MAYBE

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

Strict Trs:
  { sort(nil()) -> nil()
  , sort(cons(x, y)) -> insert(x, sort(y))
  , insert(x, nil()) -> cons(x, nil())
  , insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v)
  , choose(x, cons(v, w), y, 0()) -> cons(x, cons(v, w))
  , choose(x, cons(v, w), 0(), s(z)) -> cons(v, insert(x, w))
  , choose(x, cons(v, w), s(y), s(z)) ->
    choose(x, cons(v, w), y, z) }
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:
     { sort^#(nil()) -> c_1()
     , sort^#(cons(x, y)) -> c_2(insert^#(x, sort(y)))
     , insert^#(x, nil()) -> c_3(x)
     , insert^#(x, cons(v, w)) -> c_4(choose^#(x, cons(v, w), x, v))
     , choose^#(x, cons(v, w), y, 0()) -> c_5(x, v, w)
     , choose^#(x, cons(v, w), 0(), s(z)) -> c_6(v, insert^#(x, w))
     , choose^#(x, cons(v, w), s(y), s(z)) ->
       c_7(choose^#(x, cons(v, w), y, z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { sort^#(nil()) -> c_1()
     , sort^#(cons(x, y)) -> c_2(insert^#(x, sort(y)))
     , insert^#(x, nil()) -> c_3(x)
     , insert^#(x, cons(v, w)) -> c_4(choose^#(x, cons(v, w), x, v))
     , choose^#(x, cons(v, w), y, 0()) -> c_5(x, v, w)
     , choose^#(x, cons(v, w), 0(), s(z)) -> c_6(v, insert^#(x, w))
     , choose^#(x, cons(v, w), s(y), s(z)) ->
       c_7(choose^#(x, cons(v, w), y, z)) }
   Strict Trs:
     { sort(nil()) -> nil()
     , sort(cons(x, y)) -> insert(x, sort(y))
     , insert(x, nil()) -> cons(x, nil())
     , insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v)
     , choose(x, cons(v, w), y, 0()) -> cons(x, cons(v, w))
     , choose(x, cons(v, w), 0(), s(z)) -> cons(v, insert(x, w))
     , choose(x, cons(v, w), s(y), s(z)) ->
       choose(x, cons(v, w), y, z) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1} by applications of
   Pre({1}) = {3,5,6}. Here rules are labeled as follows:
   
     DPs:
       { 1: sort^#(nil()) -> c_1()
       , 2: sort^#(cons(x, y)) -> c_2(insert^#(x, sort(y)))
       , 3: insert^#(x, nil()) -> c_3(x)
       , 4: insert^#(x, cons(v, w)) -> c_4(choose^#(x, cons(v, w), x, v))
       , 5: choose^#(x, cons(v, w), y, 0()) -> c_5(x, v, w)
       , 6: choose^#(x, cons(v, w), 0(), s(z)) -> c_6(v, insert^#(x, w))
       , 7: choose^#(x, cons(v, w), s(y), s(z)) ->
            c_7(choose^#(x, cons(v, w), y, z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { sort^#(cons(x, y)) -> c_2(insert^#(x, sort(y)))
     , insert^#(x, nil()) -> c_3(x)
     , insert^#(x, cons(v, w)) -> c_4(choose^#(x, cons(v, w), x, v))
     , choose^#(x, cons(v, w), y, 0()) -> c_5(x, v, w)
     , choose^#(x, cons(v, w), 0(), s(z)) -> c_6(v, insert^#(x, w))
     , choose^#(x, cons(v, w), s(y), s(z)) ->
       c_7(choose^#(x, cons(v, w), y, z)) }
   Strict Trs:
     { sort(nil()) -> nil()
     , sort(cons(x, y)) -> insert(x, sort(y))
     , insert(x, nil()) -> cons(x, nil())
     , insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v)
     , choose(x, cons(v, w), y, 0()) -> cons(x, cons(v, w))
     , choose(x, cons(v, w), 0(), s(z)) -> cons(v, insert(x, w))
     , choose(x, cons(v, w), s(y), s(z)) ->
       choose(x, cons(v, w), y, z) }
   Weak DPs: { sort^#(nil()) -> c_1() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..