MAYBE
* Step 1: WeightGap 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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(cons) = {2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
               p(0) = [0]                  
             p(2nd) = [1] x1 + [4]         
            p(cons) = [1] x1 + [1] x2 + [2]
            p(from) = [1] x1 + [0]         
            p(head) = [1] x1 + [2]         
             p(nil) = [0]                  
               p(s) = [0]                  
             p(sel) = [1] x2 + [0]         
            p(take) = [2] x2 + [3]         
          
          Following rules are strictly oriented:
                2nd(cons(X,XS)) = [1] X + [1] XS + [6]
                                > [1] XS + [2]        
                                = head(XS)            
          
               head(cons(X,XS)) = [1] X + [1] XS + [4]
                                > [1] X + [0]         
                                = X                   
          
            sel(0(),cons(X,XS)) = [1] X + [1] XS + [2]
                                > [1] X + [0]         
                                = X                   
          
           sel(s(N),cons(X,XS)) = [1] X + [1] XS + [2]
                                > [1] XS + [0]        
                                = sel(N,XS)           
          
                   take(0(),XS) = [2] XS + [3]        
                                > [0]                 
                                = nil()               
          
          take(s(N),cons(X,XS)) = [2] X + [2] XS + [7]
                                > [1] X + [2] XS + [5]
                                = cons(X,take(N,XS))  
          
          
          Following rules are (at-least) weakly oriented:
          from(X) =  [1] X + [0]       
                  >= [1] X + [2]       
                  =  cons(X,from(s(X)))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          from(X) -> cons(X,from(s(X)))
      - Weak TRS:
          2nd(cons(X,XS)) -> head(XS)
          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:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE