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

** Step 1.b:1: NaturalPI 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:
        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:
          {goal,revapp}
        TcT has computed the following interpretation:
            p(Cons) = x2      
             p(Nil) = 0       
            p(goal) = 1 + 8*x2
          p(revapp) = 8*x2    
        
        Following rules are strictly oriented:
        goal(xs,ys) = 1 + 8*ys     
                    > 8*ys         
                    = revapp(xs,ys)
        
        
        Following rules are (at-least) weakly oriented:
        revapp(Cons(x,xs),rest) =  8*rest                 
                                >= 8*rest                 
                                =  revapp(xs,Cons(x,rest))
        
             revapp(Nil(),rest) =  8*rest                 
                                >= rest                   
                                =  rest                   
        
** Step 1.b:2: NaturalPI 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:
        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:
          {goal,revapp}
        TcT has computed the following interpretation:
            p(Cons) = x2      
             p(Nil) = 1       
            p(goal) = 4 + 4*x2
          p(revapp) = 4 + 4*x2
        
        Following rules are strictly oriented:
        revapp(Nil(),rest) = 4 + 4*rest
                           > rest      
                           = rest      
        
        
        Following rules are (at-least) weakly oriented:
                    goal(xs,ys) =  4 + 4*ys               
                                >= 4 + 4*ys               
                                =  revapp(xs,ys)          
        
        revapp(Cons(x,xs),rest) =  4 + 4*rest             
                                >= 4 + 4*rest             
                                =  revapp(xs,Cons(x,rest))
        
** Step 1.b:3: NaturalMI 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:
        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 + [1] 
             p(Nil) = [1]                   
            p(goal) = [10] x1 + [6] x2 + [8]
          p(revapp) = [8] x1 + [4] x2 + [1] 
        
        Following rules are strictly oriented:
        revapp(Cons(x,xs),rest) = [4] rest + [8] x + [8] xs + [9]
                                > [4] rest + [4] x + [8] xs + [5]
                                = revapp(xs,Cons(x,rest))        
        
        
        Following rules are (at-least) weakly oriented:
               goal(xs,ys) =  [10] xs + [6] ys + [8]
                           >= [8] xs + [4] ys + [1] 
                           =  revapp(xs,ys)         
        
        revapp(Nil(),rest) =  [4] rest + [9]        
                           >= [1] rest + [0]        
                           =  rest                  
        
** Step 1.b: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(Omega(n^1),O(n^1))