WORST_CASE(?,O(n^2))
* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            add(0(),y) -> y
            add(s(x),y) -> s(add(x,y))
            mult(0(),y) -> 0()
            mult(s(x),y) -> add(x,mult(x,y))
        - Signature:
            {add/2,mult/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,mult} 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:
          uargs(add) = {2},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {add,mult}
        TcT has computed the following interpretation:
             p(0) = 0         
           p(add) = x2        
          p(mult) = 2 + 2*x1^2
             p(s) = x1        
        
        Following rules are strictly oriented:
        mult(0(),y) = 2  
                    > 0  
                    = 0()
        
        
        Following rules are (at-least) weakly oriented:
          add(0(),y) =  y               
                     >= y               
                     =  y               
        
         add(s(x),y) =  y               
                     >= y               
                     =  s(add(x,y))     
        
        mult(s(x),y) =  2 + 2*x^2       
                     >= 2 + 2*x^2       
                     =  add(x,mult(x,y))
        
* Step 2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            add(0(),y) -> y
            add(s(x),y) -> s(add(x,y))
            mult(s(x),y) -> add(x,mult(x,y))
        - Weak TRS:
            mult(0(),y) -> 0()
        - Signature:
            {add/2,mult/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,mult} 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:
          uargs(add) = {2},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {add,mult}
        TcT has computed the following interpretation:
             p(0) = 0            
           p(add) = 3 + 4*x1 + x2
          p(mult) = x1^2 + x2^2  
             p(s) = 2 + x1       
        
        Following rules are strictly oriented:
          add(0(),y) = 3 + y              
                     > y                  
                     = y                  
        
         add(s(x),y) = 11 + 4*x + y       
                     > 5 + 4*x + y        
                     = s(add(x,y))        
        
        mult(s(x),y) = 4 + 4*x + x^2 + y^2
                     > 3 + 4*x + x^2 + y^2
                     = add(x,mult(x,y))   
        
        
        Following rules are (at-least) weakly oriented:
        mult(0(),y) =  y^2
                    >= 0  
                    =  0()
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            add(0(),y) -> y
            add(s(x),y) -> s(add(x,y))
            mult(0(),y) -> 0()
            mult(s(x),y) -> add(x,mult(x,y))
        - Signature:
            {add/2,mult/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,mult} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))