(1) -> 3*
    c0(1) -> 4*
    1 -> 5,17
    17 -> 67,21,29
    18 -> 20,66,28
    22 -> 24*
    27 -> 59,61,4,2
    29 -> 31*
    31 -> 58*
    32 -> 69*
    33 -> 35,68
    39 -> 22,24,3
    59 -> 61*
    61 -> 63*
    63 -> 32,4
    67 -> 21*
    69 -> 36*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 SRS aprove00

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 SRS aprove00

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(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1))))))))))
     , b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1))))))))))))
     , c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1)))))))))
     , p(p(s(x1))) -> p(x1)
     , p(s(x1)) -> 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:
         {  a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1))))))))))
          , b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1))))))))))))
          , c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1)))))))))
          , p(p(s(x1))) -> p(x1)
          , p(s(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(15) -> 1
        , a_1(15) -> 5
        , a_1(15) -> 14
        , a_1(15) -> 19
        , a_1(15) -> 21
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 8
        , s_0(2) -> 15
        , s_0(2) -> 17
        , s_1(2) -> 9
        , s_1(2) -> 11
        , s_1(3) -> 1
        , s_1(3) -> 5
        , s_1(3) -> 7
        , s_1(3) -> 14
        , s_1(3) -> 19
        , s_1(3) -> 21
        , s_1(4) -> 3
        , s_1(5) -> 4
        , s_1(7) -> 6
        , s_1(11) -> 10
        , s_1(13) -> 12
        , s_1(14) -> 6
        , s_1(14) -> 13
        , s_1(17) -> 16
        , s_1(19) -> 18
        , s_1(21) -> 20
        , p_0(2) -> 1
        , p_1(6) -> 5
        , p_1(9) -> 8
        , p_1(10) -> 9
        , p_1(11) -> 15
        , p_1(11) -> 17
        , p_1(12) -> 6
        , p_1(16) -> 15
        , p_1(18) -> 1
        , p_1(18) -> 5
        , p_1(18) -> 14
        , p_1(20) -> 1
        , p_1(20) -> 5
        , p_1(20) -> 14
        , p_1(20) -> 19
        , p_2(11) -> 8
        , p_2(13) -> 5
        , b_0(2) -> 1
        , b_1(8) -> 5
        , b_1(8) -> 7
        , c_0(2) -> 1
        , c_1(15) -> 5
        , c_1(15) -> 14}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 SRS aprove00

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 SRS aprove00

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(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1))))))))))
     , b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1))))))))))))
     , c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1)))))))))
     , p(p(s(x1))) -> p(x1)
     , p(s(x1)) -> 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:
         {  a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1))))))))))
          , b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1))))))))))))
          , c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1)))))))))
          , p(p(s(x1))) -> p(x1)
          , p(s(x1)) -> x1}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(15) -> 1
        , a_1(15) -> 5
        , a_1(15) -> 14
        , a_1(15) -> 19
        , a_1(15) -> 21
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 8
        , s_0(2) -> 15
        , s_0(2) -> 17
        , s_1(2) -> 9
        , s_1(2) -> 11
        , s_1(3) -> 1
        , s_1(3) -> 5
        , s_1(3) -> 7
        , s_1(3) -> 14
        , s_1(3) -> 19
        , s_1(3) -> 21
        , s_1(4) -> 3
        , s_1(5) -> 4
        , s_1(7) -> 6
        , s_1(11) -> 10
        , s_1(13) -> 12
        , s_1(14) -> 6
        , s_1(14) -> 13
        , s_1(17) -> 16
        , s_1(19) -> 18
        , s_1(21) -> 20
        , p_0(2) -> 1
        , p_1(6) -> 5
        , p_1(9) -> 8
        , p_1(10) -> 9
        , p_1(11) -> 15
        , p_1(11) -> 17
        , p_1(12) -> 6
        , p_1(16) -> 15
        , p_1(18) -> 1
        , p_1(18) -> 5
        , p_1(18) -> 14
        , p_1(20) -> 1
        , p_1(20) -> 5
        , p_1(20) -> 14
        , p_1(20) -> 19
        , p_2(11) -> 8
        , p_2(13) -> 5
        , b_0(2) -> 1
        , b_1(8) -> 5
        , b_1(8) -> 7
        , c_0(2) -> 1
        , c_1(15) -> 5
        , c_1(15) -> 14}