Problem Transformed CSR 04 Ex5 Zan97 Z

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex5 Zan97 Z

stdout:

YES(?,O(n^1))

Problem:
f(X) -> if(X,c(),n__f(true()))
if(true(),X,Y) -> X
if(false(),X,Y) -> activate(Y)
f(X) -> n__f(X)
activate(n__f(X)) -> f(X)
activate(X) -> X

Proof:
Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {7,6,5}
   transitions:
    true3() -> 20*
    f1(2) -> 6,7
    f1(4) -> 6,7
    f1(1) -> 6,7
    f1(3) -> 6,7
    n__f1(2) -> 5*
    n__f1(4) -> 5*
    n__f1(1) -> 5*
    n__f1(8) -> 9*
    n__f1(3) -> 5*
    activate1(15) -> 6,7
    activate1(2) -> 6*
    activate1(9) -> 5*
    activate1(4) -> 6*
    activate1(1) -> 6*
    activate1(3) -> 6*
    if1(1,10,9) -> 5*
    if1(3,10,9) -> 5*
    if1(2,10,9) -> 5*
    if1(4,10,9) -> 5*
    c1() -> 10*
    true1() -> 8*
    n__f2(2) -> 6,7
    n__f2(14) -> 15*
    n__f2(4) -> 6,7
    n__f2(1) -> 6,7
    n__f2(3) -> 6,7
    if2(4,16,15) -> 6,7
    if2(1,16,15) -> 6,7
    if2(3,16,15) -> 6,7
    if2(2,16,15) -> 6,7
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    c2() -> 16*
    if0(3,4,2) -> 6*
    if0(1,1,4) -> 6*
    if0(1,3,4) -> 6*
    if0(4,1,2) -> 6*
    if0(1,1,1) -> 6*
    if0(4,3,2) -> 6*
    if0(1,3,1) -> 6*
    if0(2,2,4) -> 6*
    if0(2,4,4) -> 6*
    if0(1,2,3) -> 6*
    if0(1,4,3) -> 6*
    if0(2,2,1) -> 6*
    if0(2,4,1) -> 6*
    if0(3,1,4) -> 6*
    if0(3,3,4) -> 6*
    if0(2,1,3) -> 6*
    if0(2,3,3) -> 6*
    if0(3,1,1) -> 6*
    if0(1,1,2) -> 6*
    if0(3,3,1) -> 6*
    if0(1,3,2) -> 6*
    if0(4,2,4) -> 6*
    if0(4,4,4) -> 6*
    if0(3,2,3) -> 6*
    if0(3,4,3) -> 6*
    if0(4,2,1) -> 6*
    if0(2,2,2) -> 6*
    if0(4,4,1) -> 6*
    if0(2,4,2) -> 6*
    if0(4,1,3) -> 6*
    if0(4,3,3) -> 6*
    if0(3,1,2) -> 6*
    if0(3,3,2) -> 6*
    if0(1,2,4) -> 6*
    if0(1,4,4) -> 6*
    if0(4,2,2) -> 6*
    if0(1,2,1) -> 6*
    if0(4,4,2) -> 6*
    if0(1,4,1) -> 6*
    if0(2,1,4) -> 6*
    if0(2,3,4) -> 6*
    if0(1,1,3) -> 6*
    if0(1,3,3) -> 6*
    if0(2,1,1) -> 6*
    if0(2,3,1) -> 6*
    if0(3,2,4) -> 6*
    if0(3,4,4) -> 6*
    if0(2,2,3) -> 6*
    if0(2,4,3) -> 6*
    if0(3,2,1) -> 6*
    if0(1,2,2) -> 6*
    if0(3,4,1) -> 6*
    if0(1,4,2) -> 6*
    if0(4,1,4) -> 6*
    if0(4,3,4) -> 6*
    if0(3,1,3) -> 6*
    if0(3,3,3) -> 6*
    if0(4,1,1) -> 6*
    if0(2,1,2) -> 6*
    if0(4,3,1) -> 6*
    if0(2,3,2) -> 6*
    if0(4,2,3) -> 6*
    if0(4,4,3) -> 6*
    if0(3,2,2) -> 6*
    true2() -> 14*
    c0() -> 1*
    f2(14) -> 6,7
    f2(8) -> 5*
    n__f0(2) -> 2*
    n__f0(4) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    n__f3(20) -> 21*
    n__f3(14) -> 6,7
    n__f3(8) -> 5*
    true0() -> 3*
    if3(8,22,21) -> 5*
    if3(14,22,21) -> 6,7
    false0() -> 4*
    c3() -> 22*
    activate0(2) -> 7*
    activate0(4) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,6
    2 -> 7,6
    3 -> 7,6
    4 -> 7,6
    9 -> 5*
    10 -> 5*
    15 -> 6,7
    16 -> 6,7
    22 -> 6,7,5
