MAYBE

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

Strict Trs:
  { first(0(), X) -> nil()
  , first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
  , from(X) -> cons(X, from(s(X))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { first^#(0(), X) -> c_1()
  , first^#(s(X), cons(Y, Z)) -> c_2(first^#(X, Z))
  , from^#(X) -> c_3(from^#(s(X))) }

and mark the set of starting terms.

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

Strict DPs:
  { first^#(0(), X) -> c_1()
  , first^#(s(X), cons(Y, Z)) -> c_2(first^#(X, Z))
  , from^#(X) -> c_3(from^#(s(X))) }
Strict Trs:
  { first(0(), X) -> nil()
  , first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
  , from(X) -> cons(X, from(s(X))) }
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:
  { first^#(0(), X) -> c_1()
  , first^#(s(X), cons(Y, Z)) -> c_2(first^#(X, Z))
  , from^#(X) -> c_3(from^#(s(X))) }
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.

                [0] = [1]                  
                                           
            [s](x1) = [1] x1 + [1]         
                                           
     [cons](x1, x2) = [1] x2 + [2]         
                                           
  [first^#](x1, x2) = [2] x1 + [2] x2 + [1]
                                           
              [c_1] = [2]                  
                                           
          [c_2](x1) = [1] x1 + [1]         
                                           
       [from^#](x1) = [1] x1 + [2]         
                                           
          [c_3](x1) = [1] x1 + [2]         

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: { from^#(X) -> c_3(from^#(s(X))) }
Weak DPs:
  { first^#(0(), X) -> c_1()
  , first^#(s(X), cons(Y, Z)) -> c_2(first^#(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.

{ first^#(0(), X) -> c_1()
, first^#(s(X), cons(Y, Z)) -> c_2(first^#(X, Z)) }

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

Strict DPs: { from^#(X) -> c_3(from^#(s(X))) }
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..