WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + 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(f) = {1}
        
        Following symbols are considered usable:
          {g,h}
        TcT has computed the following interpretation:
          p(f) = 1 + x1         
          p(g) = 1 + 2*x1 + 2*x2
          p(h) = 2*x1 + 2*x2    
        
        Following rules are strictly oriented:
        g(x,y) = 1 + 2*x + 2*y
               > 2*x + 2*y    
               = h(x,y)       
        
        
        Following rules are (at-least) weakly oriented:
        h(f(x),y) =  2 + 2*x + 2*y
                  >= 2 + 2*x + 2*y
                  =  f(g(x,y))    
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(f(x),y) -> f(g(x,y))
        - Weak TRS:
            g(x,y) -> h(x,y)
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + 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(f) = {1}
        
        Following symbols are considered usable:
          {g,h}
        TcT has computed the following interpretation:
          p(f) = 2 + x1  
          p(g) = 4 + 9*x1
          p(h) = 2 + 9*x1
        
        Following rules are strictly oriented:
        h(f(x),y) = 20 + 9*x 
                  > 6 + 9*x  
                  = f(g(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        g(x,y) =  4 + 9*x
               >= 2 + 9*x
               =  h(x,y) 
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))