MAYBE

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

Strict Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , c^#() -> c_2()
  , f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
  , g^#(X) -> c_4()
  , activate^#(X) -> c_5()
  , activate^#(n__g(X)) -> c_6(g^#(X))
  , activate^#(n__c()) -> c_7(c^#()) }

and mark the set of starting terms.

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

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , c^#() -> c_2()
  , f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
  , g^#(X) -> c_4()
  , activate^#(X) -> c_5()
  , activate^#(n__g(X)) -> c_6(g^#(X))
  , activate^#(n__c()) -> c_7(c^#()) }
Weak Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {2,4,5} by applications of
Pre({2,4,5}) = {3,6,7}. Here rules are labeled as follows:

  DPs:
    { 1: c^#() -> c_1(f^#(n__g(n__c())))
    , 2: c^#() -> c_2()
    , 3: f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
    , 4: g^#(X) -> c_4()
    , 5: activate^#(X) -> c_5()
    , 6: activate^#(n__g(X)) -> c_6(g^#(X))
    , 7: activate^#(n__c()) -> c_7(c^#()) }

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

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
  , activate^#(n__g(X)) -> c_6(g^#(X))
  , activate^#(n__c()) -> c_7(c^#()) }
Weak DPs:
  { c^#() -> c_2()
  , g^#(X) -> c_4()
  , activate^#(X) -> c_5() }
Weak Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: c^#() -> c_1(f^#(n__g(n__c())))
    , 2: f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
    , 3: activate^#(n__g(X)) -> c_6(g^#(X))
    , 4: activate^#(n__c()) -> c_7(c^#())
    , 5: c^#() -> c_2()
    , 6: g^#(X) -> c_4()
    , 7: activate^#(X) -> c_5() }

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

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
  , activate^#(n__c()) -> c_7(c^#()) }
Weak DPs:
  { c^#() -> c_2()
  , g^#(X) -> c_4()
  , activate^#(X) -> c_5()
  , activate^#(n__g(X)) -> c_6(g^#(X)) }
Weak Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
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.

{ c^#() -> c_2()
, g^#(X) -> c_4()
, activate^#(X) -> c_5()
, activate^#(n__g(X)) -> c_6(g^#(X)) }

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

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X))
  , activate^#(n__c()) -> c_7(c^#()) }
Weak Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { f^#(n__g(X)) -> c_3(g^#(activate(X)), activate^#(X)) }

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

Strict DPs:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , f^#(n__g(X)) -> c_2(activate^#(X))
  , activate^#(n__c()) -> c_3(c^#()) }
Weak Trs:
  { c() -> f(n__g(n__c()))
  , c() -> n__c()
  , f(n__g(X)) -> g(activate(X))
  , g(X) -> n__g(X)
  , activate(X) -> X
  , activate(n__g(X)) -> g(X)
  , activate(n__c()) -> c() }
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:
  { c^#() -> c_1(f^#(n__g(n__c())))
  , f^#(n__g(X)) -> c_2(activate^#(X))
  , activate^#(n__c()) -> c_3(c^#()) }
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..