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)
  , head(cons(X, XS)) -> X
  , 2nd(cons(X, XS)) -> head(activate(XS))
  , activate(X) -> X
  , activate(n__from(X)) -> from(X)
  , activate(n__take(X1, X2)) -> take(X1, X2)
  , take(X1, X2) -> n__take(X1, X2)
  , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
  , take(0(), XS) -> nil()
  , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
  , sel(0(), cons(X, XS)) -> 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) '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
      
      2) '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
      
   
   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)
     , head^#(cons(X, XS)) -> c_3(X)
     , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS)))
     , activate^#(X) -> c_5(X)
     , activate^#(n__from(X)) -> c_6(from^#(X))
     , activate^#(n__take(X1, X2)) -> c_7(take^#(X1, X2))
     , take^#(X1, X2) -> c_8(X1, X2)
     , take^#(s(N), cons(X, XS)) -> c_9(X, N, activate^#(XS))
     , take^#(0(), XS) -> c_10()
     , sel^#(s(N), cons(X, XS)) -> c_11(sel^#(N, activate(XS)))
     , sel^#(0(), cons(X, XS)) -> c_12(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)
     , head^#(cons(X, XS)) -> c_3(X)
     , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS)))
     , activate^#(X) -> c_5(X)
     , activate^#(n__from(X)) -> c_6(from^#(X))
     , activate^#(n__take(X1, X2)) -> c_7(take^#(X1, X2))
     , take^#(X1, X2) -> c_8(X1, X2)
     , take^#(s(N), cons(X, XS)) -> c_9(X, N, activate^#(XS))
     , take^#(0(), XS) -> c_10()
     , sel^#(s(N), cons(X, XS)) -> c_11(sel^#(N, activate(XS)))
     , sel^#(0(), cons(X, XS)) -> c_12(X) }
   Strict Trs:
     { from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , head(cons(X, XS)) -> X
     , 2nd(cons(X, XS)) -> head(activate(XS))
     , activate(X) -> X
     , activate(n__from(X)) -> from(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , take(X1, X2) -> n__take(X1, X2)
     , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
     , take(0(), XS) -> nil()
     , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
     , sel(0(), cons(X, XS)) -> X }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {10} by applications of
   Pre({10}) = {1,2,3,5,7,8,9,12}. Here rules are labeled as follows:
   
     DPs:
       { 1: from^#(X) -> c_1(X, X)
       , 2: from^#(X) -> c_2(X)
       , 3: head^#(cons(X, XS)) -> c_3(X)
       , 4: 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS)))
       , 5: activate^#(X) -> c_5(X)
       , 6: activate^#(n__from(X)) -> c_6(from^#(X))
       , 7: activate^#(n__take(X1, X2)) -> c_7(take^#(X1, X2))
       , 8: take^#(X1, X2) -> c_8(X1, X2)
       , 9: take^#(s(N), cons(X, XS)) -> c_9(X, N, activate^#(XS))
       , 10: take^#(0(), XS) -> c_10()
       , 11: sel^#(s(N), cons(X, XS)) -> c_11(sel^#(N, activate(XS)))
       , 12: sel^#(0(), cons(X, XS)) -> c_12(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)
     , head^#(cons(X, XS)) -> c_3(X)
     , 2nd^#(cons(X, XS)) -> c_4(head^#(activate(XS)))
     , activate^#(X) -> c_5(X)
     , activate^#(n__from(X)) -> c_6(from^#(X))
     , activate^#(n__take(X1, X2)) -> c_7(take^#(X1, X2))
     , take^#(X1, X2) -> c_8(X1, X2)
     , take^#(s(N), cons(X, XS)) -> c_9(X, N, activate^#(XS))
     , sel^#(s(N), cons(X, XS)) -> c_11(sel^#(N, activate(XS)))
     , sel^#(0(), cons(X, XS)) -> c_12(X) }
   Strict Trs:
     { from(X) -> cons(X, n__from(s(X)))
     , from(X) -> n__from(X)
     , head(cons(X, XS)) -> X
     , 2nd(cons(X, XS)) -> head(activate(XS))
     , activate(X) -> X
     , activate(n__from(X)) -> from(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , take(X1, X2) -> n__take(X1, X2)
     , take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
     , take(0(), XS) -> nil()
     , sel(s(N), cons(X, XS)) -> sel(N, activate(XS))
     , sel(0(), cons(X, XS)) -> X }
   Weak DPs: { take^#(0(), XS) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..