WORST_CASE(?,O(n^1))
* Step 1: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            +(0(),y) -> y
            +(s(x),0()) -> s(x)
            +(s(x),s(y)) -> s(+(s(x),+(y,0())))
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+} 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(+) = {2},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
            p(+) = [1] x1 + [1] x2 + [0]
            p(0) = [1]                  
            p(s) = [1] x1 + [0]         
          
          Following rules are strictly oriented:
             +(0(),y) = [1] y + [1]
                      > [1] y + [0]
                      = y          
          
          +(s(x),0()) = [1] x + [1]
                      > [1] x + [0]
                      = s(x)       
          
          
          Following rules are (at-least) weakly oriented:
          +(s(x),s(y)) =  [1] x + [1] y + [0]
                       >= [1] x + [1] y + [1]
                       =  s(+(s(x),+(y,0())))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            +(s(x),s(y)) -> s(+(s(x),+(y,0())))
        - Weak TRS:
            +(0(),y) -> y
            +(s(x),0()) -> s(x)
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+} and constructors {0,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:
          uargs(+) = {2},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {+}
        TcT has computed the following interpretation:
          p(+) = [1] x1 + [8] x2 + [1]
          p(0) = [0]                  
          p(s) = [1] x1 + [3]         
        
        Following rules are strictly oriented:
        +(s(x),s(y)) = [1] x + [8] y + [28]
                     > [1] x + [8] y + [15]
                     = s(+(s(x),+(y,0()))) 
        
        
        Following rules are (at-least) weakly oriented:
           +(0(),y) =  [8] y + [1]
                    >= [1] y + [0]
                    =  y          
        
        +(s(x),0()) =  [1] x + [4]
                    >= [1] x + [3]
                    =  s(x)       
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(0(),y) -> y
            +(s(x),0()) -> s(x)
            +(s(x),s(y)) -> s(+(s(x),+(y,0())))
        - Signature:
            {+/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))