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