WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add0(0(),x2) -> x2
            add0(S(x),x2) -> +(S(0()),add0(x2,x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,add0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add0(0(),x2) -> x2
            add0(S(x),x2) -> +(S(0()),add0(x2,x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,add0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(+) = {2}
        
        Following symbols are considered usable:
          {+,add0}
        TcT has computed the following interpretation:
             p(+) = x1 + x2        
             p(0) = 2              
             p(S) = 2 + x1         
          p(add0) = 2 + 8*x1 + 8*x2
        
        Following rules are strictly oriented:
         add0(0(),x2) = 18 + 8*x2           
                      > x2                  
                      = x2                  
        
        add0(S(x),x2) = 18 + 8*x + 8*x2     
                      > 6 + 8*x + 8*x2      
                      = +(S(0()),add0(x2,x))
        
        
        Following rules are (at-least) weakly oriented:
        +(x,S(0())) =  4 + x
                    >= 2 + x
                    =  S(x) 
        
        +(S(0()),y) =  4 + y
                    >= 2 + y
                    =  S(y) 
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(0(),x2) -> x2
            add0(S(x),x2) -> +(S(0()),add0(x2,x))
        - Signature:
            {+/2,add0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))