MAYBE

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

Strict Trs:
  { f(x, empty()) -> x
  , f(empty(), cons(a, k)) -> f(cons(a, k), k)
  , f(cons(a, k), y) -> f(y, k) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(x, empty()) -> c_1()
  , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k))
  , f^#(cons(a, k), y) -> c_3(f^#(y, k)) }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(x, empty()) -> c_1()
  , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k))
  , f^#(cons(a, k), y) -> c_3(f^#(y, k)) }
Strict Trs:
  { f(x, empty()) -> x
  , f(empty(), cons(a, k)) -> f(cons(a, k), k)
  , f(cons(a, k), y) -> f(y, k) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { f^#(x, empty()) -> c_1()
  , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k))
  , f^#(cons(a, k), y) -> c_3(f^#(y, k)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_2) = {1}, Uargs(c_3) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

         [empty] = [1]                  
                                        
  [cons](x1, x2) = [1] x1 + [1] x2 + [1]
                                        
   [f^#](x1, x2) = [1]                  
                                        
           [c_1] = [0]                  
                                        
       [c_2](x1) = [1] x1 + [1]         
                                        
       [c_3](x1) = [1] x1 + [1]         

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Strict DPs:
  { f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k))
  , f^#(cons(a, k), y) -> c_3(f^#(y, k)) }
Weak DPs: { f^#(x, empty()) -> c_1() }
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.

{ f^#(x, empty()) -> c_1() }

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

Strict DPs:
  { f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k))
  , f^#(cons(a, k), y) -> c_3(f^#(y, k)) }
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..