MAYBE

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

Strict Trs:
  { from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , first(X1, X2) -> n__first(X1, X2)
  , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
  , first(0(), Z) -> nil()
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , activate(n__first(X1, X2)) -> first(X1, X2)
  , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
  , sel(0(), cons(X, Z)) -> X }
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:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , first^#(X1, X2) -> c_3(X1, X2)
     , first^#(s(X), cons(Y, Z)) -> c_4(Y, X, activate^#(Z))
     , first^#(0(), Z) -> c_5()
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__first(X1, X2)) -> c_8(first^#(X1, X2))
     , sel^#(s(X), cons(Y, Z)) -> c_9(sel^#(X, activate(Z)))
     , sel^#(0(), cons(X, Z)) -> c_10(X) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , first^#(X1, X2) -> c_3(X1, X2)
     , first^#(s(X), cons(Y, Z)) -> c_4(Y, X, activate^#(Z))
     , first^#(0(), Z) -> c_5()
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__first(X1, X2)) -> c_8(first^#(X1, X2))
     , sel^#(s(X), cons(Y, Z)) -> c_9(sel^#(X, activate(Z)))
     , sel^#(0(), cons(X, Z)) -> c_10(X) }
   Strict Trs:
     { from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , first(X1, X2) -> n__first(X1, X2)
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , first(0(), Z) -> nil()
     , activate(X) -> X
     , activate(n__from(X)) -> from(X)
     , activate(n__first(X1, X2)) -> first(X1, X2)
     , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
     , sel(0(), cons(X, Z)) -> X }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5} by applications of
   Pre({5}) = {1,2,3,4,6,8,10}. Here rules are labeled as follows:
   
     DPs:
       { 1: from^#(X) -> c_1(X, X)
       , 2: from^#(X) -> c_2(X)
       , 3: first^#(X1, X2) -> c_3(X1, X2)
       , 4: first^#(s(X), cons(Y, Z)) -> c_4(Y, X, activate^#(Z))
       , 5: first^#(0(), Z) -> c_5()
       , 6: activate^#(X) -> c_6(X)
       , 7: activate^#(n__from(X)) -> c_7(from^#(X))
       , 8: activate^#(n__first(X1, X2)) -> c_8(first^#(X1, X2))
       , 9: sel^#(s(X), cons(Y, Z)) -> c_9(sel^#(X, activate(Z)))
       , 10: sel^#(0(), cons(X, Z)) -> c_10(X) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(X, X)
     , from^#(X) -> c_2(X)
     , first^#(X1, X2) -> c_3(X1, X2)
     , first^#(s(X), cons(Y, Z)) -> c_4(Y, X, activate^#(Z))
     , activate^#(X) -> c_6(X)
     , activate^#(n__from(X)) -> c_7(from^#(X))
     , activate^#(n__first(X1, X2)) -> c_8(first^#(X1, X2))
     , sel^#(s(X), cons(Y, Z)) -> c_9(sel^#(X, activate(Z)))
     , sel^#(0(), cons(X, Z)) -> c_10(X) }
   Strict Trs:
     { from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , first(X1, X2) -> n__first(X1, X2)
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , first(0(), Z) -> nil()
     , activate(X) -> X
     , activate(n__from(X)) -> from(X)
     , activate(n__first(X1, X2)) -> first(X1, X2)
     , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
     , sel(0(), cons(X, Z)) -> X }
   Weak DPs: { first^#(0(), Z) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..