Problem SK90 2.03

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

Problem:
minus(minus(x)) -> x
minus(h(x)) -> h(minus(x))
minus(f(x,y)) -> f(minus(y),minus(x))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    f1(4,4) -> 4,3
    minus1(2) -> 4*
    minus1(1) -> 4*
    h1(4) -> 4,3
    minus0(2) -> 3*
    minus0(1) -> 3*
    h0(2) -> 1*
    h0(1) -> 1*
    f0(1,2) -> 2*
    f0(2,1) -> 2*
    f0(1,1) -> 2*
    f0(2,2) -> 2*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
         {  minus(minus(x)) -> x
          , minus(h(x)) -> h(minus(x))
          , minus(f(x, y)) -> f(minus(y), minus(x))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  minus_0(2) -> 1
        , minus_1(2) -> 3
        , h_0(2) -> 2
        , h_1(3) -> 1
        , h_1(3) -> 3
        , f_0(2, 2) -> 2
        , f_1(3, 3) -> 1
        , f_1(3, 3) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
         {  minus(minus(x)) -> x
          , minus(h(x)) -> h(minus(x))
          , minus(f(x, y)) -> f(minus(y), minus(x))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  minus_0(2) -> 1
        , minus_1(2) -> 3
        , h_0(2) -> 2
        , h_1(3) -> 1
        , h_1(3) -> 3
        , f_0(2, 2) -> 2
        , f_1(3, 3) -> 1
        , f_1(3, 3) -> 3}

Tool pair1rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
     {  minus_0(2) -> 1
      , minus_1(2) -> 3
      , h_0(2) -> 2
      , h_1(3) -> 1
      , h_1(3) -> 3
      , f_0(2, 2) -> 2
      , f_1(3, 3) -> 1
      , f_1(3, 3) -> 3}


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

Tool pair2rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
     {  minus_0(2) -> 1
      , minus_1(2) -> 3
      , h_0(2) -> 2
      , h_1(3) -> 1
      , h_1(3) -> 3
      , f_0(2, 2) -> 2
      , f_1(3, 3) -> 1
      , f_1(3, 3) -> 3}


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

Tool pair3irc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
     {  minus_0(2) -> 1
      , minus_0(3) -> 1
      , minus_1(2) -> 4
      , minus_1(3) -> 4
      , h_0(2) -> 2
      , h_0(3) -> 2
      , h_1(4) -> 1
      , h_1(4) -> 4
      , f_0(2, 2) -> 3
      , f_0(2, 3) -> 3
      , f_0(3, 2) -> 3
      , f_0(3, 3) -> 3
      , f_1(4, 4) -> 1
      , f_1(4, 4) -> 4}


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

Tool pair3rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
     {  minus_0(2) -> 1
      , minus_0(3) -> 1
      , minus_1(2) -> 4
      , minus_1(3) -> 4
      , h_0(2) -> 2
      , h_0(3) -> 2
      , h_1(4) -> 1
      , h_1(4) -> 4
      , f_0(2, 2) -> 3
      , f_0(2, 3) -> 3
      , f_0(3, 2) -> 3
      , f_0(3, 3) -> 3
      , f_1(4, 4) -> 1
      , f_1(4, 4) -> 4}


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

Tool rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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 perSymbol-enrichment and initial automaton 'match' (timeout of 5.0 seconds)' proved the goal fastest:

  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  minus_0(2) -> 1
   , minus_0(3) -> 1
   , minus_1(2) -> 4
   , minus_1(3) -> 4
   , h_0(2) -> 2
   , h_0(3) -> 2
   , h_1(4) -> 1
   , h_1(4) -> 4
   , f_0(2, 2) -> 3
   , f_0(2, 3) -> 3
   , f_0(3, 2) -> 3
   , f_0(3, 3) -> 3
   , f_1(4, 4) -> 1
   , f_1(4, 4) -> 4}

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

Tool tup3irc

Execution Time	7.190299e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.03

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
    {  minus(minus(x)) -> x
     , minus(h(x)) -> h(minus(x))
     , minus(f(x, y)) -> f(minus(y), minus(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:
     {  minus_0(2) -> 1
      , minus_1(2) -> 3
      , h_0(2) -> 2
      , h_1(3) -> 1
      , h_1(3) -> 3
      , f_0(2, 2) -> 2
      , f_1(3, 3) -> 1
      , f_1(3, 3) -> 3}


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