Problem Transformed CSR 04 Ex9 BLR02 L

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

Problem:
filter(cons(X),0(),M) -> cons(0())
filter(cons(X),s(N),M) -> cons(X)
sieve(cons(0())) -> cons(0())
sieve(cons(s(N))) -> cons(s(N))
nats(N) -> cons(N)
zprimes() -> sieve(nats(s(s(0()))))

Proof:
Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5,4}
   transitions:
    sieve1(12) -> 7*
    nats1(11) -> 12*
    s1(10) -> 11*
    s1(2) -> 9*
    s1(9) -> 10*
    s1(1) -> 9*
    s1(3) -> 9*
    01() -> 9*
    cons1(2) -> 6,4
    cons1(9) -> 5,4
    cons1(1) -> 6,4
    cons1(3) -> 6,4
    cons2(16) -> 7*
    cons2(11) -> 12*
    s2(10) -> 16*
    filter0(1,1,1) -> 4*
    filter0(1,3,1) -> 4*
    filter0(1,2,3) -> 4*
    filter0(2,2,1) -> 4*
    filter0(2,1,3) -> 4*
    filter0(2,3,3) -> 4*
    filter0(3,1,1) -> 4*
    filter0(1,1,2) -> 4*
    filter0(3,3,1) -> 4*
    filter0(1,3,2) -> 4*
    filter0(3,2,3) -> 4*
    filter0(2,2,2) -> 4*
    filter0(3,1,2) -> 4*
    filter0(3,3,2) -> 4*
    filter0(1,2,1) -> 4*
    filter0(1,1,3) -> 4*
    filter0(1,3,3) -> 4*
    filter0(2,1,1) -> 4*
    filter0(2,3,1) -> 4*
    filter0(2,2,3) -> 4*
    filter0(3,2,1) -> 4*
    filter0(1,2,2) -> 4*
    filter0(3,1,3) -> 4*
    filter0(3,3,3) -> 4*
    filter0(2,1,2) -> 4*
    filter0(2,3,2) -> 4*
    filter0(3,2,2) -> 4*
    cons0(2) -> 1*
    cons0(1) -> 1*
    cons0(3) -> 1*
    00() -> 2*
    s0(2) -> 3*
    s0(1) -> 3*
    s0(3) -> 3*
    sieve0(2) -> 5*
    sieve0(1) -> 5*
    sieve0(3) -> 5*
    nats0(2) -> 6*
    nats0(1) -> 6*
    nats0(3) -> 6*
    zprimes0() -> 7*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 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:
    {  filter(cons(X), 0(), M) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , sieve(cons(0())) -> cons(0())
     , sieve(cons(s(N))) -> cons(s(N))
     , nats(N) -> cons(N)
     , zprimes() -> sieve(nats(s(s(0()))))}

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:
         {  filter(cons(X), 0(), M) -> cons(0())
          , filter(cons(X), s(N), M) -> cons(X)
          , sieve(cons(0())) -> cons(0())
          , sieve(cons(s(N))) -> cons(s(N))
          , nats(N) -> cons(N)
          , zprimes() -> sieve(nats(s(s(0()))))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  filter_0(2, 2, 2) -> 1
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , cons_1(3) -> 1
        , cons_2(5) -> 4
        , cons_2(7) -> 1
        , 0_0() -> 2
        , 0_1() -> 3
        , s_0(2) -> 2
        , s_1(2) -> 2
        , s_1(3) -> 6
        , s_1(6) -> 5
        , s_2(6) -> 7
        , sieve_0(2) -> 1
        , sieve_1(4) -> 1
        , nats_0(2) -> 1
        , nats_1(5) -> 4
        , zprimes_0() -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 L

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex9 BLR02 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:
    {  filter(cons(X), 0(), M) -> cons(0())
     , filter(cons(X), s(N), M) -> cons(X)
     , sieve(cons(0())) -> cons(0())
     , sieve(cons(s(N))) -> cons(s(N))
     , nats(N) -> cons(N)
     , zprimes() -> sieve(nats(s(s(0()))))}

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:
         {  filter(cons(X), 0(), M) -> cons(0())
          , filter(cons(X), s(N), M) -> cons(X)
          , sieve(cons(0())) -> cons(0())
          , sieve(cons(s(N))) -> cons(s(N))
          , nats(N) -> cons(N)
          , zprimes() -> sieve(nats(s(s(0()))))}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  filter_0(2, 2, 2) -> 1
        , cons_0(2) -> 2
        , cons_1(2) -> 1
        , cons_1(3) -> 1
        , cons_2(5) -> 4
        , cons_2(7) -> 1
        , 0_0() -> 2
        , 0_1() -> 3
        , s_0(2) -> 2
        , s_1(2) -> 2
        , s_1(3) -> 6
        , s_1(6) -> 5
        , s_2(6) -> 7
        , sieve_0(2) -> 1
        , sieve_1(4) -> 1
        , nats_0(2) -> 1
        , nats_1(5) -> 4
        , zprimes_0() -> 1}