MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
            f(n__a(),X,X) -> f(activate(X),b(),n__b())
        - Signature:
            {a/0,activate/1,b/0,f/3} / {n__a/0,n__b/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,b,f} and constructors {n__a,n__b}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#() -> c_1()
          activate#(X) -> c_2()
          activate#(n__a()) -> c_3(a#())
          activate#(n__b()) -> c_4(b#())
          b#() -> c_5(a#())
          b#() -> c_6()
          f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__b()) -> c_4(b#())
            b#() -> c_5(a#())
            b#() -> c_6()
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
            f(n__a(),X,X) -> f(activate(X),b(),n__b())
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          a() -> n__a()
          activate(X) -> X
          activate(n__a()) -> a()
          activate(n__b()) -> b()
          b() -> a()
          b() -> n__b()
          a#() -> c_1()
          activate#(X) -> c_2()
          activate#(n__a()) -> c_3(a#())
          activate#(n__b()) -> c_4(b#())
          b#() -> c_5(a#())
          b#() -> c_6()
          f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__b()) -> c_4(b#())
            b#() -> c_5(a#())
            b#() -> c_6()
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,6}
        by application of
          Pre({1,2,6}) = {3,4,5,7}.
        Here rules are labelled as follows:
          1: a#() -> c_1()
          2: activate#(X) -> c_2()
          3: activate#(n__a()) -> c_3(a#())
          4: activate#(n__b()) -> c_4(b#())
          5: b#() -> c_5(a#())
          6: b#() -> c_6()
          7: f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__a()) -> c_3(a#())
            activate#(n__b()) -> c_4(b#())
            b#() -> c_5(a#())
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            b#() -> c_6()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3}
        by application of
          Pre({1,3}) = {2,4}.
        Here rules are labelled as follows:
          1: activate#(n__a()) -> c_3(a#())
          2: activate#(n__b()) -> c_4(b#())
          3: b#() -> c_5(a#())
          4: f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
          5: a#() -> c_1()
          6: activate#(X) -> c_2()
          7: b#() -> c_6()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__b()) -> c_4(b#())
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            b#() -> c_5(a#())
            b#() -> c_6()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2}.
        Here rules are labelled as follows:
          1: activate#(n__b()) -> c_4(b#())
          2: f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
          3: a#() -> c_1()
          4: activate#(X) -> c_2()
          5: activate#(n__a()) -> c_3(a#())
          6: b#() -> c_5(a#())
          7: b#() -> c_6()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__b()) -> c_4(b#())
            b#() -> c_5(a#())
            b#() -> c_6()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
             -->_3 b#() -> c_5(a#()):6
             -->_2 activate#(n__b()) -> c_4(b#()):5
             -->_2 activate#(n__a()) -> c_3(a#()):4
             -->_3 b#() -> c_6():7
             -->_2 activate#(X) -> c_2():3
             -->_1 f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#()):1
          
          2:W:a#() -> c_1()
             
          
          3:W:activate#(X) -> c_2()
             
          
          4:W:activate#(n__a()) -> c_3(a#())
             -->_1 a#() -> c_1():2
          
          5:W:activate#(n__b()) -> c_4(b#())
             -->_1 b#() -> c_5(a#()):6
             -->_1 b#() -> c_6():7
          
          6:W:b#() -> c_5(a#())
             -->_1 a#() -> c_1():2
          
          7:W:b#() -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: activate#(X) -> c_2()
          4: activate#(n__a()) -> c_3(a#())
          5: activate#(n__b()) -> c_4(b#())
          7: b#() -> c_6()
          6: b#() -> c_5(a#())
          2: a#() -> c_1()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__b()) -> b()
            b() -> a()
            b() -> n__b()
        - Signature:
            {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
            ,c_7/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#())
             -->_1 f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()),activate#(X),b#()):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()))
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(n__a(),X,X) -> c_7(f#(activate(X),b(),n__b()))
      - Weak TRS:
          a() -> n__a()
          activate(X) -> X
          activate(n__a()) -> a()
          activate(n__b()) -> b()
          b() -> a()
          b() -> n__b()
      - Signature:
          {a/0,activate/1,b/0,f/3,a#/0,activate#/1,b#/0,f#/3} / {n__a/0,n__b/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0
          ,c_7/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a#,activate#,b#,f#} and constructors {n__a,n__b}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE