MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            badd(x,Nil()) -> x
            badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
            goal(x,y) -> badd(x,y)
        - Signature:
            {badd/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {badd,goal} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          badd#(x,Nil()) -> c_1()
          badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
          goal#(x,y) -> c_3(badd#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            badd#(x,Nil()) -> c_1()
            badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
            goal#(x,y) -> c_3(badd#(x,y))
        - Weak TRS:
            badd(x,Nil()) -> x
            badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
            goal(x,y) -> badd(x,y)
        - Signature:
            {badd/2,goal/2,badd#/2,goal#/2} / {Cons/2,Nil/0,c_1/0,c_2/2,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {badd#,goal#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          badd(x,Nil()) -> x
          badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
          badd#(x,Nil()) -> c_1()
          badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
          goal#(x,y) -> c_3(badd#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            badd#(x,Nil()) -> c_1()
            badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
            goal#(x,y) -> c_3(badd#(x,y))
        - Weak TRS:
            badd(x,Nil()) -> x
            badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
        - Signature:
            {badd/2,goal/2,badd#/2,goal#/2} / {Cons/2,Nil/0,c_1/0,c_2/2,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {badd#,goal#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2,3}.
        Here rules are labelled as follows:
          1: badd#(x,Nil()) -> c_1()
          2: badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
          3: goal#(x,y) -> c_3(badd#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
            goal#(x,y) -> c_3(badd#(x,y))
        - Weak DPs:
            badd#(x,Nil()) -> c_1()
        - Weak TRS:
            badd(x,Nil()) -> x
            badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
        - Signature:
            {badd/2,goal/2,badd#/2,goal#/2} / {Cons/2,Nil/0,c_1/0,c_2/2,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {badd#,goal#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
             -->_2 badd#(x,Nil()) -> c_1():3
             -->_1 badd#(x,Nil()) -> c_1():3
             -->_2 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
             -->_1 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
          
          2:S:goal#(x,y) -> c_3(badd#(x,y))
             -->_1 badd#(x,Nil()) -> c_1():3
             -->_1 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
          
          3:W:badd#(x,Nil()) -> c_1()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: badd#(x,Nil()) -> c_1()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
            goal#(x,y) -> c_3(badd#(x,y))
        - Weak TRS:
            badd(x,Nil()) -> x
            badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
        - Signature:
            {badd/2,goal/2,badd#/2,goal#/2} / {Cons/2,Nil/0,c_1/0,c_2/2,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {badd#,goal#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
           -->_2 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
           -->_1 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
        
        2:S:goal#(x,y) -> c_3(badd#(x,y))
           -->_1 badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs)):1
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(2,goal#(x,y) -> c_3(badd#(x,y)))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          badd#(x',Cons(x,xs)) -> c_2(badd#(Cons(Nil(),Nil()),badd(x',xs)),badd#(x',xs))
      - Weak TRS:
          badd(x,Nil()) -> x
          badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs))
      - Signature:
          {badd/2,goal/2,badd#/2,goal#/2} / {Cons/2,Nil/0,c_1/0,c_2/2,c_3/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {badd#,goal#} and constructors {Cons,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE