MAYBE

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

Strict Trs:
  { U11(tt(), N, X, XS) ->
    U12(splitAt(activate(N), activate(XS)), activate(X))
  , U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
  , splitAt(0(), XS) -> pair(nil(), XS)
  , splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
  , activate(X) -> X
  , activate(n__natsFrom(X)) -> natsFrom(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , afterNth(N, XS) -> snd(splitAt(N, XS))
  , snd(pair(X, Y)) -> Y
  , and(tt(), X) -> activate(X)
  , fst(pair(X, Y)) -> X
  , head(cons(N, XS)) -> N
  , natsFrom(N) -> cons(N, n__natsFrom(n__s(N)))
  , natsFrom(X) -> n__natsFrom(X)
  , sel(N, XS) -> head(afterNth(N, XS))
  , s(X) -> n__s(X)
  , tail(cons(N, XS)) -> activate(XS)
  , take(N, XS) -> fst(splitAt(N, XS)) }
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:
     { U11^#(tt(), N, X, XS) ->
       c_1(U12^#(splitAt(activate(N), activate(XS)), activate(X)))
     , U12^#(pair(YS, ZS), X) -> c_2(activate^#(X), YS, ZS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__natsFrom(X)) -> c_6(natsFrom^#(activate(X)))
     , activate^#(n__s(X)) -> c_7(s^#(activate(X)))
     , splitAt^#(0(), XS) -> c_3(XS)
     , splitAt^#(s(N), cons(X, XS)) ->
       c_4(U11^#(tt(), N, X, activate(XS)))
     , natsFrom^#(N) -> c_13(N, N)
     , natsFrom^#(X) -> c_14(X)
     , s^#(X) -> c_16(X)
     , afterNth^#(N, XS) -> c_8(snd^#(splitAt(N, XS)))
     , snd^#(pair(X, Y)) -> c_9(Y)
     , and^#(tt(), X) -> c_10(activate^#(X))
     , fst^#(pair(X, Y)) -> c_11(X)
     , head^#(cons(N, XS)) -> c_12(N)
     , sel^#(N, XS) -> c_15(head^#(afterNth(N, XS)))
     , tail^#(cons(N, XS)) -> c_17(activate^#(XS))
     , take^#(N, XS) -> c_18(fst^#(splitAt(N, XS))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), N, X, XS) ->
       c_1(U12^#(splitAt(activate(N), activate(XS)), activate(X)))
     , U12^#(pair(YS, ZS), X) -> c_2(activate^#(X), YS, ZS)
     , activate^#(X) -> c_5(X)
     , activate^#(n__natsFrom(X)) -> c_6(natsFrom^#(activate(X)))
     , activate^#(n__s(X)) -> c_7(s^#(activate(X)))
     , splitAt^#(0(), XS) -> c_3(XS)
     , splitAt^#(s(N), cons(X, XS)) ->
       c_4(U11^#(tt(), N, X, activate(XS)))
     , natsFrom^#(N) -> c_13(N, N)
     , natsFrom^#(X) -> c_14(X)
     , s^#(X) -> c_16(X)
     , afterNth^#(N, XS) -> c_8(snd^#(splitAt(N, XS)))
     , snd^#(pair(X, Y)) -> c_9(Y)
     , and^#(tt(), X) -> c_10(activate^#(X))
     , fst^#(pair(X, Y)) -> c_11(X)
     , head^#(cons(N, XS)) -> c_12(N)
     , sel^#(N, XS) -> c_15(head^#(afterNth(N, XS)))
     , tail^#(cons(N, XS)) -> c_17(activate^#(XS))
     , take^#(N, XS) -> c_18(fst^#(splitAt(N, XS))) }
   Strict Trs:
     { U11(tt(), N, X, XS) ->
       U12(splitAt(activate(N), activate(XS)), activate(X))
     , U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
     , activate(X) -> X
     , activate(n__natsFrom(X)) -> natsFrom(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , afterNth(N, XS) -> snd(splitAt(N, XS))
     , snd(pair(X, Y)) -> Y
     , and(tt(), X) -> activate(X)
     , fst(pair(X, Y)) -> X
     , head(cons(N, XS)) -> N
     , natsFrom(N) -> cons(N, n__natsFrom(n__s(N)))
     , natsFrom(X) -> n__natsFrom(X)
     , sel(N, XS) -> head(afterNth(N, XS))
     , s(X) -> n__s(X)
     , tail(cons(N, XS)) -> activate(XS)
     , take(N, XS) -> fst(splitAt(N, XS)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..