MAYBE

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

Strict Trs:
  { f(x, x) -> f(g(x), x)
  , g(x) -> s(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(x, x) -> c_1(f^#(g(x), x))
  , g^#(x) -> c_2() }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(x, x) -> c_1(f^#(g(x), x))
  , g^#(x) -> c_2() }
Strict Trs:
  { f(x, x) -> f(g(x), x)
  , g(x) -> s(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Strict Usable Rules: { g(x) -> s(x) }

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

Strict DPs:
  { f^#(x, x) -> c_1(f^#(g(x), x))
  , g^#(x) -> c_2() }
Strict Trs: { g(x) -> 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(f^#) = {1}, Uargs(c_1) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

        [g](x1) = [2]         
                              
        [s](x1) = [1]         
                              
  [f^#](x1, x2) = [1] x1 + [2]
                              
      [c_1](x1) = [1] x1 + [2]
                              
      [g^#](x1) = [1]         
                              
          [c_2] = [1]         

This order satisfies following ordering constraints:

  [g(x)] = [2]   
         > [1]   
         = [s(x)]
                 

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^#(x, x) -> c_1(f^#(g(x), x))
  , g^#(x) -> c_2() }
Weak Trs: { g(x) -> s(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: f^#(x, x) -> c_1(f^#(g(x), x))
    , 2: g^#(x) -> c_2() }

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

Strict DPs: { f^#(x, x) -> c_1(f^#(g(x), x)) }
Weak DPs: { g^#(x) -> c_2() }
Weak Trs: { g(x) -> s(x) }
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.

{ g^#(x) -> c_2() }

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

Strict DPs: { f^#(x, x) -> c_1(f^#(g(x), x)) }
Weak Trs: { g(x) -> 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..