MAYBE

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

Strict Trs:
  { msort(nil()) -> nil()
  , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
  , min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { msort^#(nil()) -> c_1()
  , msort^#(.(x, y)) ->
    c_2(min^#(x, y),
        msort^#(del(min(x, y), .(x, y))),
        del^#(min(x, y), .(x, y)),
        min^#(x, y))
  , min^#(x, nil()) -> c_3()
  , min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
  , del^#(x, nil()) -> c_5()
  , del^#(x, .(y, z)) -> c_6(del^#(x, z)) }

and mark the set of starting terms.

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

Strict DPs:
  { msort^#(nil()) -> c_1()
  , msort^#(.(x, y)) ->
    c_2(min^#(x, y),
        msort^#(del(min(x, y), .(x, y))),
        del^#(min(x, y), .(x, y)),
        min^#(x, y))
  , min^#(x, nil()) -> c_3()
  , min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
  , del^#(x, nil()) -> c_5()
  , del^#(x, .(y, z)) -> c_6(del^#(x, z)) }
Weak Trs:
  { msort(nil()) -> nil()
  , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
  , min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
Obligation:
  innermost 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: msort^#(nil()) -> c_1()
    , 2: msort^#(.(x, y)) ->
         c_2(min^#(x, y),
             msort^#(del(min(x, y), .(x, y))),
             del^#(min(x, y), .(x, y)),
             min^#(x, y))
    , 3: min^#(x, nil()) -> c_3()
    , 4: min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
    , 5: del^#(x, nil()) -> c_5()
    , 6: del^#(x, .(y, z)) -> c_6(del^#(x, z)) }

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

Strict DPs:
  { msort^#(.(x, y)) ->
    c_2(min^#(x, y),
        msort^#(del(min(x, y), .(x, y))),
        del^#(min(x, y), .(x, y)),
        min^#(x, y))
  , min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
  , del^#(x, .(y, z)) -> c_6(del^#(x, z)) }
Weak DPs:
  { msort^#(nil()) -> c_1()
  , min^#(x, nil()) -> c_3()
  , del^#(x, nil()) -> c_5() }
Weak Trs:
  { msort(nil()) -> nil()
  , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
  , min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ msort^#(nil()) -> c_1()
, min^#(x, nil()) -> c_3()
, del^#(x, nil()) -> c_5() }

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

Strict DPs:
  { msort^#(.(x, y)) ->
    c_2(min^#(x, y),
        msort^#(del(min(x, y), .(x, y))),
        del^#(min(x, y), .(x, y)),
        min^#(x, y))
  , min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
  , del^#(x, .(y, z)) -> c_6(del^#(x, z)) }
Weak Trs:
  { msort(nil()) -> nil()
  , msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y))))
  , min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { min(x, nil()) -> x
    , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
    , del(x, nil()) -> nil()
    , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }

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

Strict DPs:
  { msort^#(.(x, y)) ->
    c_2(min^#(x, y),
        msort^#(del(min(x, y), .(x, y))),
        del^#(min(x, y), .(x, y)),
        min^#(x, y))
  , min^#(x, .(y, z)) -> c_4(min^#(x, z), min^#(y, z))
  , del^#(x, .(y, z)) -> c_6(del^#(x, z)) }
Weak Trs:
  { min(x, nil()) -> x
  , min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z))
  , del(x, nil()) -> nil()
  , del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      Following exception was raised:
        stack overflow
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..