WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} 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:
          {anchored,goal}
        TcT has computed the following interpretation:
              p(Cons) = [0]           
               p(Nil) = [8]           
          p(anchored) = [8] x2 + [11] 
              p(goal) = [12] x2 + [11]
        
        Following rules are strictly oriented:
        anchored(Nil(),y) = [8] y + [11]
                          > [1] y + [0] 
                          = y           
        
        
        Following rules are (at-least) weakly oriented:
        anchored(Cons(x,xs),y) =  [8] y + [11]                          
                               >= [11]                                  
                               =  anchored(xs,Cons(Cons(Nil(),Nil()),y))
        
                     goal(x,y) =  [12] y + [11]                         
                               >= [8] y + [11]                          
                               =  anchored(x,y)                         
        
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            goal(x,y) -> anchored(x,y)
        - Weak TRS:
            anchored(Nil(),y) -> y
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          {anchored,goal}
        TcT has computed the following interpretation:
              p(Cons) = x2      
               p(Nil) = 4       
          p(anchored) = 8*x2    
              p(goal) = 8 + 8*x2
        
        Following rules are strictly oriented:
        goal(x,y) = 8 + 8*y      
                  > 8*y          
                  = anchored(x,y)
        
        
        Following rules are (at-least) weakly oriented:
        anchored(Cons(x,xs),y) =  8*y                                   
                               >= 8*y                                   
                               =  anchored(xs,Cons(Cons(Nil(),Nil()),y))
        
             anchored(Nil(),y) =  8*y                                   
                               >= y                                     
                               =  y                                     
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
        - Weak TRS:
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} 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:
          {anchored,goal}
        TcT has computed the following interpretation:
              p(Cons) = [1] x2 + [2]         
               p(Nil) = [0]                  
          p(anchored) = [4] x1 + [3] x2 + [2]
              p(goal) = [6] x1 + [3] x2 + [3]
        
        Following rules are strictly oriented:
        anchored(Cons(x,xs),y) = [4] xs + [3] y + [10]                 
                               > [4] xs + [3] y + [8]                  
                               = anchored(xs,Cons(Cons(Nil(),Nil()),y))
        
        
        Following rules are (at-least) weakly oriented:
        anchored(Nil(),y) =  [3] y + [2]        
                          >= [1] y + [0]        
                          =  y                  
        
                goal(x,y) =  [6] x + [3] y + [3]
                          >= [4] x + [3] y + [2]
                          =  anchored(x,y)      
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))