* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            f(f(X)) -> c(n__f(g(n__f(X))))
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: InnermostRuleRemoval WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            f(f(X)) -> c(n__f(g(n__f(X))))
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          f(f(X)) -> c(n__f(g(n__f(X))))
        All above mentioned rules can be savely removed.
* Step 3: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__d(X)) -> c_2(d#(X))
          activate#(n__f(X)) -> c_3(f#(X))
          c#(X) -> c_4(d#(activate(X)),activate#(X))
          d#(X) -> c_5()
          f#(X) -> c_6()
          h#(X) -> c_7(c#(n__d(X)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 4: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__d(X)) -> c_2(d#(X))
            activate#(n__f(X)) -> c_3(f#(X))
            c#(X) -> c_4(d#(activate(X)),activate#(X))
            d#(X) -> c_5()
            f#(X) -> c_6()
            h#(X) -> c_7(c#(n__d(X)))
        - Weak TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1,activate#/1,c#/1,d#/1,f#/1,h#/1} / {g/1,n__d/1,n__f/1,c_1/0,c_2/1,c_3/1,c_4/2
            ,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,f#,h#} and constructors {g,n__d,n__f}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__d(X)) -> d(X)
          activate(n__f(X)) -> f(X)
          d(X) -> n__d(X)
          f(X) -> n__f(X)
          activate#(X) -> c_1()
          activate#(n__d(X)) -> c_2(d#(X))
          activate#(n__f(X)) -> c_3(f#(X))
          c#(X) -> c_4(d#(activate(X)),activate#(X))
          d#(X) -> c_5()
          f#(X) -> c_6()
          h#(X) -> c_7(c#(n__d(X)))
* Step 5: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__d(X)) -> c_2(d#(X))
            activate#(n__f(X)) -> c_3(f#(X))
            c#(X) -> c_4(d#(activate(X)),activate#(X))
            d#(X) -> c_5()
            f#(X) -> c_6()
            h#(X) -> c_7(c#(n__d(X)))
        - Weak TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            d(X) -> n__d(X)
            f(X) -> n__f(X)
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1,activate#/1,c#/1,d#/1,f#/1,h#/1} / {g/1,n__d/1,n__f/1,c_1/0,c_2/1,c_3/1,c_4/2
            ,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,f#,h#} and constructors {g,n__d,n__f}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:activate#(X) -> c_1()
             
          
          2:S:activate#(n__d(X)) -> c_2(d#(X))
             -->_1 d#(X) -> c_5():5
          
          3:S:activate#(n__f(X)) -> c_3(f#(X))
             -->_1 f#(X) -> c_6():6
          
          4:S:c#(X) -> c_4(d#(activate(X)),activate#(X))
             -->_1 d#(X) -> c_5():5
             -->_2 activate#(n__f(X)) -> c_3(f#(X)):3
             -->_2 activate#(n__d(X)) -> c_2(d#(X)):2
             -->_2 activate#(X) -> c_1():1
          
          5:S:d#(X) -> c_5()
             
          
          6:S:f#(X) -> c_6()
             
          
          7:S:h#(X) -> c_7(c#(n__d(X)))
             -->_1 c#(X) -> c_4(d#(activate(X)),activate#(X)):4
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(X)
            d(X) -> n__d(X)
            f(X) -> n__f(X)
        - Signature:
            {activate/1,c/1,d/1,f/1,h/1,activate#/1,c#/1,d#/1,f#/1,h#/1} / {g/1,n__d/1,n__f/1,c_1/0,c_2/1,c_3/1,c_4/2
            ,c_5/0,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,f#,h#} and constructors {g,n__d,n__f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))