WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),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:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(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:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          anchored(y,z){y -> Cons(x,y)} =
            anchored(Cons(x,y),z) ->^+ anchored(y,Cons(Cons(Nil(),Nil()),z))
              = C[anchored(y,Cons(Cons(Nil(),Nil()),z)) = anchored(y,z){z -> Cons(Cons(Nil(),Nil()),z)}]

** Step 1.b:1: NaturalPI 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:
        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) = 2 + x2      
               p(Nil) = 0           
          p(anchored) = 10*x1 + 8*x2
              p(goal) = 10*x1 + 8*x2
        
        Following rules are strictly oriented:
        anchored(Cons(x,xs),y) = 20 + 10*xs + 8*y                      
                               > 16 + 10*xs + 8*y                      
                               = anchored(xs,Cons(Cons(Nil(),Nil()),y))
        
        
        Following rules are (at-least) weakly oriented:
        anchored(Nil(),y) =  8*y          
                          >= y            
                          =  y            
        
                goal(x,y) =  10*x + 8*y   
                          >= 10*x + 8*y   
                          =  anchored(x,y)
        
** Step 1.b:2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Weak TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),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) = x1 + x2
               p(Nil) = 0      
          p(anchored) = 10 + x2
              p(goal) = 10 + x2
        
        Following rules are strictly oriented:
        anchored(Nil(),y) = 10 + y
                          > y     
                          = y     
        
        
        Following rules are (at-least) weakly oriented:
        anchored(Cons(x,xs),y) =  10 + y                                
                               >= 10 + y                                
                               =  anchored(xs,Cons(Cons(Nil(),Nil()),y))
        
                     goal(x,y) =  10 + y                                
                               >= 10 + y                                
                               =  anchored(x,y)                         
        
** Step 1.b:3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(x,y) -> anchored(x,y)
        - Weak TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            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) = 1            
          p(anchored) = 8*x2         
              p(goal) = 9 + x1 + 8*x2
        
        Following rules are strictly oriented:
        goal(x,y) = 9 + x + 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 1.b: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(Omega(n^1),O(n^1))