Problem Zantema 05 z26

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 05 z26

stdout:

YES(?,O(n^1))

Problem:
a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
f(a(x),a(y)) -> a(f(x,y))
f(b(x),b(y)) -> b(f(x,y))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(5) -> 5,3
    f1(1,1) -> 5*
    a0(1) -> 2*
    f0(1,1) -> 3*
    b0(1) -> 1*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 05 z26

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 05 z26

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(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
     , f(a(x), a(y)) -> a(f(x, y))
     , f(b(x), b(y)) -> b(f(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:
         {  a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
          , f(a(x), a(y)) -> a(f(x, y))
          , f(b(x), b(y)) -> b(f(x, y))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , f_0(2, 2) -> 1
        , f_1(2, 2) -> 3
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 05 z26

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 05 z26

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(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
     , f(a(x), a(y)) -> a(f(x, y))
     , f(b(x), b(y)) -> b(f(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:
         {  a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y))))))
          , f(a(x), a(y)) -> a(f(x, y))
          , f(b(x), b(y)) -> b(f(x, y))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  a_0(2) -> 1
        , f_0(2, 2) -> 1
        , f_1(2, 2) -> 3
        , b_0(2) -> 2
        , b_1(3) -> 1
        , b_1(3) -> 3}