MAYBE
* Step 1: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first,from,sel} 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) = [1]                  
             p(cons) = [1] x1 + [1] x2 + [0]
            p(first) = [1] x2 + [3]         
             p(from) = [1] x1 + [1]         
              p(nil) = [1]                  
                p(s) = [1]                  
              p(sel) = [2] x2 + [4]         
          
          Following rules are strictly oriented:
                first(0(),Z) = [1] Z + [3]        
                             > [1]                
                             = nil()              
          
          sel(0(),cons(X,Z)) = [2] X + [2] Z + [4]
                             > [1] X + [0]        
                             = X                  
          
          
          Following rules are (at-least) weakly oriented:
          first(s(X),cons(Y,Z)) =  [1] Y + [1] Z + [3]
                                >= [1] Y + [1] Z + [3]
                                =  cons(Y,first(X,Z)) 
          
                        from(X) =  [1] X + [1]        
                                >= [1] X + [2]        
                                =  cons(X,from(s(X))) 
          
            sel(s(X),cons(Y,Z)) =  [2] Y + [2] Z + [4]
                                >= [2] Z + [4]        
                                =  sel(X,Z)           
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Weak TRS:
            first(0(),Z) -> nil()
            sel(0(),cons(X,Z)) -> X
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first,from,sel} 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) = [1]                  
             p(cons) = [1] x1 + [1] x2 + [3]
            p(first) = [2] x2 + [14]        
             p(from) = [2] x1 + [3]         
              p(nil) = [0]                  
                p(s) = [4]                  
              p(sel) = [6] x2 + [3]         
          
          Following rules are strictly oriented:
          first(s(X),cons(Y,Z)) = [2] Y + [2] Z + [20]
                                > [1] Y + [2] Z + [17]
                                = cons(Y,first(X,Z))  
          
            sel(s(X),cons(Y,Z)) = [6] Y + [6] Z + [21]
                                > [6] Z + [3]         
                                = sel(X,Z)            
          
          
          Following rules are (at-least) weakly oriented:
                first(0(),Z) =  [2] Z + [14]        
                             >= [0]                 
                             =  nil()               
          
                     from(X) =  [2] X + [3]         
                             >= [1] X + [14]        
                             =  cons(X,from(s(X)))  
          
          sel(0(),cons(X,Z)) =  [6] X + [6] Z + [21]
                             >= [1] X + [0]         
                             =  X                   
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          from(X) -> cons(X,from(s(X)))
      - Weak TRS:
          first(0(),Z) -> nil()
          first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
          sel(0(),cons(X,Z)) -> X
          sel(s(X),cons(Y,Z)) -> sel(X,Z)
      - Signature:
          {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {first,from,sel} and constructors {0,cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE