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