*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        active(f(X)) -> f(active(X))
        active(f(f(a()))) -> mark(f(g(f(a()))))
        f(mark(X)) -> mark(f(X))
        f(ok(X)) -> ok(f(X))
        g(ok(X)) -> ok(g(X))
        proper(a()) -> ok(a())
        proper(f(X)) -> f(proper(X))
        proper(g(X)) -> g(proper(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
      Obligation:
        Full
        basic terms: {active,f,g,proper,top}/{a,mark,ok}
    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() -> 2
        a_1() -> 3
        active_0(2) -> 1
        active_1(2) -> 4
        active_2(2) -> 6
        active_2(3) -> 5
        f_0(2) -> 1
        f_1(2) -> 3
        f_2(6) -> 5
        g_0(2) -> 1
        g_1(2) -> 3
        mark_0(2) -> 2
        mark_1(3) -> 1
        mark_1(3) -> 3
        ok_0(2) -> 2
        ok_1(3) -> 1
        ok_1(3) -> 3
        ok_1(3) -> 4
        proper_0(2) -> 1
        proper_1(2) -> 4
        top_0(2) -> 1
        top_1(4) -> 1
        top_2(5) -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        active(f(X)) -> f(active(X))
        active(f(f(a()))) -> mark(f(g(f(a()))))
        f(mark(X)) -> mark(f(X))
        f(ok(X)) -> ok(f(X))
        g(ok(X)) -> ok(g(X))
        proper(a()) -> ok(a())
        proper(f(X)) -> f(proper(X))
        proper(g(X)) -> g(proper(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Signature:
        {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
      Obligation:
        Full
        basic terms: {active,f,g,proper,top}/{a,mark,ok}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).