WORST_CASE(?,O(n^2))
* Step 1: WeightGap WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            sum(0()) -> 0()
            sum(s(x)) -> +(sum(x),s(x))
        - Signature:
            {+/2,sum/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,sum} 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(+) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(+) = [1] x1 + [1]
              p(0) = [6]         
              p(s) = [1] x1 + [8]
            p(sum) = [2] x1 + [0]
          
          Following rules are strictly oriented:
           +(x,0()) = [1] x + [1]   
                    > [1] x + [0]   
                    = x             
          
           sum(0()) = [12]          
                    > [6]           
                    = 0()           
          
          sum(s(x)) = [2] x + [16]  
                    > [2] x + [1]   
                    = +(sum(x),s(x))
          
          
          Following rules are (at-least) weakly oriented:
          +(x,s(y)) =  [1] x + [1]
                    >= [1] x + [9]
                    =  s(+(x,y))  
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            +(x,s(y)) -> s(+(x,y))
        - Weak TRS:
            +(x,0()) -> x
            sum(0()) -> 0()
            sum(s(x)) -> +(sum(x),s(x))
        - Signature:
            {+/2,sum/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,sum} and constructors {0,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 2, maxDegree = 2, araTimeout = 15, araFindStrictRules = Just 1}
    + Details:
        Signatures used:
        ----------------
          + :: [A(0, 0) x A(2, 0)] -(7)-> A(0, 0)
          0 :: [] -(0)-> A(2, 0)
          0 :: [] -(0)-> A(0, 13)
          0 :: [] -(0)-> A(7, 7)
          s :: [A(2, 0)] -(2)-> A(2, 0)
          s :: [A(13, 13)] -(13)-> A(0, 13)
          s :: [A(0, 0)] -(0)-> A(0, 0)
          sum :: [A(0, 13)] -(1)-> A(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
          + :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
          0 :: [] -(0)-> A_cf(0, 0)
          0 :: [] -(0)-> A_cf(1, 0)
          0 :: [] -(0)-> A_cf(3, 2)
          s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
          s :: [A_cf(1, 0)] -(1)-> A_cf(1, 0)
          sum :: [A_cf(1, 0)] -(1)-> A_cf(0, 0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1, 0)
          0_A :: [] -(0)-> A(0, 1)
          s_A :: [A(1, 0)] -(1)-> A(1, 0)
          s_A :: [A(1, 1)] -(1)-> A(0, 1)
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          +(x,s(y)) -> s(+(x,y))
        2. Weak:
          
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            sum(0()) -> 0()
            sum(s(x)) -> +(sum(x),s(x))
        - Signature:
            {+/2,sum/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,sum} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))