MAYBE

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

Strict Trs:
  { active(primes()) -> mark(sieve(from(s(s(0())))))
  , active(sieve(X)) -> sieve(active(X))
  , active(sieve(cons(X, Y))) -> mark(cons(X, filter(X, sieve(Y))))
  , active(from(X)) -> mark(cons(X, from(s(X))))
  , active(from(X)) -> from(active(X))
  , active(s(X)) -> s(active(X))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(head(X)) -> head(active(X))
  , active(head(cons(X, Y))) -> mark(X)
  , active(tail(X)) -> tail(active(X))
  , active(tail(cons(X, Y))) -> mark(Y)
  , active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
  , active(if(true(), X, Y)) -> mark(X)
  , active(if(false(), X, Y)) -> mark(Y)
  , active(filter(X1, X2)) -> filter(X1, active(X2))
  , active(filter(X1, X2)) -> filter(active(X1), X2)
  , active(filter(s(s(X)), cons(Y, Z))) ->
    mark(if(divides(s(s(X)), Y),
            filter(s(s(X)), Z),
            cons(Y, filter(X, sieve(Y)))))
  , active(divides(X1, X2)) -> divides(X1, active(X2))
  , active(divides(X1, X2)) -> divides(active(X1), X2)
  , sieve(mark(X)) -> mark(sieve(X))
  , sieve(ok(X)) -> ok(sieve(X))
  , from(mark(X)) -> mark(from(X))
  , from(ok(X)) -> ok(from(X))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , head(mark(X)) -> mark(head(X))
  , head(ok(X)) -> ok(head(X))
  , tail(mark(X)) -> mark(tail(X))
  , tail(ok(X)) -> ok(tail(X))
  , if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
  , if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
  , filter(X1, mark(X2)) -> mark(filter(X1, X2))
  , filter(mark(X1), X2) -> mark(filter(X1, X2))
  , filter(ok(X1), ok(X2)) -> ok(filter(X1, X2))
  , divides(X1, mark(X2)) -> mark(divides(X1, X2))
  , divides(mark(X1), X2) -> mark(divides(X1, X2))
  , divides(ok(X1), ok(X2)) -> ok(divides(X1, X2))
  , proper(primes()) -> ok(primes())
  , proper(sieve(X)) -> sieve(proper(X))
  , proper(from(X)) -> from(proper(X))
  , proper(s(X)) -> s(proper(X))
  , proper(0()) -> ok(0())
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(head(X)) -> head(proper(X))
  , proper(tail(X)) -> tail(proper(X))
  , proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
  , proper(true()) -> ok(true())
  , proper(false()) -> ok(false())
  , proper(filter(X1, X2)) -> filter(proper(X1), proper(X2))
  , proper(divides(X1, X2)) -> divides(proper(X1), proper(X2))
  , top(mark(X)) -> top(proper(X))
  , top(ok(X)) -> top(active(X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.

2) 'Best' failed due to the following reason:
   
   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 input cannot be shown compatible
         
         2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
      
      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.
         
      
   


Arrrr..