Problem SK90 2.49

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {7,6,5,4}
   transitions:
    b1(20) -> 21*
    b1(26) -> 27*
    b1(28) -> 29*
    c1(10) -> 11*
    c1(12) -> 13*
    c1(18) -> 19*
    a0(2) -> 4*
    a0(1) -> 4*
    a0(3) -> 4*
    c0(2) -> 1*
    c0(1) -> 1*
    c0(3) -> 1*
    d0(2) -> 2*
    d0(1) -> 2*
    d0(3) -> 2*
    u0(2) -> 5*
    u0(1) -> 5*
    u0(3) -> 5*
    b0(2) -> 3*
    b0(1) -> 3*
    b0(3) -> 3*
    v0(2) -> 6*
    v0(1) -> 6*
    v0(3) -> 6*
    w0(2) -> 7*
    w0(1) -> 7*
    w0(3) -> 7*
    1 -> 26,12
    2 -> 20,10
    3 -> 28,18
    11 -> 4*
    13 -> 4*
    19 -> 4*
    21 -> 7,6,5
    27 -> 7,6,5
    29 -> 7,6,5
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

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

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , c_0(2) -> 2
        , c_1(2) -> 1
        , d_0(2) -> 2
        , u_0(2) -> 1
        , b_0(2) -> 2
        , b_1(2) -> 1
        , v_0(2) -> 1
        , w_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

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

Proof Output:
  'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with perSymbol-enrichment and initial automaton 'match''
     ----------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  a(c(d(x))) -> c(x)
          , u(b(d(d(x)))) -> b(x)
          , v(a(a(x))) -> u(v(x))
          , v(a(c(x))) -> u(b(d(x)))
          , v(c(x)) -> b(x)
          , w(a(a(x))) -> u(w(x))
          , w(a(c(x))) -> u(b(d(x)))
          , w(c(x)) -> b(x)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , a_0(3) -> 1
        , a_0(5) -> 1
        , c_0(2) -> 2
        , c_0(3) -> 2
        , c_0(5) -> 2
        , c_1(2) -> 1
        , c_1(3) -> 1
        , c_1(5) -> 1
        , d_0(2) -> 3
        , d_0(3) -> 3
        , d_0(5) -> 3
        , u_0(2) -> 4
        , u_0(3) -> 4
        , u_0(5) -> 4
        , b_0(2) -> 5
        , b_0(3) -> 5
        , b_0(5) -> 5
        , b_1(2) -> 4
        , b_1(2) -> 6
        , b_1(2) -> 7
        , b_1(3) -> 4
        , b_1(3) -> 6
        , b_1(3) -> 7
        , b_1(5) -> 4
        , b_1(5) -> 6
        , b_1(5) -> 7
        , v_0(2) -> 6
        , v_0(3) -> 6
        , v_0(5) -> 6
        , w_0(2) -> 7
        , w_0(3) -> 7
        , w_0(5) -> 7}

Tool pair1rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

Certificate: YES(?,O(n^1))

Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
  The processor is not applicable, reason is:
   Input problem is not restricted to innermost rewriting

  We abort the transformation and continue with the subprocessor on the problem

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

  1) 'Fastest' proved the goal fastest:

     'Fastest' proved the goal fastest:

     'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:

     The problem is match-bounded by 1.
     The enriched problem is compatible with the following automaton:
     {  a_0(2) -> 1
      , a_0(3) -> 1
      , a_0(5) -> 1
      , c_0(2) -> 2
      , c_0(3) -> 2
      , c_0(5) -> 2
      , c_1(2) -> 1
      , c_1(3) -> 1
      , c_1(5) -> 1
      , d_0(2) -> 3
      , d_0(3) -> 3
      , d_0(5) -> 3
      , u_0(2) -> 4
      , u_0(3) -> 4
      , u_0(5) -> 4
      , b_0(2) -> 5
      , b_0(3) -> 5
      , b_0(5) -> 5
      , b_1(2) -> 4
      , b_1(2) -> 6
      , b_1(2) -> 7
      , b_1(3) -> 4
      , b_1(3) -> 6
      , b_1(3) -> 7
      , b_1(5) -> 4
      , b_1(5) -> 6
      , b_1(5) -> 7
      , v_0(2) -> 6
      , v_0(3) -> 6
      , v_0(5) -> 6
      , w_0(2) -> 7
      , w_0(3) -> 7
      , w_0(5) -> 7}


