*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(activate(X))
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        f(f(a())) -> c(n__f(n__g(n__f(n__a()))))
        g(X) -> n__g(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1}
      Obligation:
        Innermost
        basic terms: {a,activate,f,g}/{c,n__a,n__f,n__g}
    Applied Processor:
      InnermostRuleRemoval
    Proof:
      Arguments of following rules are not normal-forms.
        f(f(a())) -> c(n__f(n__g(n__f(n__a()))))
      All above mentioned rules can be savely removed.
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(activate(X))
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        g(X) -> n__g(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1}
      Obligation:
        Innermost
        basic terms: {a,activate,f,g}/{c,n__a,n__f,n__g}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        a_0() -> 1
        a_1() -> 1
        a_1() -> 3
        activate_0(2) -> 1
        activate_1(2) -> 3
        c_0(2) -> 1
        c_0(2) -> 2
        c_0(2) -> 3
        f_0(2) -> 1
        f_1(3) -> 1
        f_1(3) -> 3
        g_0(2) -> 1
        g_1(3) -> 1
        g_1(3) -> 3
        n__a_0() -> 1
        n__a_0() -> 2
        n__a_0() -> 3
        n__a_1() -> 1
        n__a_2() -> 1
        n__a_2() -> 3
        n__f_0(2) -> 1
        n__f_0(2) -> 2
        n__f_0(2) -> 3
        n__f_1(2) -> 1
        n__f_2(3) -> 1
        n__f_2(3) -> 3
        n__g_0(2) -> 1
        n__g_0(2) -> 2
        n__g_0(2) -> 3
        n__g_1(2) -> 1
        n__g_2(3) -> 1
        n__g_2(3) -> 3
        2 -> 1
        2 -> 3
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(activate(X))
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        g(X) -> n__g(X)
      Signature:
        {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1}
      Obligation:
        Innermost
        basic terms: {a,activate,f,g}/{c,n__a,n__f,n__g}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).