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

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x,y) -> g(x,y)
            g(h(x),y) -> h(f(x,y))
            g(h(x),y) -> h(g(x,y))
        - Signature:
            {f/2,g/2} / {h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {h}
    + 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(h) = {1}
        
        Following symbols are considered usable:
          {f,g}
        TcT has computed the following interpretation:
          p(f) = 8 + 8*x1 + 12*x2
          p(g) = 8*x1 + 12*x2    
          p(h) = 2 + x1          
        
        Following rules are strictly oriented:
           f(x,y) = 8 + 8*x + 12*y 
                  > 8*x + 12*y     
                  = g(x,y)         
        
        g(h(x),y) = 16 + 8*x + 12*y
                  > 10 + 8*x + 12*y
                  = h(f(x,y))      
        
        g(h(x),y) = 16 + 8*x + 12*y
                  > 2 + 8*x + 12*y 
                  = h(g(x,y))      
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(x,y) -> g(x,y)
            g(h(x),y) -> h(f(x,y))
            g(h(x),y) -> h(g(x,y))
        - Signature:
            {f/2,g/2} / {h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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