* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(activate(X))
            activate(n__true()) -> true()
            f(X) -> if(X,c(),n__f(n__true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
            true() -> n__true()
        - Signature:
            {activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f
            ,n__true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(activate(X))
            activate(n__true()) -> true()
            f(X) -> if(X,c(),n__f(n__true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
            true() -> n__true()
        - Signature:
            {activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f
            ,n__true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__f(x)} =
            activate(n__f(x)) ->^+ f(activate(x))
              = C[activate(x) = activate(x){}]

** Step 1.b:1: InnermostRuleRemoval WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(activate(X))
            activate(n__true()) -> true()
            f(X) -> if(X,c(),n__f(n__true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
            true() -> n__true()
        - Signature:
            {activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f
            ,n__true}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          if(true(),X,Y) -> X
        All above mentioned rules can be savely removed.
** Step 1.b:2: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(activate(X))
            activate(n__true()) -> true()
            f(X) -> if(X,c(),n__f(n__true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            true() -> n__true()
        - Signature:
            {activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f
            ,n__true}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          activate_0(2) -> 1
          activate_1(2) -> 1
          activate_1(2) -> 3
          activate_1(5) -> 1
          activate_1(8) -> 1
          activate_1(8) -> 3
          activate_2(6) -> 10
          activate_2(9) -> 10
          c_0() -> 1
          c_0() -> 2
          c_0() -> 3
          c_1() -> 4
          c_2() -> 7
          c_3() -> 11
          f_0(2) -> 1
          f_1(3) -> 1
          f_1(3) -> 3
          f_2(10) -> 1
          f_2(10) -> 3
          false_0() -> 1
          false_0() -> 2
          false_0() -> 3
          if_0(2,2,2) -> 1
          if_1(2,4,5) -> 1
          if_2(3,7,8) -> 1
          if_2(3,7,8) -> 3
          if_3(10,11,12) -> 1
          if_3(10,11,12) -> 3
          n__f_0(2) -> 1
          n__f_0(2) -> 2
          n__f_0(2) -> 3
          n__f_1(2) -> 1
          n__f_1(6) -> 1
          n__f_1(6) -> 5
          n__f_2(3) -> 1
          n__f_2(3) -> 3
          n__f_2(9) -> 1
          n__f_2(9) -> 3
          n__f_2(9) -> 8
          n__f_3(10) -> 1
          n__f_3(10) -> 3
          n__f_3(13) -> 12
          n__true_0() -> 1
          n__true_0() -> 2
          n__true_0() -> 3
          n__true_1() -> 1
          n__true_1() -> 6
          n__true_1() -> 10
          n__true_2() -> 1
          n__true_2() -> 3
          n__true_2() -> 9
          n__true_2() -> 10
          n__true_3() -> 10
          n__true_3() -> 13
          n__true_4() -> 10
          true_0() -> 1
          true_1() -> 1
          true_1() -> 3
          true_2() -> 10
          true_3() -> 10
          2 -> 1
          2 -> 3
          5 -> 1
          6 -> 10
          8 -> 1
          8 -> 3
          9 -> 10
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(activate(X))
            activate(n__true()) -> true()
            f(X) -> if(X,c(),n__f(n__true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            true() -> n__true()
        - Signature:
            {activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f
            ,n__true}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))