Problem Zantema 04 z074

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z074

stdout:

YES(?,O(n^1))

Problem:
r(r(x1)) -> s(r(x1))
r(s(x1)) -> s(r(x1))
r(n(x1)) -> s(r(x1))
r(b(x1)) -> u(s(b(x1)))
r(u(x1)) -> u(r(x1))
s(u(x1)) -> u(s(x1))
n(u(x1)) -> u(n(x1))
t(r(u(x1))) -> t(c(r(x1)))
t(s(u(x1))) -> t(c(r(x1)))
t(n(u(x1))) -> t(c(r(x1)))
c(u(x1)) -> u(c(x1))
c(s(x1)) -> s(c(x1))
c(r(x1)) -> r(c(x1))
c(n(x1)) -> n(c(x1))
c(n(x1)) -> n(x1)

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {7,6,5,4,3}
   transitions:
    u1(52) -> 53*
    u1(42) -> 43*
    u1(32) -> 33*
    u1(14) -> 15*
    c1(54) -> 55*
    c1(51) -> 52*
    n1(44) -> 45*
    n1(41) -> 42*
    s1(34) -> 35*
    s1(31) -> 32*
    s1(13) -> 14*
    r1(22) -> 23*
    r1(24) -> 25*
    b1(12) -> 13*
    b1(16) -> 17*
    r0(2) -> 3*
    r0(1) -> 3*
    s0(2) -> 4*
    s0(1) -> 4*
    n0(2) -> 5*
    n0(1) -> 5*
    b0(2) -> 1*
    b0(1) -> 1*
    u0(2) -> 2*
    u0(1) -> 2*
    t0(2) -> 6*
    t0(1) -> 6*
    c0(2) -> 7*
    c0(1) -> 7*
    1 -> 54,44,34,24,16
    2 -> 51,41,31,22,12
    15 -> 23,25,14,3
    17 -> 13*
    23 -> 14*
    25 -> 14*
    33 -> 32,4
    35 -> 32*
    43 -> 42,5
    45 -> 42*
    53 -> 52,7
    55 -> 52*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z074

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z074

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:
    {  r(r(x1)) -> s(r(x1))
     , r(s(x1)) -> s(r(x1))
     , r(n(x1)) -> s(r(x1))
     , r(b(x1)) -> u(s(b(x1)))
     , r(u(x1)) -> u(r(x1))
     , s(u(x1)) -> u(s(x1))
     , n(u(x1)) -> u(n(x1))
     , t(r(u(x1))) -> t(c(r(x1)))
     , t(s(u(x1))) -> t(c(r(x1)))
     , t(n(u(x1))) -> t(c(r(x1)))
     , c(u(x1)) -> u(c(x1))
     , c(s(x1)) -> s(c(x1))
     , c(r(x1)) -> r(c(x1))
     , c(n(x1)) -> n(c(x1))
     , c(n(x1)) -> n(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:
         {  r(r(x1)) -> s(r(x1))
          , r(s(x1)) -> s(r(x1))
          , r(n(x1)) -> s(r(x1))
          , r(b(x1)) -> u(s(b(x1)))
          , r(u(x1)) -> u(r(x1))
          , s(u(x1)) -> u(s(x1))
          , n(u(x1)) -> u(n(x1))
          , t(r(u(x1))) -> t(c(r(x1)))
          , t(s(u(x1))) -> t(c(r(x1)))
          , t(n(u(x1))) -> t(c(r(x1)))
          , c(u(x1)) -> u(c(x1))
          , c(s(x1)) -> s(c(x1))
          , c(r(x1)) -> r(c(x1))
          , c(n(x1)) -> n(c(x1))
          , c(n(x1)) -> n(x1)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  r_0(2) -> 1
        , r_1(2) -> 3
        , s_0(2) -> 1
        , s_1(2) -> 3
        , s_1(4) -> 3
        , n_0(2) -> 1
        , n_1(2) -> 3
        , b_0(2) -> 2
        , b_1(2) -> 4
        , u_0(2) -> 2
        , u_1(3) -> 1
        , u_1(3) -> 3
        , t_0(2) -> 1
        , c_0(2) -> 1
        , c_1(2) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z074

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 04 z074

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  r(r(x1)) -> s(r(x1))
     , r(s(x1)) -> s(r(x1))
     , r(n(x1)) -> s(r(x1))
     , r(b(x1)) -> u(s(b(x1)))
     , r(u(x1)) -> u(r(x1))
     , s(u(x1)) -> u(s(x1))
     , n(u(x1)) -> u(n(x1))
     , t(r(u(x1))) -> t(c(r(x1)))
     , t(s(u(x1))) -> t(c(r(x1)))
     , t(n(u(x1))) -> t(c(r(x1)))
     , c(u(x1)) -> u(c(x1))
     , c(s(x1)) -> s(c(x1))
     , c(r(x1)) -> r(c(x1))
     , c(n(x1)) -> n(c(x1))
     , c(n(x1)) -> n(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:
         {  r(r(x1)) -> s(r(x1))
          , r(s(x1)) -> s(r(x1))
          , r(n(x1)) -> s(r(x1))
          , r(b(x1)) -> u(s(b(x1)))
          , r(u(x1)) -> u(r(x1))
          , s(u(x1)) -> u(s(x1))
          , n(u(x1)) -> u(n(x1))
          , t(r(u(x1))) -> t(c(r(x1)))
          , t(s(u(x1))) -> t(c(r(x1)))
          , t(n(u(x1))) -> t(c(r(x1)))
          , c(u(x1)) -> u(c(x1))
          , c(s(x1)) -> s(c(x1))
          , c(r(x1)) -> r(c(x1))
          , c(n(x1)) -> n(c(x1))
          , c(n(x1)) -> n(x1)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  r_0(2) -> 1
        , r_1(2) -> 3
        , s_0(2) -> 1
        , s_1(2) -> 3
        , s_1(4) -> 3
        , n_0(2) -> 1
        , n_1(2) -> 3
        , b_0(2) -> 2
        , b_1(2) -> 4
        , u_0(2) -> 2
        , u_1(3) -> 1
        , u_1(3) -> 3
        , t_0(2) -> 1
        , c_0(2) -> 1
        , c_1(2) -> 3}