MAYBE

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

Strict Trs:
  { filter(X1, X2, X3) -> n__filter(X1, X2, X3)
  , filter(cons(X, Y), 0(), M) ->
    cons(0(), n__filter(activate(Y), M, M))
  , filter(cons(X, Y), s(N), M) ->
    cons(X, n__filter(activate(Y), N, M))
  , activate(X) -> X
  , activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3)
  , activate(n__sieve(X)) -> sieve(X)
  , activate(n__nats(X)) -> nats(X)
  , sieve(X) -> n__sieve(X)
  , sieve(cons(0(), Y)) -> cons(0(), n__sieve(activate(Y)))
  , sieve(cons(s(N), Y)) ->
    cons(s(N), n__sieve(filter(activate(Y), N, N)))
  , nats(N) -> cons(N, n__nats(s(N)))
  , nats(X) -> n__nats(X)
  , zprimes() -> sieve(nats(s(s(0())))) }
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 perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-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:
     { filter^#(X1, X2, X3) -> c_1(X1, X2, X3)
     , filter^#(cons(X, Y), 0(), M) -> c_2(activate^#(Y), M, M)
     , filter^#(cons(X, Y), s(N), M) -> c_3(X, activate^#(Y), N, M)
     , activate^#(X) -> c_4(X)
     , activate^#(n__filter(X1, X2, X3)) -> c_5(filter^#(X1, X2, X3))
     , activate^#(n__sieve(X)) -> c_6(sieve^#(X))
     , activate^#(n__nats(X)) -> c_7(nats^#(X))
     , sieve^#(X) -> c_8(X)
     , sieve^#(cons(0(), Y)) -> c_9(activate^#(Y))
     , sieve^#(cons(s(N), Y)) -> c_10(N, filter^#(activate(Y), N, N))
     , nats^#(N) -> c_11(N, N)
     , nats^#(X) -> c_12(X)
     , zprimes^#() -> c_13(sieve^#(nats(s(s(0()))))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { filter^#(X1, X2, X3) -> c_1(X1, X2, X3)
     , filter^#(cons(X, Y), 0(), M) -> c_2(activate^#(Y), M, M)
     , filter^#(cons(X, Y), s(N), M) -> c_3(X, activate^#(Y), N, M)
     , activate^#(X) -> c_4(X)
     , activate^#(n__filter(X1, X2, X3)) -> c_5(filter^#(X1, X2, X3))
     , activate^#(n__sieve(X)) -> c_6(sieve^#(X))
     , activate^#(n__nats(X)) -> c_7(nats^#(X))
     , sieve^#(X) -> c_8(X)
     , sieve^#(cons(0(), Y)) -> c_9(activate^#(Y))
     , sieve^#(cons(s(N), Y)) -> c_10(N, filter^#(activate(Y), N, N))
     , nats^#(N) -> c_11(N, N)
     , nats^#(X) -> c_12(X)
     , zprimes^#() -> c_13(sieve^#(nats(s(s(0()))))) }
   Strict Trs:
     { filter(X1, X2, X3) -> n__filter(X1, X2, X3)
     , filter(cons(X, Y), 0(), M) ->
       cons(0(), n__filter(activate(Y), M, M))
     , filter(cons(X, Y), s(N), M) ->
       cons(X, n__filter(activate(Y), N, M))
     , activate(X) -> X
     , activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3)
     , activate(n__sieve(X)) -> sieve(X)
     , activate(n__nats(X)) -> nats(X)
     , sieve(X) -> n__sieve(X)
     , sieve(cons(0(), Y)) -> cons(0(), n__sieve(activate(Y)))
     , sieve(cons(s(N), Y)) ->
       cons(s(N), n__sieve(filter(activate(Y), N, N)))
     , nats(N) -> cons(N, n__nats(s(N)))
     , nats(X) -> n__nats(X)
     , zprimes() -> sieve(nats(s(s(0())))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..