WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            rev(++(x,x)) -> rev(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(a()) -> a()
            rev(b()) -> b()
        - Signature:
            {rev/1} / {++/2,a/0,b/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            rev(++(x,x)) -> rev(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(a()) -> a()
            rev(b()) -> b()
        - Signature:
            {rev/1} / {++/2,a/0,b/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          rev(y){y -> ++(x,y)} =
            rev(++(x,y)) ->^+ ++(rev(y),rev(x))
              = C[rev(y) = rev(y){}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            rev(++(x,x)) -> rev(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(a()) -> a()
            rev(b()) -> b()
        - Signature:
            {rev/1} / {++/2,a/0,b/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b}
    + 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:
          uargs(++) = {1,2}
        
        Following symbols are considered usable:
          {rev}
        TcT has computed the following interpretation:
           p(++) = 8 + x1 + x2
            p(a) = 1          
            p(b) = 2          
          p(rev) = 1 + 2*x1   
        
        Following rules are strictly oriented:
        rev(++(x,x)) = 17 + 4*x         
                     > 1 + 2*x          
                     = rev(x)           
        
        rev(++(x,y)) = 17 + 2*x + 2*y   
                     > 10 + 2*x + 2*y   
                     = ++(rev(y),rev(x))
        
            rev(a()) = 3                
                     > 1                
                     = a()              
        
            rev(b()) = 5                
                     > 2                
                     = b()              
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            rev(++(x,x)) -> rev(x)
            rev(++(x,y)) -> ++(rev(y),rev(x))
            rev(a()) -> a()
            rev(b()) -> b()
        - Signature:
            {rev/1} / {++/2,a/0,b/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))