WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),x2) -> 0()
            f(S(x),x2) -> f(x2,x)
        - Signature:
            {f/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),x2) -> 0()
            f(S(x),x2) -> f(x2,x)
        - Signature:
            {f/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,S}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          {f}
        TcT has computed the following interpretation:
          p(0) = 2
          p(S) = 0
          p(f) = 6
        
        Following rules are strictly oriented:
        f(0(),x2) = 6  
                  > 2  
                  = 0()
        
        
        Following rules are (at-least) weakly oriented:
        f(S(x),x2) =  6      
                   >= 6      
                   =  f(x2,x)
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(S(x),x2) -> f(x2,x)
        - Weak TRS:
            f(0(),x2) -> 0()
        - Signature:
            {f/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} 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:
          none
        
        Following symbols are considered usable:
          {f}
        TcT has computed the following interpretation:
          p(0) = 0          
          p(S) = 5 + x1     
          p(f) = 4*x1 + 4*x2
        
        Following rules are strictly oriented:
        f(S(x),x2) = 20 + 4*x + 4*x2
                   > 4*x + 4*x2     
                   = f(x2,x)        
        
        
        Following rules are (at-least) weakly oriented:
        f(0(),x2) =  4*x2
                  >= 0   
                  =  0() 
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(0(),x2) -> 0()
            f(S(x),x2) -> f(x2,x)
        - Signature:
            {f/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))