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