Problem Zantema 08 yoyo 3

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 yoyo 3

stdout:

YES(?,O(n^1))

Problem:
a(a(a(x))) -> c()
b(u(x)) -> b(d(x))
d(a(x)) -> a(d(x))
d(b(x)) -> u(a(b(x)))
a(u(x)) -> u(a(x))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    u1(17) -> 18*
    a1(24) -> 25*
    a1(16) -> 17*
    b1(7) -> 8*
    d1(14) -> 15*
    d1(6) -> 7*
    a0(2) -> 3*
    a0(1) -> 3*
    c0() -> 1*
    b0(2) -> 4*
    b0(1) -> 4*
    u0(2) -> 2*
    u0(1) -> 2*
    d0(2) -> 5*
    d0(1) -> 5*
    1 -> 24,14
    2 -> 16,6
    8 -> 4*
    15 -> 7*
    18 -> 17,3
    25 -> 17*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 yoyo 3

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 yoyo 3

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(a(a(x))) -> c()
     , b(u(x)) -> b(d(x))
     , d(a(x)) -> a(d(x))
     , d(b(x)) -> u(a(b(x)))
     , a(u(x)) -> u(a(x))}

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(a(a(x))) -> c()
          , b(u(x)) -> b(d(x))
          , d(a(x)) -> a(d(x))
          , d(b(x)) -> u(a(b(x)))
          , a(u(x)) -> u(a(x))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 4
        , c_0() -> 2
        , b_0(2) -> 1
        , b_1(3) -> 1
        , u_0(2) -> 2
        , u_1(4) -> 1
        , u_1(4) -> 4
        , d_0(2) -> 1
        , d_1(2) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 yoyo 3

stdout:

YES(?,O(n^1))
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 08 yoyo 3

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(a(a(x))) -> c()
     , b(u(x)) -> b(d(x))
     , d(a(x)) -> a(d(x))
     , d(b(x)) -> u(a(b(x)))
     , a(u(x)) -> u(a(x))}

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(a(a(x))) -> c()
          , b(u(x)) -> b(d(x))
          , d(a(x)) -> a(d(x))
          , d(b(x)) -> u(a(b(x)))
          , a(u(x)) -> u(a(x))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_1(2) -> 4
        , c_0() -> 2
        , b_0(2) -> 1
        , b_1(3) -> 1
        , u_0(2) -> 2
        , u_1(4) -> 1
        , u_1(4) -> 4
        , d_0(2) -> 1
        , d_1(2) -> 3}