MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            goal(x) -> nestinc(x)
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
            nestinc(Cons(x,xs)) -> nestinc(inc(Cons(x,xs)))
            nestinc(Nil()) -> number17(Nil())
            number17(x) -> Cons(Nil()
                               ,Cons(Nil()
                                    ,Cons(Nil()
                                         ,Cons(Nil()
                                              ,Cons(Nil()
                                                   ,Cons(Nil()
                                                        ,Cons(Nil()
                                                             ,Cons(Nil()
                                                                  ,Cons(Nil()
                                                                       ,Cons(Nil()
                                                                            ,Cons(Nil()
                                                                                 ,Cons(Nil()
                                                                                      ,Cons(Nil()
                                                                                           ,Cons(Nil()
                                                                                                ,Cons(Nil()
                                                                                                     ,Cons(Nil()
                                                                                                          ,Cons(Nil()
                                                                                                               ,Nil())))))))))))))))))
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,inc,nestinc,number17} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          goal#(x) -> c_1(nestinc#(x))
          inc#(Cons(x,xs)) -> c_2(inc#(xs))
          inc#(Nil()) -> c_3()
          nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
          nestinc#(Nil()) -> c_5(number17#(Nil()))
          number17#(x) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x) -> c_1(nestinc#(x))
            inc#(Cons(x,xs)) -> c_2(inc#(xs))
            inc#(Nil()) -> c_3()
            nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
            nestinc#(Nil()) -> c_5(number17#(Nil()))
            number17#(x) -> c_6()
        - Weak TRS:
            goal(x) -> nestinc(x)
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
            nestinc(Cons(x,xs)) -> nestinc(inc(Cons(x,xs)))
            nestinc(Nil()) -> number17(Nil())
            number17(x) -> Cons(Nil()
                               ,Cons(Nil()
                                    ,Cons(Nil()
                                         ,Cons(Nil()
                                              ,Cons(Nil()
                                                   ,Cons(Nil()
                                                        ,Cons(Nil()
                                                             ,Cons(Nil()
                                                                  ,Cons(Nil()
                                                                       ,Cons(Nil()
                                                                            ,Cons(Nil()
                                                                                 ,Cons(Nil()
                                                                                      ,Cons(Nil()
                                                                                           ,Cons(Nil()
                                                                                                ,Cons(Nil()
                                                                                                     ,Cons(Nil()
                                                                                                          ,Cons(Nil()
                                                                                                               ,Nil())))))))))))))))))
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
            ,c_4/2,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
            ,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
          inc(Nil()) -> Cons(Nil(),Nil())
          goal#(x) -> c_1(nestinc#(x))
          inc#(Cons(x,xs)) -> c_2(inc#(xs))
          inc#(Nil()) -> c_3()
          nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
          nestinc#(Nil()) -> c_5(number17#(Nil()))
          number17#(x) -> c_6()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x) -> c_1(nestinc#(x))
            inc#(Cons(x,xs)) -> c_2(inc#(xs))
            inc#(Nil()) -> c_3()
            nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
            nestinc#(Nil()) -> c_5(number17#(Nil()))
            number17#(x) -> c_6()
        - Weak TRS:
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
            ,c_4/2,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
            ,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,6}
        by application of
          Pre({3,6}) = {2,5}.
        Here rules are labelled as follows:
          1: goal#(x) -> c_1(nestinc#(x))
          2: inc#(Cons(x,xs)) -> c_2(inc#(xs))
          3: inc#(Nil()) -> c_3()
          4: nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
          5: nestinc#(Nil()) -> c_5(number17#(Nil()))
          6: number17#(x) -> c_6()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x) -> c_1(nestinc#(x))
            inc#(Cons(x,xs)) -> c_2(inc#(xs))
            nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
            nestinc#(Nil()) -> c_5(number17#(Nil()))
        - Weak DPs:
            inc#(Nil()) -> c_3()
            number17#(x) -> c_6()
        - Weak TRS:
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
            ,c_4/2,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
            ,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4}
        by application of
          Pre({4}) = {1,3}.
        Here rules are labelled as follows:
          1: goal#(x) -> c_1(nestinc#(x))
          2: inc#(Cons(x,xs)) -> c_2(inc#(xs))
          3: nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
          4: nestinc#(Nil()) -> c_5(number17#(Nil()))
          5: inc#(Nil()) -> c_3()
          6: number17#(x) -> c_6()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x) -> c_1(nestinc#(x))
            inc#(Cons(x,xs)) -> c_2(inc#(xs))
            nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
        - Weak DPs:
            inc#(Nil()) -> c_3()
            nestinc#(Nil()) -> c_5(number17#(Nil()))
            number17#(x) -> c_6()
        - Weak TRS:
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
            ,c_4/2,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
            ,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:goal#(x) -> c_1(nestinc#(x))
             -->_1 nestinc#(Nil()) -> c_5(number17#(Nil())):5
             -->_1 nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs))):3
          
          2:S:inc#(Cons(x,xs)) -> c_2(inc#(xs))
             -->_1 inc#(Nil()) -> c_3():4
             -->_1 inc#(Cons(x,xs)) -> c_2(inc#(xs)):2
          
          3:S:nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
             -->_1 nestinc#(Nil()) -> c_5(number17#(Nil())):5
             -->_1 nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs))):3
             -->_2 inc#(Cons(x,xs)) -> c_2(inc#(xs)):2
          
          4:W:inc#(Nil()) -> c_3()
             
          
          5:W:nestinc#(Nil()) -> c_5(number17#(Nil()))
             -->_1 number17#(x) -> c_6():6
          
          6:W:number17#(x) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: inc#(Nil()) -> c_3()
          5: nestinc#(Nil()) -> c_5(number17#(Nil()))
          6: number17#(x) -> c_6()
* Step 6: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            goal#(x) -> c_1(nestinc#(x))
            inc#(Cons(x,xs)) -> c_2(inc#(xs))
            nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
        - Weak TRS:
            inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
            inc(Nil()) -> Cons(Nil(),Nil())
        - Signature:
            {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
            ,c_4/2,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
            ,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:goal#(x) -> c_1(nestinc#(x))
           -->_1 nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs))):3
        
        2:S:inc#(Cons(x,xs)) -> c_2(inc#(xs))
           -->_1 inc#(Cons(x,xs)) -> c_2(inc#(xs)):2
        
        3:S:nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
           -->_1 nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs))):3
           -->_2 inc#(Cons(x,xs)) -> c_2(inc#(xs)):2
        
        
        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).
        
        [(1,goal#(x) -> c_1(nestinc#(x)))]
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          inc#(Cons(x,xs)) -> c_2(inc#(xs))
          nestinc#(Cons(x,xs)) -> c_4(nestinc#(inc(Cons(x,xs))),inc#(Cons(x,xs)))
      - Weak TRS:
          inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
          inc(Nil()) -> Cons(Nil(),Nil())
      - Signature:
          {goal/1,inc/1,nestinc/1,number17/1,goal#/1,inc#/1,nestinc#/1,number17#/1} / {Cons/2,Nil/0,c_1/1,c_2/1,c_3/0
          ,c_4/2,c_5/1,c_6/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {goal#,inc#,nestinc#,number17#} and constructors {Cons
          ,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE