MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            f(x) -> g(f(x))
            g(x) -> a()
            g(f(x)) -> x
        - Signature:
            {f/1,g/1} / {a/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {a}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          g(f(x)) -> x
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(x) -> g(f(x))
            g(x) -> a()
        - Signature:
            {f/1,g/1} / {a/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {a}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(x) -> c_1(g#(f(x)),f#(x))
          g#(x) -> c_2()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(x) -> c_1(g#(f(x)),f#(x))
            g#(x) -> c_2()
        - Weak TRS:
            f(x) -> g(f(x))
            g(x) -> a()
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {a/0,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {a}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2}
        by application of
          Pre({2}) = {1}.
        Here rules are labelled as follows:
          1: f#(x) -> c_1(g#(f(x)),f#(x))
          2: g#(x) -> c_2()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(x) -> c_1(g#(f(x)),f#(x))
        - Weak DPs:
            g#(x) -> c_2()
        - Weak TRS:
            f(x) -> g(f(x))
            g(x) -> a()
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {a/0,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {a}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(x) -> c_1(g#(f(x)),f#(x))
             -->_1 g#(x) -> c_2():2
             -->_2 f#(x) -> c_1(g#(f(x)),f#(x)):1
          
          2:W:g#(x) -> c_2()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: g#(x) -> c_2()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(x) -> c_1(g#(f(x)),f#(x))
        - Weak TRS:
            f(x) -> g(f(x))
            g(x) -> a()
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {a/0,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {a}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(x) -> c_1(g#(f(x)),f#(x))
             -->_2 f#(x) -> c_1(g#(f(x)),f#(x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(x) -> c_1(f#(x))
* Step 6: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(x) -> c_1(f#(x))
        - Weak TRS:
            f(x) -> g(f(x))
            g(x) -> a()
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {a/0,c_1/1,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {a}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(x) -> c_1(f#(x))
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(x) -> c_1(f#(x))
      - Signature:
          {f/1,g/1,f#/1,g#/1} / {a/0,c_1/1,c_2/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {a}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE