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