MAYBE

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

Strict Trs:
  { qsort(nil()) -> nil()
  , qsort(.(x, y)) ->
    ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
  , lowers(x, nil()) -> nil()
  , lowers(x, .(y, z)) ->
    if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
  , greaters(x, nil()) -> nil()
  , greaters(x, .(y, z)) ->
    if(<=(y, x), greaters(x, z), .(y, greaters(x, 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) '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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-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:
     { qsort^#(nil()) -> c_1()
     , qsort^#(.(x, y)) ->
       c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y)))
     , lowers^#(x, nil()) -> c_3()
     , lowers^#(x, .(y, z)) ->
       c_4(y, x, y, lowers^#(x, z), lowers^#(x, z))
     , greaters^#(x, nil()) -> c_5()
     , greaters^#(x, .(y, z)) ->
       c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { qsort^#(nil()) -> c_1()
     , qsort^#(.(x, y)) ->
       c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y)))
     , lowers^#(x, nil()) -> c_3()
     , lowers^#(x, .(y, z)) ->
       c_4(y, x, y, lowers^#(x, z), lowers^#(x, z))
     , greaters^#(x, nil()) -> c_5()
     , greaters^#(x, .(y, z)) ->
       c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) }
   Strict Trs:
     { qsort(nil()) -> nil()
     , qsort(.(x, y)) ->
       ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
     , lowers(x, nil()) -> nil()
     , lowers(x, .(y, z)) ->
       if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
     , greaters(x, nil()) -> nil()
     , greaters(x, .(y, z)) ->
       if(<=(y, x), greaters(x, z), .(y, greaters(x, z))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,3,5} by applications of
   Pre({1,3,5}) = {2,4,6}. Here rules are labeled as follows:
   
     DPs:
       { 1: qsort^#(nil()) -> c_1()
       , 2: qsort^#(.(x, y)) ->
            c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y)))
       , 3: lowers^#(x, nil()) -> c_3()
       , 4: lowers^#(x, .(y, z)) ->
            c_4(y, x, y, lowers^#(x, z), lowers^#(x, z))
       , 5: greaters^#(x, nil()) -> c_5()
       , 6: greaters^#(x, .(y, z)) ->
            c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { qsort^#(.(x, y)) ->
       c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y)))
     , lowers^#(x, .(y, z)) ->
       c_4(y, x, y, lowers^#(x, z), lowers^#(x, z))
     , greaters^#(x, .(y, z)) ->
       c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) }
   Strict Trs:
     { qsort(nil()) -> nil()
     , qsort(.(x, y)) ->
       ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
     , lowers(x, nil()) -> nil()
     , lowers(x, .(y, z)) ->
       if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
     , greaters(x, nil()) -> nil()
     , greaters(x, .(y, z)) ->
       if(<=(y, x), greaters(x, z), .(y, greaters(x, z))) }
   Weak DPs:
     { qsort^#(nil()) -> c_1()
     , lowers^#(x, nil()) -> c_3()
     , greaters^#(x, nil()) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..