Problem Transformed CSR 04 ExProp7 Luc06 Z

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 Z

stdout:

YES(?,O(n^1))

Problem:
f(0()) -> cons(0(),n__f(s(0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
f(X) -> n__f(X)
activate(n__f(X)) -> f(X)
activate(X) -> X

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5}
   transitions:
    f1(15) -> 7,5
    f1(2) -> 7*
    f1(4) -> 7*
    f1(1) -> 7*
    f1(3) -> 7*
    n__f1(2) -> 5*
    n__f1(9) -> 10*
    n__f1(4) -> 5*
    n__f1(1) -> 5*
    n__f1(3) -> 5*
    p1(9) -> 15*
    s1(8) -> 9*
    01() -> 8*
    cons1(8,10) -> 7,5
    n__f2(15) -> 7,5
    n__f2(17) -> 18*
    n__f2(2) -> 7*
    n__f2(4) -> 7*
    n__f2(1) -> 7*
    n__f2(3) -> 7*
    cons2(16,18) -> 5,7
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    02() -> 16*
    00() -> 1*
    s2(16) -> 17*
    cons0(3,1) -> 2*
    cons0(3,3) -> 2*
    cons0(4,2) -> 2*
    cons0(4,4) -> 2*
    cons0(1,2) -> 2*
    cons0(1,4) -> 2*
    cons0(2,1) -> 2*
    cons0(2,3) -> 2*
    cons0(3,2) -> 2*
    cons0(3,4) -> 2*
    cons0(4,1) -> 2*
    cons0(4,3) -> 2*
    cons0(1,1) -> 2*
    cons0(1,3) -> 2*
    cons0(2,2) -> 2*
    cons0(2,4) -> 2*
    n__f0(2) -> 3*
    n__f0(4) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    s0(2) -> 4*
    s0(4) -> 4*
    s0(1) -> 4*
    s0(3) -> 4*
    p0(2) -> 6*
    p0(4) -> 6*
    p0(1) -> 6*
    p0(3) -> 6*
    activate0(2) -> 7*
    activate0(4) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,6
    2 -> 7,6
    3 -> 7,6
    4 -> 7,6
    8 -> 15*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 Z

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(0()) -> cons(0(), n__f(s(0())))
     , f(s(0())) -> f(p(s(0())))
     , p(s(X)) -> X
     , f(X) -> n__f(X)
     , activate(n__f(X)) -> f(X)
     , activate(X) -> 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:
         {  f(0()) -> cons(0(), n__f(s(0())))
          , f(s(0())) -> f(p(s(0())))
          , p(s(X)) -> X
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(X)
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_1(7) -> 1
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 3
        , 0_1() -> 6
        , 0_1() -> 7
        , 0_2() -> 8
        , 0_2() -> 11
        , cons_0(2, 2) -> 1
        , cons_0(2, 2) -> 2
        , cons_1(3, 4) -> 1
        , cons_2(8, 9) -> 1
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_1(5) -> 4
        , n__f_2(2) -> 1
        , n__f_2(7) -> 1
        , n__f_2(10) -> 9
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_1(6) -> 5
        , s_2(11) -> 10
        , p_0(2) -> 1
        , p_1(5) -> 7
        , activate_0(2) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 Z

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(0()) -> cons(0(), n__f(s(0())))
     , f(s(0())) -> f(p(s(0())))
     , p(s(X)) -> X
     , f(X) -> n__f(X)
     , activate(n__f(X)) -> f(X)
     , activate(X) -> 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:
         {  f(0()) -> cons(0(), n__f(s(0())))
          , f(s(0())) -> f(p(s(0())))
          , p(s(X)) -> X
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(X)
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_1(7) -> 1
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 3
        , 0_1() -> 6
        , 0_1() -> 7
        , 0_2() -> 8
        , 0_2() -> 11
        , cons_0(2, 2) -> 1
        , cons_0(2, 2) -> 2
        , cons_1(3, 4) -> 1
        , cons_2(8, 9) -> 1
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_1(5) -> 4
        , n__f_2(2) -> 1
        , n__f_2(7) -> 1
        , n__f_2(10) -> 9
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_1(6) -> 5
        , s_2(11) -> 10
        , p_0(2) -> 1
        , p_1(5) -> 7
        , activate_0(2) -> 1}