WORST_CASE(?,O(n^2))
* Step 1: Sum WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            fac(0()) -> s(0())
            fac(s(x)) -> times(s(x),fac(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {fac/1,p/1} / {0/0,s/1,times/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            fac(0()) -> s(0())
            fac(s(x)) -> times(s(x),fac(p(s(x))))
            p(s(x)) -> x
        - Signature:
            {fac/1,p/1} / {0/0,s/1,times/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times}
    + 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(fac) = {1},
          uargs(times) = {2}
        
        Following symbols are considered usable:
          {fac,p}
        TcT has computed the following interpretation:
              p(0) = 4   
            p(fac) = 4*x1
              p(p) = x1  
              p(s) = x1  
          p(times) = x2  
        
        Following rules are strictly oriented:
        fac(0()) = 16    
                 > 4     
                 = s(0())
        
        
        Following rules are (at-least) weakly oriented:
        fac(s(x)) =  4*x                     
                  >= 4*x                     
                  =  times(s(x),fac(p(s(x))))
        
          p(s(x)) =  x                       
                  >= x                       
                  =  x                       
        
* Step 3: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            fac(s(x)) -> times(s(x),fac(p(s(x))))
            p(s(x)) -> x
        - Weak TRS:
            fac(0()) -> s(0())
        - Signature:
            {fac/1,p/1} / {0/0,s/1,times/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times}
    + 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:
          uargs(fac) = {1},
          uargs(times) = {2}
        
        Following symbols are considered usable:
          {fac,p}
        TcT has computed the following interpretation:
              p(0) = 3     
            p(fac) = 4*x1  
              p(p) = x1    
              p(s) = 2 + x1
          p(times) = x2    
        
        Following rules are strictly oriented:
        p(s(x)) = 2 + x
                > x    
                = x    
        
        
        Following rules are (at-least) weakly oriented:
         fac(0()) =  12                      
                  >= 5                       
                  =  s(0())                  
        
        fac(s(x)) =  8 + 4*x                 
                  >= 8 + 4*x                 
                  =  times(s(x),fac(p(s(x))))
        
* Step 4: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            fac(s(x)) -> times(s(x),fac(p(s(x))))
        - Weak TRS:
            fac(0()) -> s(0())
            p(s(x)) -> x
        - Signature:
            {fac/1,p/1} / {0/0,s/1,times/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 2, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(2, 2)
          0 :: [] -(0)-> "A"(0, 0)
          fac :: ["A"(2, 2)] -(0)-> "A"(0, 0)
          p :: ["A"(0, 2)] -(0)-> "A"(2, 2)
          s :: ["A"(4, 2)] -(2)-> "A"(2, 2)
          s :: ["A"(2, 2)] -(0)-> "A"(0, 2)
          s :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          s :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          times :: ["A"(0, 0) x "A"(0, 0)] -(0)-> "A"(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        

WORST_CASE(?,O(n^2))