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