MAYBE

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

Strict Trs:
  { splitD(@pivot, @l) -> splitD#1(@l, @pivot)
  , quicksort#2(tuple#2(@xs, @ys), @z) ->
    append(quicksort(@xs), ::(@z, quicksort(@ys)))
  , split#3(#true(), @ls, @rs, @x) -> tuple#2(@ls, ::(@x, @rs))
  , split#3(#false(), @ls, @rs, @x) -> tuple#2(::(@x, @ls), @rs)
  , append(@l, @ys) -> append#1(@l, @ys)
  , split#1(nil(), @pivot) -> tuple#2(nil(), nil())
  , split#1(::(@x, @xs), @pivot) ->
    split#2(split(@pivot, @xs), @pivot, @x)
  , split(@pivot, @l) -> split#1(@l, @pivot)
  , splitD#1(nil(), @pivot) -> tuple#2(nil(), nil())
  , splitD#1(::(@x, @xs), @pivot) ->
    splitD#2(splitD(@pivot, @xs), @pivot, @x)
  , quicksortD#2(tuple#2(@xs, @ys), @z) ->
    appendD(quicksortD(@xs), ::(@z, quicksortD(@ys)))
  , quicksortD(@l) -> quicksortD#1(@l)
  , appendD#1(nil(), @ys) -> @ys
  , appendD#1(::(@x, @xs), @ys) -> ::(@x, appendD(@xs, @ys))
  , split#2(tuple#2(@ls, @rs), @pivot, @x) ->
    split#3(#greater(@x, @pivot), @ls, @rs, @x)
  , #greater(@x, @y) -> #ckgt(#compare(@x, @y))
  , splitD#2(tuple#2(@ls, @rs), @pivot, @x) ->
    splitD#3(#greater(@x, @pivot), @ls, @rs, @x)
  , quicksort#1(nil()) -> nil()
  , quicksort#1(::(@z, @zs)) -> quicksort#2(split(@z, @zs), @z)
  , append#1(nil(), @ys) -> @ys
  , append#1(::(@x, @xs), @ys) -> ::(@x, append(@xs, @ys))
  , testQuicksort2(@x) -> quicksort(testList(#unit()))
  , quicksort(@l) -> quicksort#1(@l)
  , splitD#3(#true(), @ls, @rs, @x) -> tuple#2(@ls, ::(@x, @rs))
  , splitD#3(#false(), @ls, @rs, @x) -> tuple#2(::(@x, @ls), @rs)
  , testQuicksort(@x) -> quicksort(testList(#unit()))
  , testList(@x) ->
    ::(#abs(#0()),
       ::(#abs(#pos(#s(#s(#s(#s(#0())))))),
          ::(#abs(#pos(#s(#s(#s(#s(#s(#0()))))))),
             ::(#abs(#pos(#s(#s(#s(#s(#s(#s(#s(#s(#s(#0()))))))))))),
                ::(#abs(#pos(#s(#s(#s(#s(#s(#s(#s(#0()))))))))),
                   ::(#abs(#pos(#s(#0()))),
                      ::(#abs(#pos(#s(#s(#0())))),
                         ::(#abs(#pos(#s(#s(#s(#s(#s(#s(#s(#s(#0())))))))))),
                            ::(#abs(#pos(#s(#s(#s(#s(#s(#s(#0())))))))),
                               ::(#abs(#pos(#s(#s(#s(#0()))))), nil()))))))))))
  , quicksortD#1(nil()) -> nil()
  , quicksortD#1(::(@z, @zs)) -> quicksortD#2(splitD(@z, @zs), @z)
  , #abs(#pos(@x)) -> #pos(@x)
  , #abs(#0()) -> #0()
  , #abs(#neg(@x)) -> #pos(@x)
  , #abs(#s(@x)) -> #pos(#s(@x))
  , appendD(@l, @ys) -> appendD#1(@l, @ys) }
Weak Trs:
  { #ckgt(#EQ()) -> #false()
  , #ckgt(#LT()) -> #false()
  , #ckgt(#GT()) -> #true()
  , #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y)
  , #compare(#pos(@x), #0()) -> #GT()
  , #compare(#pos(@x), #neg(@y)) -> #GT()
  , #compare(#0(), #pos(@y)) -> #LT()
  , #compare(#0(), #0()) -> #EQ()
  , #compare(#0(), #neg(@y)) -> #GT()
  , #compare(#0(), #s(@y)) -> #LT()
  , #compare(#neg(@x), #pos(@y)) -> #LT()
  , #compare(#neg(@x), #0()) -> #LT()
  , #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x)
  , #compare(#s(@x), #0()) -> #GT()
  , #compare(#s(@x), #s(@y)) -> #compare(@x, @y) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.

2) 'Best' failed due to the following reason:
   
   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 input cannot be shown compatible
         
         2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
      
      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.
         
      
   


Arrrr..