Problem SK90 2.53

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

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

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    h1(2) -> 4,2,3
    h1(4) -> 4,2,3
    g1(1,1) -> 2*
    f1(1,1) -> 4*
    g2(1,1) -> 4*
    f0(1,1) -> 2*
    g0(1,1) -> 3*
    h0(1) -> 1*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

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

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

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2, 2) -> 1
        , f_1(2, 2) -> 3
        , g_0(2, 2) -> 1
        , g_1(2, 2) -> 1
        , g_2(2, 2) -> 3
        , h_0(2) -> 2
        , h_1(1) -> 1
        , h_1(1) -> 3
        , h_1(3) -> 1
        , h_1(3) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

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

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

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2, 2) -> 1
        , f_1(2, 2) -> 3
        , g_0(2, 2) -> 1
        , g_1(2, 2) -> 1
        , g_2(2, 2) -> 3
        , h_0(2) -> 2
        , h_1(1) -> 1
        , h_1(1) -> 3
        , h_1(3) -> 1
        , h_1(3) -> 3}

Tool pair1rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
     The enriched problem is compatible with the following automaton:
     {  f_0(2, 2) -> 1
      , f_1(2, 2) -> 3
      , g_0(2, 2) -> 1
      , g_1(2, 2) -> 1
      , g_2(2, 2) -> 3
      , h_0(2) -> 2
      , h_1(1) -> 1
      , h_1(1) -> 3
      , h_1(3) -> 1
      , h_1(3) -> 3}


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

Tool pair2rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
     The enriched problem is compatible with the following automaton:
     {  f_0(2, 2) -> 1
      , f_1(2, 2) -> 3
      , g_0(2, 2) -> 1
      , g_1(2, 2) -> 1
      , g_2(2, 2) -> 3
      , h_0(2) -> 2
      , h_1(1) -> 1
      , h_1(1) -> 3
      , h_1(3) -> 1
      , h_1(3) -> 3}


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

Tool pair3irc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
     The enriched problem is compatible with the following automaton:
     {  f_0(2, 2) -> 1
      , f_1(2, 2) -> 3
      , g_0(2, 2) -> 1
      , g_1(2, 2) -> 1
      , g_2(2, 2) -> 3
      , h_0(2) -> 2
      , h_1(1) -> 1
      , h_1(1) -> 3
      , h_1(3) -> 1
      , h_1(3) -> 3}


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

Tool pair3rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
     The enriched problem is compatible with the following automaton:
     {  f_0(2, 2) -> 1
      , f_1(2, 2) -> 3
      , g_0(2, 2) -> 1
      , g_1(2, 2) -> 1
      , g_2(2, 2) -> 3
      , h_0(2) -> 2
      , h_1(1) -> 1
      , h_1(1) -> 3
      , h_1(3) -> 1
      , h_1(3) -> 3}


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

Tool rc

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
  The enriched problem is compatible with the following automaton:
  {  f_0(2, 2) -> 1
   , f_1(2, 2) -> 3
   , g_0(2, 2) -> 1
   , g_1(2, 2) -> 1
   , g_2(2, 2) -> 3
   , h_0(2) -> 2
   , h_1(1) -> 1
   , h_1(1) -> 3
   , h_1(3) -> 1
   , h_1(3) -> 3}

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

Tool tup3irc

Execution Time	0.18813896ms
Answer	YES(?,O(n^1))
Input	SK90 2.53

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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:
    {  f(x, y) -> g(x, y)
     , g(h(x), y) -> h(f(x, y))
     , g(h(x), y) -> h(g(x, y))}
  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 2.
     The enriched problem is compatible with the following automaton:
     {  f_0(2, 2) -> 1
      , f_1(2, 2) -> 3
      , g_0(2, 2) -> 1
      , g_1(2, 2) -> 1
      , g_2(2, 2) -> 3
      , h_0(2) -> 2
      , h_1(1) -> 1
      , h_1(1) -> 3
      , h_1(3) -> 1
      , h_1(3) -> 3}


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