* Step 1: ToInnermost WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(s(0())))
            f(s(0())) -> f(p(s(0())))
            p(s(X)) -> X
        - Signature:
            {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
    + 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) -> n__f(X)
            f(0()) -> cons(0(),n__f(s(0())))
            f(s(0())) -> f(p(s(0())))
            p(s(X)) -> X
        - Signature:
            {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_0() -> 2
          0_0() -> 6
          0_1() -> 1
          0_1() -> 2
          0_1() -> 6
          0_1() -> 8
          0_1() -> 11
          0_2() -> 12
          0_2() -> 15
          activate_0(1) -> 2
          activate_0(3) -> 2
          activate_0(5) -> 2
          activate_0(7) -> 2
          cons_0(1,1) -> 2
          cons_0(1,1) -> 3
          cons_0(1,1) -> 6
          cons_0(1,3) -> 2
          cons_0(1,3) -> 3
          cons_0(1,3) -> 6
          cons_0(1,5) -> 2
          cons_0(1,5) -> 3
          cons_0(1,5) -> 6
          cons_0(1,7) -> 2
          cons_0(1,7) -> 3
          cons_0(1,7) -> 6
          cons_0(3,1) -> 2
          cons_0(3,1) -> 3
          cons_0(3,1) -> 6
          cons_0(3,3) -> 2
          cons_0(3,3) -> 3
          cons_0(3,3) -> 6
          cons_0(3,5) -> 2
          cons_0(3,5) -> 3
          cons_0(3,5) -> 6
          cons_0(3,7) -> 2
          cons_0(3,7) -> 3
          cons_0(3,7) -> 6
          cons_0(5,1) -> 2
          cons_0(5,1) -> 3
          cons_0(5,1) -> 6
          cons_0(5,3) -> 2
          cons_0(5,3) -> 3
          cons_0(5,3) -> 6
          cons_0(5,5) -> 2
          cons_0(5,5) -> 3
          cons_0(5,5) -> 6
          cons_0(5,7) -> 2
          cons_0(5,7) -> 3
          cons_0(5,7) -> 6
          cons_0(7,1) -> 2
          cons_0(7,1) -> 3
          cons_0(7,1) -> 6
          cons_0(7,3) -> 2
          cons_0(7,3) -> 3
          cons_0(7,3) -> 6
          cons_0(7,5) -> 2
          cons_0(7,5) -> 3
          cons_0(7,5) -> 6
          cons_0(7,7) -> 2
          cons_0(7,7) -> 3
          cons_0(7,7) -> 6
          cons_1(8,9) -> 2
          cons_1(11,9) -> 4
          cons_2(12,13) -> 2
          cons_2(15,13) -> 4
          f_0(1) -> 4
          f_0(3) -> 4
          f_0(5) -> 4
          f_0(7) -> 4
          f_1(1) -> 2
          f_1(1) -> 4
          f_1(3) -> 2
          f_1(5) -> 2
          f_1(7) -> 2
          n__f_0(1) -> 2
          n__f_0(1) -> 5
          n__f_0(1) -> 6
          n__f_0(3) -> 2
          n__f_0(3) -> 5
          n__f_0(3) -> 6
          n__f_0(5) -> 2
          n__f_0(5) -> 5
          n__f_0(5) -> 6
          n__f_0(7) -> 2
          n__f_0(7) -> 5
          n__f_0(7) -> 6
          n__f_1(1) -> 4
          n__f_1(3) -> 4
          n__f_1(5) -> 4
          n__f_1(7) -> 4
          n__f_1(10) -> 9
          n__f_2(1) -> 2
          n__f_2(1) -> 4
          n__f_2(3) -> 2
          n__f_2(5) -> 2
          n__f_2(7) -> 2
          n__f_2(14) -> 13
          p_0(1) -> 6
          p_0(3) -> 6
          p_0(5) -> 6
          p_0(7) -> 6
          p_1(10) -> 1
          p_1(10) -> 2
          p_1(10) -> 6
          s_0(1) -> 2
          s_0(1) -> 6
          s_0(1) -> 7
          s_0(3) -> 2
          s_0(3) -> 6
          s_0(3) -> 7
          s_0(5) -> 2
          s_0(5) -> 6
          s_0(5) -> 7
          s_0(7) -> 2
          s_0(7) -> 6
          s_0(7) -> 7
          s_1(11) -> 10
          s_2(15) -> 14
          1 -> 2
          1 -> 6
          3 -> 2
          3 -> 6
          5 -> 2
          5 -> 6
          7 -> 2
          7 -> 6
          11 -> 1
          11 -> 2
          11 -> 6
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(s(0())))
            f(s(0())) -> f(p(s(0())))
            p(s(X)) -> X
        - Signature:
            {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))