MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { primes() -> sieve(from(s(s(0()))))
  , sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y)))
  , from(X) -> cons(X, from(s(X)))
  , head(cons(X, Y)) -> X
  , tail(cons(X, Y)) -> Y
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> Y
  , filter(s(s(X)), cons(Y, Z)) ->
    if(divides(s(s(X)), Y),
       filter(s(s(X)), Z),
       cons(Y, filter(X, sieve(Y)))) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { primes^#() -> c_1(sieve^#(from(s(s(0())))))
     , sieve^#(cons(X, Y)) -> c_2(X, filter^#(X, sieve(Y)))
     , filter^#(s(s(X)), cons(Y, Z)) ->
       c_8(if^#(divides(s(s(X)), Y),
                filter(s(s(X)), Z),
                cons(Y, filter(X, sieve(Y)))))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , head^#(cons(X, Y)) -> c_4(X)
     , tail^#(cons(X, Y)) -> c_5(Y)
     , if^#(true(), X, Y) -> c_6(X)
     , if^#(false(), X, Y) -> c_7(Y) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { primes^#() -> c_1(sieve^#(from(s(s(0())))))
     , sieve^#(cons(X, Y)) -> c_2(X, filter^#(X, sieve(Y)))
     , filter^#(s(s(X)), cons(Y, Z)) ->
       c_8(if^#(divides(s(s(X)), Y),
                filter(s(s(X)), Z),
                cons(Y, filter(X, sieve(Y)))))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , head^#(cons(X, Y)) -> c_4(X)
     , tail^#(cons(X, Y)) -> c_5(Y)
     , if^#(true(), X, Y) -> c_6(X)
     , if^#(false(), X, Y) -> c_7(Y) }
   Strict Trs:
     { primes() -> sieve(from(s(s(0()))))
     , sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y)))
     , from(X) -> cons(X, from(s(X)))
     , head(cons(X, Y)) -> X
     , tail(cons(X, Y)) -> Y
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> Y
     , filter(s(s(X)), cons(Y, Z)) ->
       if(divides(s(s(X)), Y),
          filter(s(s(X)), Z),
          cons(Y, filter(X, sieve(Y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3} by applications of
   Pre({3}) = {2,4,5,6,7,8}. Here rules are labeled as follows:
   
     DPs:
       { 1: primes^#() -> c_1(sieve^#(from(s(s(0())))))
       , 2: sieve^#(cons(X, Y)) -> c_2(X, filter^#(X, sieve(Y)))
       , 3: filter^#(s(s(X)), cons(Y, Z)) ->
            c_8(if^#(divides(s(s(X)), Y),
                     filter(s(s(X)), Z),
                     cons(Y, filter(X, sieve(Y)))))
       , 4: from^#(X) -> c_3(X, from^#(s(X)))
       , 5: head^#(cons(X, Y)) -> c_4(X)
       , 6: tail^#(cons(X, Y)) -> c_5(Y)
       , 7: if^#(true(), X, Y) -> c_6(X)
       , 8: if^#(false(), X, Y) -> c_7(Y) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { primes^#() -> c_1(sieve^#(from(s(s(0())))))
     , sieve^#(cons(X, Y)) -> c_2(X, filter^#(X, sieve(Y)))
     , from^#(X) -> c_3(X, from^#(s(X)))
     , head^#(cons(X, Y)) -> c_4(X)
     , tail^#(cons(X, Y)) -> c_5(Y)
     , if^#(true(), X, Y) -> c_6(X)
     , if^#(false(), X, Y) -> c_7(Y) }
   Strict Trs:
     { primes() -> sieve(from(s(s(0()))))
     , sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y)))
     , from(X) -> cons(X, from(s(X)))
     , head(cons(X, Y)) -> X
     , tail(cons(X, Y)) -> Y
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> Y
     , filter(s(s(X)), cons(Y, Z)) ->
       if(divides(s(s(X)), Y),
          filter(s(s(X)), Z),
          cons(Y, filter(X, sieve(Y)))) }
   Weak DPs:
     { filter^#(s(s(X)), cons(Y, Z)) ->
       c_8(if^#(divides(s(s(X)), Y),
                filter(s(s(X)), Z),
                cons(Y, filter(X, sieve(Y))))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..