WORST_CASE(?,O(n^2))
* Step 1: WeightGap WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
            -(0(),y) -> 0()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {-/2,p/1} / {0/0,greater/2,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,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(-) = {2},
            uargs(if) = {2},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                  p(-) = [9] x1 + [1] x2 + [8]
                  p(0) = [2]                  
            p(greater) = [0]                  
                 p(if) = [1] x2 + [0]         
                  p(p) = [1] x1 + [11]        
                  p(s) = [1] x1 + [0]         
          
          Following rules are strictly oriented:
          -(x,0()) = [9] x + [10]
                   > [1] x + [0] 
                   = x           
          
          -(0(),y) = [1] y + [26]
                   > [2]         
                   = 0()         
          
            p(0()) = [13]        
                   > [2]         
                   = 0()         
          
           p(s(x)) = [1] x + [11]
                   > [1] x + [0] 
                   = x           
          
          
          Following rules are (at-least) weakly oriented:
          -(x,s(y)) =  [9] x + [1] y + [8]                    
                    >= [9] x + [1] y + [19]                   
                    =  if(greater(x,s(y)),s(-(x,p(s(y)))),0())
          
        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)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
        - Weak TRS:
            -(x,0()) -> x
            -(0(),y) -> 0()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {-/2,p/1} / {0/0,greater/2,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 2, maxDegree = 2, araTimeout = 15, araFindStrictRules = Just 1}
    + Details:
        Signatures used:
        ----------------
          - :: [A(12, 2) x A(15, 0)] -(1)-> A(9, 0)
          0 :: [] -(0)-> A(15, 0)
          0 :: [] -(0)-> A(12, 2)
          0 :: [] -(0)-> A(0, 15)
          0 :: [] -(0)-> A(7, 13)
          0 :: [] -(0)-> A(15, 7)
          greater :: [A(0, 0) x A(0, 0)] -(1)-> A(1, 12)
          if :: [A(0, 0) x A(0, 0) x A(0, 0)] -(0)-> A(9, 0)
          p :: [A(0, 15)] -(0)-> A(15, 0)
          s :: [A(15, 0)] -(15)-> A(15, 0)
          s :: [A(15, 0)] -(0)-> A(0, 15)
          s :: [A(0, 0)] -(0)-> A(0, 0)
          s :: [A(2, 0)] -(0)-> A(0, 2)
        
        
        Cost-free Signatures used:
        --------------------------
          - :: [A_cf(0, 0) x A_cf(0, 0)] -(1)-> A_cf(0, 0)
          0 :: [] -(0)-> A_cf(0, 0)
          0 :: [] -(0)-> A_cf(3, 3)
          0 :: [] -(0)-> A_cf(11, 11)
          0 :: [] -(0)-> A_cf(10, 10)
          greater :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 4)
          if :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(3, 0)
          p :: [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)
          greater_A :: [A(0, 0) x A(0, 0)] -(1)-> A(1, 0)
          greater_A :: [A(0, 0) x A(0, 0)] -(0)-> A(0, 1)
          if_A :: [A(0, 0) x A(0, 0) x A(0, 0)] -(0)-> A(1, 0)
          if_A :: [A(1, 0) x A(1, 0) x A(1, 1)] -(0)-> A(0, 1)
          s_A :: [A(1, 0)] -(1)-> A(1, 0)
          s_A :: [A(1, 0)] -(0)-> A(0, 1)
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
        2. Weak:
          
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            -(x,0()) -> x
            -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
            -(0(),y) -> 0()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {-/2,p/1} / {0/0,greater/2,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))