Hurray, we answered YES(?,O(n^1))

Tool pair2rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

Certificate: YES(?,O(n^1))

Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
  The processor is not applicable, reason is:
   Input problem is not restricted to innermost rewriting

  We abort the transformation and continue with the subprocessor on the problem

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

  1) 'Fastest' proved the goal fastest:

     'Fastest' proved the goal fastest:

     'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:

     The problem is match-bounded by 1.
     The enriched problem is compatible with the following automaton:
     {  a_0(2) -> 1
      , c_0(2) -> 2
      , c_1(2) -> 1
      , d_0(2) -> 2
      , u_0(2) -> 1
      , b_0(2) -> 2
      , b_1(2) -> 1
      , v_0(2) -> 1
      , w_0(2) -> 1}


Hurray, we answered YES(?,O(n^1))

Tool pair3irc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  The input problem contains no overlaps that give rise to inapplicable rules.

  We abort the transformation and continue with the subprocessor on the problem

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: innermost

  1) 'Fastest' proved the goal fastest:

     'Fastest' proved the goal fastest:

     'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:

     The problem is match-bounded by 1.
     The enriched problem is compatible with the following automaton:
     {  a_0(2) -> 1
      , a_0(3) -> 1
      , a_0(5) -> 1
      , c_0(2) -> 2
      , c_0(3) -> 2
      , c_0(5) -> 2
      , c_1(2) -> 1
      , c_1(3) -> 1
      , c_1(5) -> 1
      , d_0(2) -> 3
      , d_0(3) -> 3
      , d_0(5) -> 3
      , u_0(2) -> 4
      , u_0(3) -> 4
      , u_0(5) -> 4
      , b_0(2) -> 5
      , b_0(3) -> 5
      , b_0(5) -> 5
      , b_1(2) -> 4
      , b_1(2) -> 6
      , b_1(2) -> 7
      , b_1(3) -> 4
      , b_1(3) -> 6
      , b_1(3) -> 7
      , b_1(5) -> 4
      , b_1(5) -> 6
      , b_1(5) -> 7
      , v_0(2) -> 6
      , v_0(3) -> 6
      , v_0(5) -> 6
      , w_0(2) -> 7
      , w_0(3) -> 7
      , w_0(5) -> 7}


Hurray, we answered YES(?,O(n^1))

Tool pair3rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

Certificate: YES(?,O(n^1))

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  The processor is not applicable, reason is:
   Input problem is not restricted to innermost rewriting

  We abort the transformation and continue with the subprocessor on the problem

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: none

  1) 'Fastest' proved the goal fastest:

     'Fastest' proved the goal fastest:

     'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:

     The problem is match-bounded by 1.
     The enriched problem is compatible with the following automaton:
     {  a_0(2) -> 1
      , c_0(2) -> 2
      , c_1(2) -> 1
      , d_0(2) -> 2
      , u_0(2) -> 1
      , b_0(2) -> 2
      , b_1(2) -> 1
      , v_0(2) -> 1
      , w_0(2) -> 1}


Hurray, we answered YES(?,O(n^1))

Tool rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

Tool tup3irc

Execution Time	7.242489e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.49

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
  The input problem contains no overlaps that give rise to inapplicable rules.

  We abort the transformation and continue with the subprocessor on the problem

  Strict Trs:
    {  a(c(d(x))) -> c(x)
     , u(b(d(d(x)))) -> b(x)
     , v(a(a(x))) -> u(v(x))
     , v(a(c(x))) -> u(b(d(x)))
     , v(c(x)) -> b(x)
     , w(a(a(x))) -> u(w(x))
     , w(a(c(x))) -> u(b(d(x)))
     , w(c(x)) -> b(x)}
  StartTerms: basic terms
  Strategy: innermost

  1) 'Fastest' proved the goal fastest:

     'Fastest' proved the goal fastest:

     'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:

     The problem is match-bounded by 1.
     The enriched problem is compatible with the following automaton:
     {  a_0(2) -> 1
      , c_0(2) -> 2
      , c_1(2) -> 1
      , d_0(2) -> 2
      , u_0(2) -> 1
      , b_0(2) -> 2
      , b_1(2) -> 1
      , v_0(2) -> 1
      , w_0(2) -> 1}


Hurray, we answered YES(?,O(n^1))