MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            dbls(nil()) -> nil()
            from(X) -> cons(X,from(s(X)))
            indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            indx(nil(),X) -> nil()
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {dbl/1,dbls/1,from/1,indx/2,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,dbls,from,indx,sel} and constructors {0,cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          dbl#(0()) -> c_1()
          dbl#(s(X)) -> c_2(dbl#(X))
          dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
          dbls#(nil()) -> c_4()
          from#(X) -> c_5(from#(s(X)))
          indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
          indx#(nil(),X) -> c_7()
          sel#(0(),cons(X,Y)) -> c_8()
          sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            dbl#(0()) -> c_1()
            dbl#(s(X)) -> c_2(dbl#(X))
            dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
            dbls#(nil()) -> c_4()
            from#(X) -> c_5(from#(s(X)))
            indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
            indx#(nil(),X) -> c_7()
            sel#(0(),cons(X,Y)) -> c_8()
            sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
        - Weak TRS:
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            dbls(nil()) -> nil()
            from(X) -> cons(X,from(s(X)))
            indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            indx(nil(),X) -> nil()
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {dbl/1,dbls/1,from/1,indx/2,sel/2,dbl#/1,dbls#/1,from#/1,indx#/2,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1
            ,c_3/2,c_4/0,c_5/1,c_6/2,c_7/0,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl#,dbls#,from#,indx#,sel#} and constructors {0,cons,nil
            ,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          dbl#(0()) -> c_1()
          dbl#(s(X)) -> c_2(dbl#(X))
          dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
          dbls#(nil()) -> c_4()
          from#(X) -> c_5(from#(s(X)))
          indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
          indx#(nil(),X) -> c_7()
          sel#(0(),cons(X,Y)) -> c_8()
          sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            dbl#(0()) -> c_1()
            dbl#(s(X)) -> c_2(dbl#(X))
            dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
            dbls#(nil()) -> c_4()
            from#(X) -> c_5(from#(s(X)))
            indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
            indx#(nil(),X) -> c_7()
            sel#(0(),cons(X,Y)) -> c_8()
            sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
        - Signature:
            {dbl/1,dbls/1,from/1,indx/2,sel/2,dbl#/1,dbls#/1,from#/1,indx#/2,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1
            ,c_3/2,c_4/0,c_5/1,c_6/2,c_7/0,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl#,dbls#,from#,indx#,sel#} and constructors {0,cons,nil
            ,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,7,8}
        by application of
          Pre({1,4,7,8}) = {2,3,6,9}.
        Here rules are labelled as follows:
          1: dbl#(0()) -> c_1()
          2: dbl#(s(X)) -> c_2(dbl#(X))
          3: dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
          4: dbls#(nil()) -> c_4()
          5: from#(X) -> c_5(from#(s(X)))
          6: indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
          7: indx#(nil(),X) -> c_7()
          8: sel#(0(),cons(X,Y)) -> c_8()
          9: sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            dbl#(s(X)) -> c_2(dbl#(X))
            dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
            from#(X) -> c_5(from#(s(X)))
            indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
            sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
        - Weak DPs:
            dbl#(0()) -> c_1()
            dbls#(nil()) -> c_4()
            indx#(nil(),X) -> c_7()
            sel#(0(),cons(X,Y)) -> c_8()
        - Signature:
            {dbl/1,dbls/1,from/1,indx/2,sel/2,dbl#/1,dbls#/1,from#/1,indx#/2,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1
            ,c_3/2,c_4/0,c_5/1,c_6/2,c_7/0,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl#,dbls#,from#,indx#,sel#} and constructors {0,cons,nil
            ,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:dbl#(s(X)) -> c_2(dbl#(X))
             -->_1 dbl#(0()) -> c_1():6
             -->_1 dbl#(s(X)) -> c_2(dbl#(X)):1
          
          2:S:dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
             -->_2 dbls#(nil()) -> c_4():7
             -->_1 dbl#(0()) -> c_1():6
             -->_2 dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y)):2
             -->_1 dbl#(s(X)) -> c_2(dbl#(X)):1
          
          3:S:from#(X) -> c_5(from#(s(X)))
             -->_1 from#(X) -> c_5(from#(s(X))):3
          
          4:S:indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
             -->_1 sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z)):5
             -->_1 sel#(0(),cons(X,Y)) -> c_8():9
             -->_2 indx#(nil(),X) -> c_7():8
             -->_2 indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z)):4
          
          5:S:sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
             -->_1 sel#(0(),cons(X,Y)) -> c_8():9
             -->_1 sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z)):5
          
          6:W:dbl#(0()) -> c_1()
             
          
          7:W:dbls#(nil()) -> c_4()
             
          
          8:W:indx#(nil(),X) -> c_7()
             
          
          9:W:sel#(0(),cons(X,Y)) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: indx#(nil(),X) -> c_7()
          9: sel#(0(),cons(X,Y)) -> c_8()
          7: dbls#(nil()) -> c_4()
          6: dbl#(0()) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          dbl#(s(X)) -> c_2(dbl#(X))
          dbls#(cons(X,Y)) -> c_3(dbl#(X),dbls#(Y))
          from#(X) -> c_5(from#(s(X)))
          indx#(cons(X,Y),Z) -> c_6(sel#(X,Z),indx#(Y,Z))
          sel#(s(X),cons(Y,Z)) -> c_9(sel#(X,Z))
      - Signature:
          {dbl/1,dbls/1,from/1,indx/2,sel/2,dbl#/1,dbls#/1,from#/1,indx#/2,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1
          ,c_3/2,c_4/0,c_5/1,c_6/2,c_7/0,c_8/0,c_9/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {dbl#,dbls#,from#,indx#,sel#} and constructors {0,cons,nil
          ,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE