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

** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(f(x,y)) -> f(minus(y),minus(x))
            minus(h(x)) -> h(minus(x))
            minus(minus(x)) -> x
        - Signature:
            {minus/1} / {f/2,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
    + 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) = {1,2},
          uargs(h) = {1}
        
        Following symbols are considered usable:
          {minus}
        TcT has computed the following interpretation:
              p(f) = [1] x1 + [1] x2 + [9]
              p(h) = [1] x1 + [0]         
          p(minus) = [2] x1 + [4]         
        
        Following rules are strictly oriented:
          minus(f(x,y)) = [2] x + [2] y + [22]
                        > [2] x + [2] y + [17]
                        = f(minus(y),minus(x))
        
        minus(minus(x)) = [4] x + [12]        
                        > [1] x + [0]         
                        = x                   
        
        
        Following rules are (at-least) weakly oriented:
        minus(h(x)) =  [2] x + [4]
                    >= [2] x + [4]
                    =  h(minus(x))
        
** Step 1.b:2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(h(x)) -> h(minus(x))
        - Weak TRS:
            minus(f(x,y)) -> f(minus(y),minus(x))
            minus(minus(x)) -> x
        - Signature:
            {minus/1} / {f/2,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
    + 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) = {1,2},
          uargs(h) = {1}
        
        Following symbols are considered usable:
          {minus}
        TcT has computed the following interpretation:
              p(f) = [1] x1 + [1] x2 + [0]
              p(h) = [1] x1 + [4]         
          p(minus) = [4] x1 + [0]         
        
        Following rules are strictly oriented:
        minus(h(x)) = [4] x + [16]
                    > [4] x + [4] 
                    = h(minus(x)) 
        
        
        Following rules are (at-least) weakly oriented:
          minus(f(x,y)) =  [4] x + [4] y + [0] 
                        >= [4] x + [4] y + [0] 
                        =  f(minus(y),minus(x))
        
        minus(minus(x)) =  [16] x + [0]        
                        >= [1] x + [0]         
                        =  x                   
        
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            minus(f(x,y)) -> f(minus(y),minus(x))
            minus(h(x)) -> h(minus(x))
            minus(minus(x)) -> x
        - Signature:
            {minus/1} / {f/2,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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