WORST_CASE(?,O(n^2))
* Step 1: WeightGap WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            max(L(x)) -> x
            max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
            max(N(L(0()),L(y))) -> y
            max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
        - Signature:
            {max/1} / {0/0,L/1,N/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,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(L) = {1},
            uargs(N) = {2},
            uargs(max) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(0) = [0]                  
              p(L) = [1] x1 + [0]         
              p(N) = [1] x1 + [1] x2 + [2]
            p(max) = [1] x1 + [5]         
              p(s) = [1] x1 + [1]         
          
          Following rules are strictly oriented:
                        max(L(x)) = [1] x + [5]         
                                  > [1] x + [0]         
                                  = x                   
          
              max(N(L(0()),L(y))) = [1] y + [7]         
                                  > [1] y + [0]         
                                  = y                   
          
          max(N(L(s(x)),L(s(y)))) = [1] x + [1] y + [9] 
                                  > [1] x + [1] y + [8] 
                                  = s(max(N(L(x),L(y))))
          
          
          Following rules are (at-least) weakly oriented:
          max(N(L(x),N(y,z))) =  [1] x + [1] y + [1] z + [9] 
                              >= [1] x + [1] y + [1] z + [14]
                              =  max(N(L(x),L(max(N(y,z))))) 
          
        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:
            max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
        - Weak TRS:
            max(L(x)) -> x
            max(N(L(0()),L(y))) -> y
            max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
        - Signature:
            {max/1} / {0/0,L/1,N/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 2, maxDegree = 2, araTimeout = 15, araFindStrictRules = Just 1}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(4, 0)
          L :: [A(4, 0)] -(0)-> A(0, 4)
          L :: [A(4, 0)] -(0)-> A(4, 4)
          L :: [A(4, 0)] -(0)-> A(7, 4)
          L :: [A(4, 0)] -(0)-> A(5, 4)
          N :: [A(0, 4) x A(4, 4)] -(0)-> A(0, 4)
          N :: [A(4, 4) x A(4, 4)] -(4)-> A(4, 4)
          max :: [A(0, 4)] -(0)-> A(4, 0)
          s :: [A(4, 0)] -(4)-> A(4, 0)
          s :: [A(4, 0)] -(4)-> A(4, 10)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0, 0)
          L :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
          N :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
          max :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
          s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1, 0)
          0_A :: [] -(0)-> A(0, 1)
          L_A :: [A(0, 0)] -(0)-> A(1, 0)
          L_A :: [A(1, 0)] -(0)-> A(0, 1)
          N_A :: [A(1, 0) x A(0, 0)] -(1)-> A(1, 0)
          N_A :: [A(0, 1) x A(1, 1)] -(0)-> A(0, 1)
          s_A :: [A(1, 0)] -(1)-> A(1, 0)
          s_A :: [A(0, 0)] -(0)-> A(0, 1)
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
        2. Weak:
          
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            max(L(x)) -> x
            max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
            max(N(L(0()),L(y))) -> y
            max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
        - Signature:
            {max/1} / {0/0,L/1,N/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))