Problem Secret 06 TRS 4

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 TRS 4

stdout:

YES(?,O(n^1))

Problem:
c(c(b(c(x)))) -> b(a(0(),c(x)))
c(c(x)) -> b(c(b(c(x))))
a(0(),x) -> c(c(x))

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    c1(2) -> 6*
    c1(6) -> 4*
    c1(1) -> 6*
    b2(10) -> 11*
    b2(12) -> 4*
    c2(2) -> 10*
    c2(11) -> 12*
    c2(1) -> 10*
    c0(2) -> 3*
    c0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    a0(1,2) -> 4*
    a0(2,1) -> 4*
    a0(1,1) -> 4*
    a0(2,2) -> 4*
    00() -> 2*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 TRS 4

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 TRS 4

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:
    {  c(c(b(c(x)))) -> b(a(0(), c(x)))
     , c(c(x)) -> b(c(b(c(x))))
     , a(0(), x) -> c(c(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:
         {  c(c(b(c(x)))) -> b(a(0(), c(x)))
          , c(c(x)) -> b(c(b(c(x))))
          , a(0(), x) -> c(c(x))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  c_0(2) -> 1
        , c_1(2) -> 3
        , c_1(3) -> 1
        , c_2(2) -> 6
        , c_2(5) -> 4
        , b_0(2) -> 2
        , b_2(4) -> 1
        , b_2(6) -> 5
        , a_0(2, 2) -> 1
        , 0_0() -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 TRS 4

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Secret 06 TRS 4

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  c(c(b(c(x)))) -> b(a(0(), c(x)))
     , c(c(x)) -> b(c(b(c(x))))
     , a(0(), x) -> c(c(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:
         {  c(c(b(c(x)))) -> b(a(0(), c(x)))
          , c(c(x)) -> b(c(b(c(x))))
          , a(0(), x) -> c(c(x))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  c_0(2) -> 1
        , c_1(2) -> 3
        , c_1(3) -> 1
        , c_2(2) -> 6
        , c_2(5) -> 4
        , b_0(2) -> 2
        , b_2(4) -> 1
        , b_2(6) -> 5
        , a_0(2, 2) -> 1
        , 0_0() -> 2}