* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(x,0()) -> x
            f(0(),y) -> y
            f(1(),g(x,y)) -> x
            f(2(),g(x,y)) -> y
            f(f(x,y),z) -> f(x,f(y,z))
            f(g(x,y),z) -> g(f(x,z),f(y,z))
            f(i(x),y) -> i(x)
        - Signature:
            {f/2} / {0/0,1/0,2/0,g/2,i/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {0,1,2,g,i}
    + 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(f) = {2},
          uargs(g) = {1,2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(0) = 0                           
          p(1) = 0                           
          p(2) = 0                           
          p(f) = 1 + x1 + x1*x2 + 2*x1^2 + x2
          p(g) = 1 + x1 + x2                 
          p(i) = 0                           
        
        Following rules are strictly oriented:
             f(x,0()) = 1 + x + 2*x^2                                                                                                                        
                      > x                                                                                                                                    
                      = x                                                                                                                                    
        
             f(0(),y) = 1 + y                                                                                                                                
                      > y                                                                                                                                    
                      = y                                                                                                                                    
        
        f(1(),g(x,y)) = 2 + x + y                                                                                                                            
                      > x                                                                                                                                    
                      = x                                                                                                                                    
        
        f(2(),g(x,y)) = 2 + x + y                                                                                                                            
                      > y                                                                                                                                    
                      = y                                                                                                                                    
        
          f(f(x,y),z) = 4 + 5*x + 9*x*y + x*y*z + 4*x*y^2 + x*z + 12*x^2 + 12*x^2*y + 2*x^2*y^2 + 2*x^2*z + 8*x^3 + 8*x^3*y + 8*x^4 + 5*y + y*z + 2*y^2 + 2*z
                      > 2 + 2*x + x*y + x*y*z + 2*x*y^2 + x*z + 2*x^2 + y + y*z + 2*y^2 + z                                                                  
                      = f(x,f(y,z))                                                                                                                          
        
          f(g(x,y),z) = 4 + 5*x + 4*x*y + x*z + 2*x^2 + 5*y + y*z + 2*y^2 + 2*z                                                                              
                      > 3 + x + x*z + 2*x^2 + y + y*z + 2*y^2 + 2*z                                                                                          
                      = g(f(x,z),f(y,z))                                                                                                                     
        
            f(i(x),y) = 1 + y                                                                                                                                
                      > 0                                                                                                                                    
                      = i(x)                                                                                                                                 
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(x,0()) -> x
            f(0(),y) -> y
            f(1(),g(x,y)) -> x
            f(2(),g(x,y)) -> y
            f(f(x,y),z) -> f(x,f(y,z))
            f(g(x,y),z) -> g(f(x,z),f(y,z))
            f(i(x),y) -> i(x)
        - Signature:
            {f/2} / {0/0,1/0,2/0,g/2,i/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {0,1,2,g,i}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))