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