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

** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {f,g}
        TcT has computed the following interpretation:
          p(c) = [1] x2 + [0] 
          p(f) = [2] x1 + [5] 
          p(g) = [8] x1 + [11]
          p(s) = [1] x1 + [2] 
        
        Following rules are strictly oriented:
        f(c(X,s(Y))) = [2] Y + [9] 
                     > [2] Y + [5] 
                     = f(c(s(X),Y))
        
        g(c(s(X),Y)) = [8] Y + [11]
                     > [2] Y + [9] 
                     = f(c(X,s(Y)))
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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