MAYBE

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

Strict Trs:
  { isEmpty(nil()) -> true()
  , isEmpty(cons(x, xs)) -> false()
  , last(cons(x, nil())) -> x
  , last(cons(x, cons(y, ys))) -> last(cons(y, ys))
  , dropLast(nil()) -> nil()
  , dropLast(cons(x, nil())) -> nil()
  , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys)))
  , append(nil(), ys) -> ys
  , append(cons(x, xs), ys) -> cons(x, append(xs, ys))
  , reverse(xs) -> rev(xs, nil())
  , rev(xs, ys) ->
    if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)
  , if(true(), xs, ys, zs) -> zs
  , if(false(), xs, ys, zs) -> rev(xs, ys) }
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) '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) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { isEmpty^#(nil()) -> c_1()
     , isEmpty^#(cons(x, xs)) -> c_2()
     , last^#(cons(x, nil())) -> c_3(x)
     , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys)))
     , dropLast^#(nil()) -> c_5()
     , dropLast^#(cons(x, nil())) -> c_6()
     , dropLast^#(cons(x, cons(y, ys))) ->
       c_7(x, dropLast^#(cons(y, ys)))
     , append^#(nil(), ys) -> c_8(ys)
     , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys))
     , reverse^#(xs) -> c_10(rev^#(xs, nil()))
     , rev^#(xs, ys) ->
       c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys))
     , if^#(true(), xs, ys, zs) -> c_12(zs)
     , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { isEmpty^#(nil()) -> c_1()
     , isEmpty^#(cons(x, xs)) -> c_2()
     , last^#(cons(x, nil())) -> c_3(x)
     , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys)))
     , dropLast^#(nil()) -> c_5()
     , dropLast^#(cons(x, nil())) -> c_6()
     , dropLast^#(cons(x, cons(y, ys))) ->
       c_7(x, dropLast^#(cons(y, ys)))
     , append^#(nil(), ys) -> c_8(ys)
     , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys))
     , reverse^#(xs) -> c_10(rev^#(xs, nil()))
     , rev^#(xs, ys) ->
       c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys))
     , if^#(true(), xs, ys, zs) -> c_12(zs)
     , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) }
   Strict Trs:
     { isEmpty(nil()) -> true()
     , isEmpty(cons(x, xs)) -> false()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, ys))) -> last(cons(y, ys))
     , dropLast(nil()) -> nil()
     , dropLast(cons(x, nil())) -> nil()
     , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys)))
     , append(nil(), ys) -> ys
     , append(cons(x, xs), ys) -> cons(x, append(xs, ys))
     , reverse(xs) -> rev(xs, nil())
     , rev(xs, ys) ->
       if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)
     , if(true(), xs, ys, zs) -> zs
     , if(false(), xs, ys, zs) -> rev(xs, ys) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,5,6} by applications
   of Pre({1,2,5,6}) = {3,7,8,9,12}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: isEmpty^#(nil()) -> c_1()
       , 2: isEmpty^#(cons(x, xs)) -> c_2()
       , 3: last^#(cons(x, nil())) -> c_3(x)
       , 4: last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys)))
       , 5: dropLast^#(nil()) -> c_5()
       , 6: dropLast^#(cons(x, nil())) -> c_6()
       , 7: dropLast^#(cons(x, cons(y, ys))) ->
            c_7(x, dropLast^#(cons(y, ys)))
       , 8: append^#(nil(), ys) -> c_8(ys)
       , 9: append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys))
       , 10: reverse^#(xs) -> c_10(rev^#(xs, nil()))
       , 11: rev^#(xs, ys) ->
             c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys))
       , 12: if^#(true(), xs, ys, zs) -> c_12(zs)
       , 13: if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { last^#(cons(x, nil())) -> c_3(x)
     , last^#(cons(x, cons(y, ys))) -> c_4(last^#(cons(y, ys)))
     , dropLast^#(cons(x, cons(y, ys))) ->
       c_7(x, dropLast^#(cons(y, ys)))
     , append^#(nil(), ys) -> c_8(ys)
     , append^#(cons(x, xs), ys) -> c_9(x, append^#(xs, ys))
     , reverse^#(xs) -> c_10(rev^#(xs, nil()))
     , rev^#(xs, ys) ->
       c_11(if^#(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys))
     , if^#(true(), xs, ys, zs) -> c_12(zs)
     , if^#(false(), xs, ys, zs) -> c_13(rev^#(xs, ys)) }
   Strict Trs:
     { isEmpty(nil()) -> true()
     , isEmpty(cons(x, xs)) -> false()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, ys))) -> last(cons(y, ys))
     , dropLast(nil()) -> nil()
     , dropLast(cons(x, nil())) -> nil()
     , dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys)))
     , append(nil(), ys) -> ys
     , append(cons(x, xs), ys) -> cons(x, append(xs, ys))
     , reverse(xs) -> rev(xs, nil())
     , rev(xs, ys) ->
       if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys)
     , if(true(), xs, ys, zs) -> zs
     , if(false(), xs, ys, zs) -> rev(xs, ys) }
   Weak DPs:
     { isEmpty^#(nil()) -> c_1()
     , isEmpty^#(cons(x, xs)) -> c_2()
     , dropLast^#(nil()) -> c_5()
     , dropLast^#(cons(x, nil())) -> c_6() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..