MAYBE

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

Strict Trs:
  { f(X1, X2) -> n__f(X1, X2)
  , f(g(X), Y) -> f(X, n__f(g(X), activate(Y)))
  , activate(X) -> X
  , activate(n__f(X1, X2)) -> f(X1, X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { f^#(X1, X2) -> c_1()
  , f^#(g(X), Y) ->
    c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y))
  , activate^#(X) -> c_3()
  , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(X1, X2) -> c_1()
  , f^#(g(X), Y) ->
    c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y))
  , activate^#(X) -> c_3()
  , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) }
Weak Trs:
  { f(X1, X2) -> n__f(X1, X2)
  , f(g(X), Y) -> f(X, n__f(g(X), activate(Y)))
  , activate(X) -> X
  , activate(n__f(X1, X2)) -> f(X1, X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3} by applications of
Pre({1,3}) = {2,4}. Here rules are labeled as follows:

  DPs:
    { 1: f^#(X1, X2) -> c_1()
    , 2: f^#(g(X), Y) ->
         c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y))
    , 3: activate^#(X) -> c_3()
    , 4: activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) }

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

Strict DPs:
  { f^#(g(X), Y) ->
    c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y))
  , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) }
Weak DPs:
  { f^#(X1, X2) -> c_1()
  , activate^#(X) -> c_3() }
Weak Trs:
  { f(X1, X2) -> n__f(X1, X2)
  , f(g(X), Y) -> f(X, n__f(g(X), activate(Y)))
  , activate(X) -> X
  , activate(n__f(X1, X2)) -> f(X1, X2) }
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^#(X1, X2) -> c_1()
, activate^#(X) -> c_3() }

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

Strict DPs:
  { f^#(g(X), Y) ->
    c_2(f^#(X, n__f(g(X), activate(Y))), activate^#(Y))
  , activate^#(n__f(X1, X2)) -> c_4(f^#(X1, X2)) }
Weak Trs:
  { f(X1, X2) -> n__f(X1, X2)
  , f(g(X), Y) -> f(X, n__f(g(X), activate(Y)))
  , activate(X) -> X
  , activate(n__f(X1, X2)) -> f(X1, X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..