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