MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            active(c()) -> mark(a())
            active(c()) -> mark(b())
            active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
            active(f(a(),b(),X)) -> mark(f(X,X,X))
            f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
            f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
            proper(a()) -> ok(a())
            proper(b()) -> ok(b())
            proper(c()) -> ok(c())
            proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/3,proper/1,top/1} / {a/0,b/0,c/0,mark/1,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {a,b,c,mark,ok}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          active#(c()) -> c_1()
          active#(c()) -> c_2()
          active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
          active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
          f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
          f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
          proper#(a()) -> c_7()
          proper#(b()) -> c_8()
          proper#(c()) -> c_9()
          proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
          top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
          top#(ok(X)) -> c_12(top#(active(X)),active#(X))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            active#(c()) -> c_1()
            active#(c()) -> c_2()
            active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
            active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
            f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
            f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
            proper#(a()) -> c_7()
            proper#(b()) -> c_8()
            proper#(c()) -> c_9()
            proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
            top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
            top#(ok(X)) -> c_12(top#(active(X)),active#(X))
        - Weak TRS:
            active(c()) -> mark(a())
            active(c()) -> mark(b())
            active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
            active(f(a(),b(),X)) -> mark(f(X,X,X))
            f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
            f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
            proper(a()) -> ok(a())
            proper(b()) -> ok(b())
            proper(c()) -> ok(c())
            proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/3,proper/1,top/1,active#/1,f#/3,proper#/1,top#/1} / {a/0,b/0,c/0,mark/1,ok/1,c_1/0,c_2/0,c_3/2
            ,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/0,c_10/4,c_11/2,c_12/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active#,f#,proper#,top#} and constructors {a,b,c,mark,ok}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          active(c()) -> mark(a())
          active(c()) -> mark(b())
          active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
          active(f(a(),b(),X)) -> mark(f(X,X,X))
          f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
          f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
          proper(a()) -> ok(a())
          proper(b()) -> ok(b())
          proper(c()) -> ok(c())
          proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
          active#(c()) -> c_1()
          active#(c()) -> c_2()
          active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
          active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
          f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
          f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
          proper#(a()) -> c_7()
          proper#(b()) -> c_8()
          proper#(c()) -> c_9()
          proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
          top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
          top#(ok(X)) -> c_12(top#(active(X)),active#(X))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            active#(c()) -> c_1()
            active#(c()) -> c_2()
            active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
            active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
            f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
            f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
            proper#(a()) -> c_7()
            proper#(b()) -> c_8()
            proper#(c()) -> c_9()
            proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
            top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
            top#(ok(X)) -> c_12(top#(active(X)),active#(X))
        - Weak TRS:
            active(c()) -> mark(a())
            active(c()) -> mark(b())
            active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
            active(f(a(),b(),X)) -> mark(f(X,X,X))
            f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
            f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
            proper(a()) -> ok(a())
            proper(b()) -> ok(b())
            proper(c()) -> ok(c())
            proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        - Signature:
            {active/1,f/3,proper/1,top/1,active#/1,f#/3,proper#/1,top#/1} / {a/0,b/0,c/0,mark/1,ok/1,c_1/0,c_2/0,c_3/2
            ,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/0,c_10/4,c_11/2,c_12/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active#,f#,proper#,top#} and constructors {a,b,c,mark,ok}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,7,8,9}
        by application of
          Pre({1,2,7,8,9}) = {3,10,11,12}.
        Here rules are labelled as follows:
          1: active#(c()) -> c_1()
          2: active#(c()) -> c_2()
          3: active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
          4: active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
          5: f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
          6: f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
          7: proper#(a()) -> c_7()
          8: proper#(b()) -> c_8()
          9: proper#(c()) -> c_9()
          10: proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
          11: top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
          12: top#(ok(X)) -> c_12(top#(active(X)),active#(X))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
            active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
            f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
            f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
            proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
            top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
            top#(ok(X)) -> c_12(top#(active(X)),active#(X))
        - Weak DPs:
            active#(c()) -> c_1()
            active#(c()) -> c_2()
            proper#(a()) -> c_7()
            proper#(b()) -> c_8()
            proper#(c()) -> c_9()
        - Weak TRS:
            active(c()) -> mark(a())
            active(c()) -> mark(b())
            active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
            active(f(a(),b(),X)) -> mark(f(X,X,X))
            f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
            f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
            proper(a()) -> ok(a())
            proper(b()) -> ok(b())
            proper(c()) -> ok(c())
            proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        - Signature:
            {active/1,f/3,proper/1,top/1,active#/1,f#/3,proper#/1,top#/1} / {a/0,b/0,c/0,mark/1,ok/1,c_1/0,c_2/0,c_3/2
            ,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/0,c_10/4,c_11/2,c_12/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active#,f#,proper#,top#} and constructors {a,b,c,mark,ok}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
             -->_1 f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3)):4
             -->_1 f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3)):3
             -->_2 active#(f(a(),b(),X)) -> c_4(f#(X,X,X)):2
             -->_2 active#(c()) -> c_2():9
             -->_2 active#(c()) -> c_1():8
             -->_2 active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3)):1
          
