WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + 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:
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {g,h}
        TcT has computed the following interpretation:
          p(f) = [1] x1 + [1]         
          p(g) = [4] x1 + [1] x2 + [8]
          p(h) = [4] x1 + [1] x2 + [9]
        
        Following rules are strictly oriented:
        g(f(x),y) = [4] x + [1] y + [12]
                  > [4] x + [1] y + [10]
                  = f(h(x,y))           
        
        
        Following rules are (at-least) weakly oriented:
        h(x,y) =  [4] x + [1] y + [9]
               >= [4] x + [1] y + [9]
               =  g(x,f(y))          
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(x,y) -> g(x,f(y))
        - Weak TRS:
            g(f(x),y) -> f(h(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + 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:
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {g,h}
        TcT has computed the following interpretation:
          p(f) = [1] x1 + [1]          
          p(g) = [8] x1 + [5] x2 + [8] 
          p(h) = [8] x1 + [5] x2 + [15]
        
        Following rules are strictly oriented:
        h(x,y) = [8] x + [5] y + [15]
               > [8] x + [5] y + [13]
               = g(x,f(y))           
        
        
        Following rules are (at-least) weakly oriented:
        g(f(x),y) =  [8] x + [5] y + [16]
                  >= [8] x + [5] y + [16]
                  =  f(h(x,y))           
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            g(f(x),y) -> f(h(x,y))
            h(x,y) -> g(x,f(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))