MAYBE
* Step 1: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {first/2,from/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first,from} 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(cons) = [1] x2 + [1]         
            p(first) = [6] x1 + [2] x2 + [0]
             p(from) = [0]                  
              p(nil) = [4]                  
                p(s) = [1] x1 + [0]         
          
          Following rules are strictly oriented:
          first(s(X),cons(Y,Z)) = [6] X + [2] Z + [2]
                                > [6] X + [2] Z + [1]
                                = cons(Y,first(X,Z)) 
          
          
          Following rules are (at-least) weakly oriented:
          first(0(),X) =  [2] X + [0]       
                       >= [4]               
                       =  nil()             
          
               from(X) =  [0]               
                       >= [1]               
                       =  cons(X,from(s(X)))
          
        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(0(),X) -> nil()
            from(X) -> cons(X,from(s(X)))
        - Weak TRS:
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
        - Signature:
            {first/2,from/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first,from} 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] x2 + [2] 
            p(first) = [2] x2 + [8] 
             p(from) = [8] x1 + [10]
              p(nil) = [1]          
                p(s) = [2]          
          
          Following rules are strictly oriented:
          first(0(),X) = [2] X + [8]
                       > [1]        
                       = nil()      
          
          
          Following rules are (at-least) weakly oriented:
          first(s(X),cons(Y,Z)) =  [2] Z + [12]      
                                >= [2] Z + [10]      
                                =  cons(Y,first(X,Z))
          
                        from(X) =  [8] X + [10]      
                                >= [28]              
                                =  cons(X,from(s(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(),X) -> nil()
          first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
      - Signature:
          {first/2,from/1} / {0/0,cons/2,nil/0,s/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {first,from} and constructors {0,cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE