MAYBE

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

Strict Trs:
  { f(X) -> if(X, c(), n__f(true()))
  , f(X) -> n__f(X)
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> activate(Y)
  , activate(X) -> X
  , activate(n__f(X)) -> f(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(X) -> c_1(if^#(X, c(), n__f(true())))
  , f^#(X) -> c_2()
  , if^#(true(), X, Y) -> c_3()
  , if^#(false(), X, Y) -> c_4(activate^#(Y))
  , activate^#(X) -> c_5()
  , activate^#(n__f(X)) -> c_6(f^#(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(if^#(X, c(), n__f(true())))
  , f^#(X) -> c_2()
  , if^#(true(), X, Y) -> c_3()
  , if^#(false(), X, Y) -> c_4(activate^#(Y))
  , activate^#(X) -> c_5()
  , activate^#(n__f(X)) -> c_6(f^#(X)) }
Strict Trs:
  { f(X) -> if(X, c(), n__f(true()))
  , f(X) -> n__f(X)
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> activate(Y)
  , activate(X) -> X
  , activate(n__f(X)) -> f(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(if^#(X, c(), n__f(true())))
  , f^#(X) -> c_2()
  , if^#(true(), X, Y) -> c_3()
  , if^#(false(), X, Y) -> c_4(activate^#(Y))
  , activate^#(X) -> c_5()
  , activate^#(n__f(X)) -> c_6(f^#(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}, Uargs(c_6) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

                 [c] = [2]                           
                                                     
          [n__f](x1) = [1] x1 + [1]                  
                                                     
              [true] = [1]                           
                                                     
             [false] = [1]                           
                                                     
           [f^#](x1) = [2] x1 + [1]                  
                                                     
           [c_1](x1) = [1] x1 + [0]                  
                                                     
  [if^#](x1, x2, x3) = [2] x1 + [1] x2 + [2] x3 + [1]
                                                     
               [c_2] = [0]                           
                                                     
               [c_3] = [2]                           
                                                     
           [c_4](x1) = [1] x1 + [1]                  
                                                     
    [activate^#](x1) = [2] x1 + [1]                  
                                                     
               [c_5] = [0]                           
                                                     
           [c_6](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(if^#(X, c(), n__f(true()))) }
Weak DPs:
  { f^#(X) -> c_2()
  , if^#(true(), X, Y) -> c_3()
  , if^#(false(), X, Y) -> c_4(activate^#(Y))
  , activate^#(X) -> c_5()
  , activate^#(n__f(X)) -> c_6(f^#(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.

{ f^#(X) -> c_2()
, if^#(true(), X, Y) -> c_3()
, activate^#(X) -> c_5() }

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

Strict DPs: { f^#(X) -> c_1(if^#(X, c(), n__f(true()))) }
Weak DPs:
  { if^#(false(), X, Y) -> c_4(activate^#(Y))
  , activate^#(n__f(X)) -> c_6(f^#(X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..