* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),y) -> 0()
            f(s(x),y) -> f(f(x,y),y)
        - Signature:
            {f/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0(),y) -> 0()
            f(s(x),y) -> f(f(x,y),y)
        - Signature:
            {f/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x,y){x -> s(x)} =
            f(s(x),y) ->^+ f(f(x,y),y)
              = C[f(x,y) = f(x,y){}]

** Step 1.b:1: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),y) -> 0()
            f(s(x),y) -> f(f(x,y),y)
        - Signature:
            {f/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + 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(0) = [0]         
            p(f) = [1] x1 + [0]
            p(s) = [1] x1 + [1]
          
          Following rules are strictly oriented:
          f(s(x),y) = [1] x + [1]
                    > [1] x + [0]
                    = f(f(x,y),y)
          
          
          Following rules are (at-least) weakly oriented:
          f(0(),y) =  [0]
                   >= [0]
                   =  0()
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 1.b:2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),y) -> 0()
        - Weak TRS:
            f(s(x),y) -> f(f(x,y),y)
        - Signature:
            {f/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + 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(0) = [2]         
            p(f) = [1] x1 + [4]
            p(s) = [1] x1 + [4]
          
          Following rules are strictly oriented:
          f(0(),y) = [6]
                   > [2]
                   = 0()
          
          
          Following rules are (at-least) weakly oriented:
          f(s(x),y) =  [1] x + [8]
                    >= [1] x + [8]
                    =  f(f(x,y),y)
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(0(),y) -> 0()
            f(s(x),y) -> f(f(x,y),y)
        - Signature:
            {f/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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