*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        activate(X) -> X
        activate(n__f(X)) -> f(activate(X))
        activate(n__h(X)) -> h(activate(X))
        f(X) -> g(n__h(n__f(X)))
        f(X) -> n__f(X)
        h(X) -> n__h(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
      Obligation:
        Full
        basic terms: {activate,f,h}/{g,n__f,n__h}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        activate(X) -> X
        activate(n__f(X)) -> f(activate(X))
        activate(n__h(X)) -> h(activate(X))
        f(X) -> g(n__h(n__f(X)))
        f(X) -> n__f(X)
        h(X) -> n__h(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
      Obligation:
        Innermost
        basic terms: {activate,f,h}/{g,n__f,n__h}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        activate_0(2) -> 1
        activate_1(2) -> 3
        f_0(2) -> 1
        f_1(3) -> 1
        f_1(3) -> 3
        g_0(2) -> 1
        g_0(2) -> 2
        g_0(2) -> 3
        g_1(4) -> 1
        g_2(6) -> 1
        g_2(6) -> 3
        h_0(2) -> 1
        h_1(3) -> 1
        h_1(3) -> 3
        n__f_0(2) -> 1
        n__f_0(2) -> 2
        n__f_0(2) -> 3
        n__f_1(2) -> 1
        n__f_1(2) -> 5
        n__f_2(3) -> 1
        n__f_2(3) -> 3
        n__f_2(3) -> 7
        n__h_0(2) -> 1
        n__h_0(2) -> 2
        n__h_0(2) -> 3
        n__h_1(2) -> 1
        n__h_1(5) -> 4
        n__h_2(3) -> 1
        n__h_2(3) -> 3
        n__h_2(7) -> 6
        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:
        activate(X) -> X
        activate(n__f(X)) -> f(activate(X))
        activate(n__h(X)) -> h(activate(X))
        f(X) -> g(n__h(n__f(X)))
        f(X) -> n__f(X)
        h(X) -> n__h(X)
      Signature:
        {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
      Obligation:
        Innermost
        basic terms: {activate,f,h}/{g,n__f,n__h}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).