* Step 1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> if(X,c(),n__f(true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
        - Signature:
            {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> if(X,c(),n__f(true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
        - Signature:
            {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 3.
        The enriched problem is compatible with follwoing automaton.
          activate_0(2) -> 1
          activate_1(2) -> 1
          activate_1(4) -> 1
          activate_1(7) -> 1
          c_0() -> 1
          c_0() -> 2
          c_1() -> 1
          c_1() -> 3
          c_2() -> 1
          c_2() -> 6
          c_3() -> 1
          c_3() -> 9
          f_0(2) -> 1
          f_1(2) -> 1
          f_2(5) -> 1
          f_2(8) -> 1
          false_0() -> 1
          false_0() -> 2
          if_0(2,2,2) -> 1
          if_1(2,3,4) -> 1
          if_2(2,6,7) -> 1
          if_3(5,9,10) -> 1
          if_3(8,9,10) -> 1
          n__f_0(2) -> 1
          n__f_0(2) -> 2
          n__f_1(2) -> 1
          n__f_1(5) -> 1
          n__f_1(5) -> 4
          n__f_2(2) -> 1
          n__f_2(8) -> 1
          n__f_2(8) -> 7
          n__f_3(5) -> 1
          n__f_3(8) -> 1
          n__f_3(11) -> 10
          true_0() -> 1
          true_0() -> 2
          true_1() -> 5
          true_2() -> 8
          true_3() -> 11
          2 -> 1
          3 -> 1
          4 -> 1
          6 -> 1
          7 -> 1
          9 -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> if(X,c(),n__f(true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
        - Signature:
            {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))