MAYBE

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

Strict Trs:
  { a__first(X1, X2) -> first(X1, X2)
  , a__first(0(), X) -> nil()
  , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
  , mark(0()) -> 0()
  , mark(nil()) -> nil()
  , mark(s(X)) -> s(mark(X))
  , mark(cons(X1, X2)) -> cons(mark(X1), X2)
  , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
  , mark(from(X)) -> a__from(mark(X))
  , a__from(X) -> cons(mark(X), from(s(X)))
  , a__from(X) -> from(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:
     { a__first^#(X1, X2) -> c_1(X1, X2)
     , a__first^#(0(), X) -> c_2()
     , a__first^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z)
     , mark^#(0()) -> c_4()
     , mark^#(nil()) -> c_5()
     , mark^#(s(X)) -> c_6(mark^#(X))
     , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2)
     , mark^#(first(X1, X2)) -> c_8(a__first^#(mark(X1), mark(X2)))
     , mark^#(from(X)) -> c_9(a__from^#(mark(X)))
     , a__from^#(X) -> c_10(mark^#(X), X)
     , a__from^#(X) -> c_11(X) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__first^#(X1, X2) -> c_1(X1, X2)
     , a__first^#(0(), X) -> c_2()
     , a__first^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z)
     , mark^#(0()) -> c_4()
     , mark^#(nil()) -> c_5()
     , mark^#(s(X)) -> c_6(mark^#(X))
     , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2)
     , mark^#(first(X1, X2)) -> c_8(a__first^#(mark(X1), mark(X2)))
     , mark^#(from(X)) -> c_9(a__from^#(mark(X)))
     , a__from^#(X) -> c_10(mark^#(X), X)
     , a__from^#(X) -> c_11(X) }
   Strict Trs:
     { a__first(X1, X2) -> first(X1, X2)
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(from(X)) -> a__from(mark(X))
     , a__from(X) -> cons(mark(X), from(s(X)))
     , a__from(X) -> from(X) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,4,5} by applications of
   Pre({2,4,5}) = {1,3,6,7,8,10,11}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: a__first^#(X1, X2) -> c_1(X1, X2)
       , 2: a__first^#(0(), X) -> c_2()
       , 3: a__first^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z)
       , 4: mark^#(0()) -> c_4()
       , 5: mark^#(nil()) -> c_5()
       , 6: mark^#(s(X)) -> c_6(mark^#(X))
       , 7: mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2)
       , 8: mark^#(first(X1, X2)) -> c_8(a__first^#(mark(X1), mark(X2)))
       , 9: mark^#(from(X)) -> c_9(a__from^#(mark(X)))
       , 10: a__from^#(X) -> c_10(mark^#(X), X)
       , 11: a__from^#(X) -> c_11(X) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__first^#(X1, X2) -> c_1(X1, X2)
     , a__first^#(s(X), cons(Y, Z)) -> c_3(mark^#(Y), X, Z)
     , mark^#(s(X)) -> c_6(mark^#(X))
     , mark^#(cons(X1, X2)) -> c_7(mark^#(X1), X2)
     , mark^#(first(X1, X2)) -> c_8(a__first^#(mark(X1), mark(X2)))
     , mark^#(from(X)) -> c_9(a__from^#(mark(X)))
     , a__from^#(X) -> c_10(mark^#(X), X)
     , a__from^#(X) -> c_11(X) }
   Strict Trs:
     { a__first(X1, X2) -> first(X1, X2)
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(from(X)) -> a__from(mark(X))
     , a__from(X) -> cons(mark(X), from(s(X)))
     , a__from(X) -> from(X) }
   Weak DPs:
     { a__first^#(0(), X) -> c_2()
     , mark^#(0()) -> c_4()
     , mark^#(nil()) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..