MAYBE

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

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

We add following weak dependency pairs:

Strict DPs:
  { f^#(X) -> c_1(f^#(X))
  , h^#(X) -> c_2()
  , activate^#(X) -> c_3()
  , activate^#(n__h(X)) -> c_4(h^#(X)) }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(X) -> c_1(f^#(X))
  , h^#(X) -> c_2()
  , activate^#(X) -> c_3()
  , activate^#(n__h(X)) -> c_4(h^#(X)) }
Strict Trs:
  { f(X) -> g(n__h(f(X)))
  , h(X) -> n__h(X)
  , activate(X) -> X
  , activate(n__h(X)) -> h(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:
  { f^#(X) -> c_1(f^#(X))
  , h^#(X) -> c_2()
  , activate^#(X) -> c_3()
  , activate^#(n__h(X)) -> c_4(h^#(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_1) = {1}, Uargs(c_4) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

        [n__h](x1) = [1] x1 + [1]
                                 
         [f^#](x1) = [2] x1 + [2]
                                 
         [c_1](x1) = [1] x1 + [1]
                                 
         [h^#](x1) = [1] x1 + [1]
                                 
             [c_2] = [0]         
                                 
  [activate^#](x1) = [1] x1 + [2]
                                 
             [c_3] = [1]         
                                 
         [c_4](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^#(X) -> c_1(f^#(X)) }
Weak DPs:
  { h^#(X) -> c_2()
  , activate^#(X) -> c_3()
  , activate^#(n__h(X)) -> c_4(h^#(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.

{ h^#(X) -> c_2()
, activate^#(X) -> c_3()
, activate^#(n__h(X)) -> c_4(h^#(X)) }

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

Strict DPs: { f^#(X) -> c_1(f^#(X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..