MAYBE

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

Strict Trs:
  { insertionsort#1(nil()) -> nil()
  , insertionsort#1(::(@x, @xs)) -> insert(@x, insertionsort(@xs))
  , insert(@x, @l) -> insert#1(@l, @x)
  , testInsertionsortD(@x) -> insertionsortD(testList(#unit()))
  , insert#2(#true(), @x, @y, @ys) -> ::(@y, insert(@x, @ys))
  , insert#2(#false(), @x, @y, @ys) -> ::(@x, ::(@y, @ys))
  , insertD#2(#true(), @x, @y, @ys) -> ::(@y, insertD(@x, @ys))
  , insertD#2(#false(), @x, @y, @ys) -> ::(@x, ::(@y, @ys))
  , insertD(@x, @l) -> insertD#1(@l, @x)
  , testInsertionsort(@x) -> insertionsort(testList(#unit()))
  , insertD#1(nil(), @x) -> ::(@x, nil())
  , insertD#1(::(@y, @ys), @x) ->
    insertD#2(#less(@y, @x), @x, @y, @ys)
  , insert#1(nil(), @x) -> ::(@x, nil())
  , insert#1(::(@y, @ys), @x) -> insert#2(#less(@y, @x), @x, @y, @ys)
  , testList(@_) ->
    ::(#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()))))))))))
  , #less(@x, @y) -> #cklt(#compare(@x, @y))
  , #abs(#pos(@x)) -> #pos(@x)
  , #abs(#0()) -> #0()
  , #abs(#neg(@x)) -> #pos(@x)
  , #abs(#s(@x)) -> #pos(#s(@x))
  , insertionsortD#1(nil()) -> nil()
  , insertionsortD#1(::(@x, @xs)) -> insertD(@x, insertionsortD(@xs))
  , insertionsortD(@l) -> insertionsortD#1(@l)
  , insertionsort(@l) -> insertionsort#1(@l) }
Weak Trs:
  { #cklt(#EQ()) -> #false()
  , #cklt(#LT()) -> #true()
  , #cklt(#GT()) -> #false()
  , #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 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..