WORST_CASE(?,O(n^1))
* Step 1: WeightGap 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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          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:
            all
          TcT has computed the following interpretation:
            p(f) = [1] x1 + [6]
            p(g) = [1] x1 + [0]
            p(h) = [1] x1 + [3]
          
          Following rules are strictly oriented:
          h(x,y) = [1] x + [3]
                 > [1] x + [0]
                 = g(x,f(y))  
          
          
          Following rules are (at-least) weakly oriented:
          g(f(x),y) =  [1] x + [6]
                    >= [1] x + [9]
                    =  f(h(x,y))  
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(f(x),y) -> f(h(x,y))
        - Weak TRS:
            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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          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:
            all
          TcT has computed the following interpretation:
            p(f) = [1] x1 + [3]         
            p(g) = [5] x1 + [1] x2 + [0]
            p(h) = [5] x1 + [1] x2 + [3]
          
          Following rules are strictly oriented:
          g(f(x),y) = [5] x + [1] y + [15]
                    > [5] x + [1] y + [6] 
                    = f(h(x,y))           
          
          
          Following rules are (at-least) weakly oriented:
          h(x,y) =  [5] x + [1] y + [3]
                 >= [5] x + [1] y + [3]
                 =  g(x,f(y))          
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* 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))