          2:S:active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
             -->_1 f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3)):4
             -->_1 f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3)):3
          
          3:S:f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
             -->_1 f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3)):4
             -->_1 f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3)):3
          
          4:S:f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
             -->_1 f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3)):4
             -->_1 f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3)):3
          
          5:S:proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
             -->_4 proper#(c()) -> c_9():12
             -->_3 proper#(c()) -> c_9():12
             -->_2 proper#(c()) -> c_9():12
             -->_4 proper#(b()) -> c_8():11
             -->_3 proper#(b()) -> c_8():11
             -->_2 proper#(b()) -> c_8():11
             -->_4 proper#(a()) -> c_7():10
             -->_3 proper#(a()) -> c_7():10
             -->_2 proper#(a()) -> c_7():10
             -->_4 proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3))
                                               ,proper#(X1)
                                               ,proper#(X2)
                                               ,proper#(X3)):5
             -->_3 proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3))
                                               ,proper#(X1)
                                               ,proper#(X2)
                                               ,proper#(X3)):5
             -->_2 proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3))
                                               ,proper#(X1)
                                               ,proper#(X2)
                                               ,proper#(X3)):5
             -->_1 f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3)):4
             -->_1 f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3)):3
          
          6:S:top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
             -->_1 top#(ok(X)) -> c_12(top#(active(X)),active#(X)):7
             -->_2 proper#(c()) -> c_9():12
             -->_2 proper#(b()) -> c_8():11
             -->_2 proper#(a()) -> c_7():10
             -->_1 top#(mark(X)) -> c_11(top#(proper(X)),proper#(X)):6
             -->_2 proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3))
                                               ,proper#(X1)
                                               ,proper#(X2)
                                               ,proper#(X3)):5
          
          7:S:top#(ok(X)) -> c_12(top#(active(X)),active#(X))
             -->_2 active#(c()) -> c_2():9
             -->_2 active#(c()) -> c_1():8
             -->_1 top#(ok(X)) -> c_12(top#(active(X)),active#(X)):7
             -->_1 top#(mark(X)) -> c_11(top#(proper(X)),proper#(X)):6
             -->_2 active#(f(a(),b(),X)) -> c_4(f#(X,X,X)):2
             -->_2 active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3)):1
          
          8:W:active#(c()) -> c_1()
             
          
          9:W:active#(c()) -> c_2()
             
          
          10:W:proper#(a()) -> c_7()
             
          
          11:W:proper#(b()) -> c_8()
             
          
          12:W:proper#(c()) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          10: proper#(a()) -> c_7()
          11: proper#(b()) -> c_8()
          12: proper#(c()) -> c_9()
          8: active#(c()) -> c_1()
          9: active#(c()) -> c_2()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          active#(f(X1,X2,X3)) -> c_3(f#(X1,X2,active(X3)),active#(X3))
          active#(f(a(),b(),X)) -> c_4(f#(X,X,X))
          f#(X1,X2,mark(X3)) -> c_5(f#(X1,X2,X3))
          f#(ok(X1),ok(X2),ok(X3)) -> c_6(f#(X1,X2,X3))
          proper#(f(X1,X2,X3)) -> c_10(f#(proper(X1),proper(X2),proper(X3)),proper#(X1),proper#(X2),proper#(X3))
          top#(mark(X)) -> c_11(top#(proper(X)),proper#(X))
          top#(ok(X)) -> c_12(top#(active(X)),active#(X))
      - Weak TRS:
          active(c()) -> mark(a())
          active(c()) -> mark(b())
          active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
          active(f(a(),b(),X)) -> mark(f(X,X,X))
          f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
          f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
          proper(a()) -> ok(a())
          proper(b()) -> ok(b())
          proper(c()) -> ok(c())
          proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
      - Signature:
          {active/1,f/3,proper/1,top/1,active#/1,f#/3,proper#/1,top#/1} / {a/0,b/0,c/0,mark/1,ok/1,c_1/0,c_2/0,c_3/2
          ,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/0,c_10/4,c_11/2,c_12/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {active#,f#,proper#,top#} and constructors {a,b,c,mark,ok}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE