MAYBE

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

Strict Trs:
  { ack(0(), y) -> s(y)
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { ack^#(0(), y) -> c_1()
  , ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
  , ack^#(s(x), s(y)) ->
    c_3(ack^#(x, ack(s(x), y)), ack^#(s(x), y)) }

and mark the set of starting terms.

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

Strict DPs:
  { ack^#(0(), y) -> c_1()
  , ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
  , ack^#(s(x), s(y)) ->
    c_3(ack^#(x, ack(s(x), y)), ack^#(s(x), y)) }
Weak Trs:
  { ack(0(), y) -> s(y)
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1} by applications of
Pre({1}) = {2,3}. Here rules are labeled as follows:

  DPs:
    { 1: ack^#(0(), y) -> c_1()
    , 2: ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
    , 3: ack^#(s(x), s(y)) ->
         c_3(ack^#(x, ack(s(x), y)), ack^#(s(x), y)) }

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

Strict DPs:
  { ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
  , ack^#(s(x), s(y)) ->
    c_3(ack^#(x, ack(s(x), y)), ack^#(s(x), y)) }
Weak DPs: { ack^#(0(), y) -> c_1() }
Weak Trs:
  { ack(0(), y) -> s(y)
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
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.

{ ack^#(0(), y) -> c_1() }

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

Strict DPs:
  { ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
  , ack^#(s(x), s(y)) ->
    c_3(ack^#(x, ack(s(x), y)), ack^#(s(x), y)) }
Weak Trs:
  { ack(0(), y) -> s(y)
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y)) }
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:
      
      The input cannot be shown compatible
   
   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..