Problem SK90 2.50

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

Problem:
a(b(x)) -> b(b(a(x)))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {2}
   transitions:
    b1(9) -> 10*
    b1(8) -> 9*
    a1(7) -> 8*
    a0(1) -> 2*
    b0(1) -> 1*
    1 -> 7*
    10 -> 8,2
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

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(b(x)) -> b(b(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(b(x)) -> b(b(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
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 4
        , b_1(4) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

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(b(x)) -> b(b(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(b(x)) -> b(b(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
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 4
        , b_1(4) -> 3}

Tool pair1rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(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(b(x)) -> b(b(a(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_1(2) -> 4
      , b_0(2) -> 2
      , b_1(3) -> 1
      , b_1(3) -> 4
      , b_1(4) -> 3}


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

Tool pair2rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(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(b(x)) -> b(b(a(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_1(2) -> 4
      , b_0(2) -> 2
      , b_1(3) -> 1
      , b_1(3) -> 4
      , b_1(4) -> 3}


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

Tool pair3irc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(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(b(x)) -> b(b(a(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_1(2) -> 4
      , b_0(2) -> 2
      , b_1(3) -> 1
      , b_1(3) -> 4
      , b_1(4) -> 3}


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

Tool pair3rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(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(b(x)) -> b(b(a(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_1(2) -> 4
      , b_0(2) -> 2
      , b_1(3) -> 1
      , b_1(3) -> 4
      , b_1(4) -> 3}


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

Tool rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(x)))}
  StartTerms: basic terms
  Strategy: none

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

Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
  'Fastest' proved the goal fastest:

  'Fastest' proved the goal fastest:

  'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' 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_1(2) -> 4
   , b_0(2) -> 2
   , b_1(3) -> 1
   , b_1(3) -> 4
   , b_1(4) -> 3}

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

Tool tup3irc

Execution Time	6.191683e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.50

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {a(b(x)) -> b(b(a(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(b(x)) -> b(b(a(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_1(2) -> 4
      , b_0(2) -> 2
      , b_1(3) -> 1
      , b_1(3) -> 4
      , b_1(4) -> 3}


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