MAYBE

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

Strict Trs:
  { #equal(@x, @y) -> #eq(@x, @y)
  , #greater(@x, @y) -> #ckgt(#compare(@x, @y))
  , append(@l, @ys) -> append#1(@l, @ys)
  , append#1(::(@x, @xs), @ys) -> ::(@x, append(@xs, @ys))
  , append#1(nil(), @ys) -> @ys
  , insert(@x, @l) -> insert#1(@x, @l, @x)
  , insert#1(tuple#2(@valX, @keyX), @l, @x) ->
    insert#2(@l, @keyX, @valX, @x)
  , insert#2(::(@l1, @ls), @keyX, @valX, @x) ->
    insert#3(@l1, @keyX, @ls, @valX, @x)
  , insert#2(nil(), @keyX, @valX, @x) ->
    ::(tuple#2(::(@valX, nil()), @keyX), nil())
  , insert#3(tuple#2(@vals1, @key1), @keyX, @ls, @valX, @x) ->
    insert#4(#equal(@key1, @keyX), @key1, @ls, @valX, @vals1, @x)
  , insert#4(#false(), @key1, @ls, @valX, @vals1, @x) ->
    ::(tuple#2(@vals1, @key1), insert(@x, @ls))
  , insert#4(#true(), @key1, @ls, @valX, @vals1, @x) ->
    ::(tuple#2(::(@valX, @vals1), @key1), @ls)
  , quicksort(@l) -> quicksort#1(@l)
  , quicksort#1(::(@z, @zs)) -> quicksort#2(splitqs(@z, @zs), @z)
  , quicksort#1(nil()) -> nil()
  , splitqs(@pivot, @l) -> splitqs#1(@l, @pivot)
  , quicksort#2(tuple#2(@xs, @ys), @z) ->
    append(quicksort(@xs), ::(@z, quicksort(@ys)))
  , sortAll(@l) -> sortAll#1(@l)
  , sortAll#1(::(@x, @xs)) -> sortAll#2(@x, @xs)
  , sortAll#1(nil()) -> nil()
  , sortAll#2(tuple#2(@vals, @key), @xs) ->
    ::(tuple#2(quicksort(@vals), @key), sortAll(@xs))
  , split(@l) -> split#1(@l)
  , split#1(::(@x, @xs)) -> insert(@x, split(@xs))
  , split#1(nil()) -> nil()
  , splitAndSort(@l) -> sortAll(split(@l))
  , splitqs#1(::(@x, @xs), @pivot) ->
    splitqs#2(splitqs(@pivot, @xs), @pivot, @x)
  , splitqs#1(nil(), @pivot) -> tuple#2(nil(), nil())
  , splitqs#2(tuple#2(@ls, @rs), @pivot, @x) ->
    splitqs#3(#greater(@x, @pivot), @ls, @rs, @x)
  , splitqs#3(#false(), @ls, @rs, @x) -> tuple#2(::(@x, @ls), @rs)
  , splitqs#3(#true(), @ls, @rs, @x) -> tuple#2(@ls, ::(@x, @rs)) }
Weak Trs:
  { #eq(::(@x_1, @x_2), ::(@y_1, @y_2)) ->
    #and(#eq(@x_1, @y_1), #eq(@x_2, @y_2))
  , #eq(::(@x_1, @x_2), nil()) -> #false()
  , #eq(::(@x_1, @x_2), tuple#2(@y_1, @y_2)) -> #false()
  , #eq(nil(), ::(@y_1, @y_2)) -> #false()
  , #eq(nil(), nil()) -> #true()
  , #eq(nil(), tuple#2(@y_1, @y_2)) -> #false()
  , #eq(tuple#2(@x_1, @x_2), ::(@y_1, @y_2)) -> #false()
  , #eq(tuple#2(@x_1, @x_2), nil()) -> #false()
  , #eq(tuple#2(@x_1, @x_2), tuple#2(@y_1, @y_2)) ->
    #and(#eq(@x_1, @y_1), #eq(@x_2, @y_2))
  , #eq(#0(), #0()) -> #true()
  , #eq(#0(), #neg(@y)) -> #false()
  , #eq(#0(), #pos(@y)) -> #false()
  , #eq(#0(), #s(@y)) -> #false()
  , #eq(#neg(@x), #0()) -> #false()
  , #eq(#neg(@x), #neg(@y)) -> #eq(@x, @y)
  , #eq(#neg(@x), #pos(@y)) -> #false()
  , #eq(#pos(@x), #0()) -> #false()
  , #eq(#pos(@x), #neg(@y)) -> #false()
  , #eq(#pos(@x), #pos(@y)) -> #eq(@x, @y)
  , #eq(#s(@x), #0()) -> #false()
  , #eq(#s(@x), #s(@y)) -> #eq(@x, @y)
  , #compare(#0(), #0()) -> #EQ()
  , #compare(#0(), #neg(@y)) -> #GT()
  , #compare(#0(), #pos(@y)) -> #LT()
  , #compare(#0(), #s(@y)) -> #LT()
  , #compare(#neg(@x), #0()) -> #LT()
  , #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x)
  , #compare(#neg(@x), #pos(@y)) -> #LT()
  , #compare(#pos(@x), #0()) -> #GT()
  , #compare(#pos(@x), #neg(@y)) -> #GT()
  , #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y)
  , #compare(#s(@x), #0()) -> #GT()
  , #compare(#s(@x), #s(@y)) -> #compare(@x, @y)
  , #ckgt(#EQ()) -> #false()
  , #ckgt(#GT()) -> #true()
  , #ckgt(#LT()) -> #false()
  , #and(#false(), #false()) -> #false()
  , #and(#false(), #true()) -> #false()
  , #and(#true(), #false()) -> #false()
  , #and(#true(), #true()) -> #true() }
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) 'Fastest' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'trivial' failed due to the following reason:
      
      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) 'Sequentially' failed due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'Polynomial Path Order (PS)' failed due to the following reason:
            
            The input cannot be shown compatible
         
         2) 'Polynomial Path Order' failed due to the following reason:
            
            The input cannot be shown compatible
         
      
   
   2) 'Fastest (timeout of 5 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.
      
   


Arrrr..