WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          {goal,revapp}
        TcT has computed the following interpretation:
            p(Cons) = [1] x1 + [1] x2 + [0]
             p(Nil) = [0]                  
            p(goal) = [3] x1 + [2] x2 + [2]
          p(revapp) = [2] x1 + [2] x2 + [0]
        
        Following rules are strictly oriented:
        goal(xs,ys) = [3] xs + [2] ys + [2]
                    > [2] xs + [2] ys + [0]
                    = revapp(xs,ys)        
        
        
        Following rules are (at-least) weakly oriented:
        revapp(Cons(x,xs),rest) =  [2] rest + [2] x + [2] xs + [0]
                                >= [2] rest + [2] x + [2] xs + [0]
                                =  revapp(xs,Cons(x,rest))        
        
             revapp(Nil(),rest) =  [2] rest + [0]                 
                                >= [1] rest + [0]                 
                                =  rest                           
        
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + 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:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(Cons) = [1] x2 + [13]        
               p(Nil) = [0]                  
              p(goal) = [1] x1 + [2] x2 + [1]
            p(revapp) = [1] x1 + [2] x2 + [1]
          
          Following rules are strictly oriented:
          revapp(Nil(),rest) = [2] rest + [1]
                             > [1] rest + [0]
                             = rest          
          
          
          Following rules are (at-least) weakly oriented:
                      goal(xs,ys) =  [1] xs + [2] ys + [1]   
                                  >= [1] xs + [2] ys + [1]   
                                  =  revapp(xs,ys)           
          
          revapp(Cons(x,xs),rest) =  [2] rest + [1] xs + [14]
                                  >= [2] rest + [1] xs + [27]
                                  =  revapp(xs,Cons(x,rest)) 
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + 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:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(Cons) = [1] x1 + [1] x2 + [2]
               p(Nil) = [0]                  
              p(goal) = [5] x1 + [4] x2 + [2]
            p(revapp) = [5] x1 + [4] x2 + [0]
          
          Following rules are strictly oriented:
          revapp(Cons(x,xs),rest) = [4] rest + [5] x + [5] xs + [10]
                                  > [4] rest + [4] x + [5] xs + [8] 
                                  = revapp(xs,Cons(x,rest))         
          
          
          Following rules are (at-least) weakly oriented:
                 goal(xs,ys) =  [5] xs + [4] ys + [2]
                             >= [5] xs + [4] ys + [0]
                             =  revapp(xs,ys)        
          
          revapp(Nil(),rest) =  [4] rest + [0]       
                             >= [1] rest + [0]       
                             =  rest                 
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            goal(xs,ys) -> revapp(xs,ys)
            revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest))
            revapp(Nil(),rest) -> rest
        - Signature:
            {goal/2,revapp/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,revapp} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))