Problem Transformed CSR 04 Ex6 Luc98 L

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 L

stdout:

YES(?,O(n^1))

Problem:
first(0(),X) -> nil()
first(s(X),cons(Y)) -> cons(Y)
from(X) -> cons(X)

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    cons1(2) -> 6,5
    cons1(4) -> 6,5
    cons1(1) -> 6,5
    cons1(3) -> 6,5
    nil1() -> 5*
    first0(3,1) -> 5*
    first0(3,3) -> 5*
    first0(4,2) -> 5*
    first0(4,4) -> 5*
    first0(1,2) -> 5*
    first0(1,4) -> 5*
    first0(2,1) -> 5*
    first0(2,3) -> 5*
    first0(3,2) -> 5*
    first0(3,4) -> 5*
    first0(4,1) -> 5*
    first0(4,3) -> 5*
    first0(1,1) -> 5*
    first0(1,3) -> 5*
    first0(2,2) -> 5*
    first0(2,4) -> 5*
    00() -> 1*
    nil0() -> 2*
    s0(2) -> 3*
    s0(4) -> 3*
    s0(1) -> 3*
    s0(3) -> 3*
    cons0(2) -> 4*
    cons0(4) -> 4*
    cons0(1) -> 4*
    cons0(3) -> 4*
    from0(2) -> 6*
    from0(4) -> 6*
    from0(1) -> 6*
    from0(3) -> 6*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex6 Luc98 L

stdout:

YES(?,O(1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 L

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:
    {  first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)
     , from(X) -> cons(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:
         {  first(0(), X) -> nil()
          , first(s(X), cons(Y)) -> cons(Y)
          , from(X) -> cons(X)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  first_0(2, 2) -> 1
        , 0_0() -> 2
        , nil_0() -> 2
        , nil_1() -> 1
        , s_0(2) -> 2
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , from_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(1))
Input	Transformed CSR 04 Ex6 Luc98 L

stdout:

YES(?,O(1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 L

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)
     , from(X) -> cons(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:
         {  first(0(), X) -> nil()
          , first(s(X), cons(Y)) -> cons(Y)
          , from(X) -> cons(X)}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  first_0(2, 2) -> 1
        , 0_0() -> 2
        , nil_0() -> 2
        , nil_1() -> 1
        , s_0(2) -> 2
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , from_0(2) -> 1}