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