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex5 Zan97 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex5 Zan97 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(X) -> if(X, c(), n__f(true()))
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> activate(Y)
     , 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(X) -> if(X, c(), n__f(true()))
          , if(true(), X, Y) -> X
          , if(false(), X, Y) -> activate(Y)
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(X)
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_2(5) -> 1
        , f_2(8) -> 1
        , if_0(2, 2, 2) -> 1
        , if_1(2, 3, 4) -> 1
        , if_2(2, 6, 7) -> 1
        , if_3(5, 9, 10) -> 1
        , if_3(8, 9, 10) -> 1
        , c_0() -> 1
        , c_0() -> 2
        , c_1() -> 1
        , c_1() -> 3
        , c_2() -> 1
        , c_2() -> 6
        , c_3() -> 1
        , c_3() -> 9
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_1(5) -> 1
        , n__f_1(5) -> 4
        , n__f_2(2) -> 1
        , n__f_2(8) -> 1
        , n__f_2(8) -> 7
        , n__f_3(5) -> 1
        , n__f_3(8) -> 1
        , n__f_3(11) -> 10
        , true_0() -> 1
        , true_0() -> 2
        , true_1() -> 5
        , true_2() -> 8
        , true_3() -> 11
        , false_0() -> 1
        , false_0() -> 2
        , activate_0(2) -> 1
        , activate_1(2) -> 1
        , activate_1(4) -> 1
        , activate_1(7) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex5 Zan97 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex5 Zan97 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(X) -> if(X, c(), n__f(true()))
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> activate(Y)
     , 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(X) -> if(X, c(), n__f(true()))
          , if(true(), X, Y) -> X
          , if(false(), X, Y) -> activate(Y)
          , f(X) -> n__f(X)
          , activate(n__f(X)) -> f(X)
          , activate(X) -> X}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , f_2(5) -> 1
        , f_2(8) -> 1
        , if_0(2, 2, 2) -> 1
        , if_1(2, 3, 4) -> 1
        , if_2(2, 6, 7) -> 1
        , if_3(5, 9, 10) -> 1
        , if_3(8, 9, 10) -> 1
        , c_0() -> 1
        , c_0() -> 2
        , c_1() -> 1
        , c_1() -> 3
        , c_2() -> 1
        , c_2() -> 6
        , c_3() -> 1
        , c_3() -> 9
        , n__f_0(2) -> 1
        , n__f_0(2) -> 2
        , n__f_1(2) -> 1
        , n__f_1(5) -> 1
        , n__f_1(5) -> 4
        , n__f_2(2) -> 1
        , n__f_2(8) -> 1
        , n__f_2(8) -> 7
        , n__f_3(5) -> 1
        , n__f_3(8) -> 1
        , n__f_3(11) -> 10
        , true_0() -> 1
        , true_0() -> 2
        , true_1() -> 5
        , true_2() -> 8
        , true_3() -> 11
        , false_0() -> 1
        , false_0() -> 2
        , activate_0(2) -> 1
        , activate_1(2) -> 1
        , activate_1(4) -> 1
        , activate_1(7) -> 1}