* Step 1: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(f) = [5]                    
          p(g) = [1] x_1 + [2] x_2 + [2]
          p(s) = [0]                    
        
        Following rules are strictly oriented:
        g(x,y) = [1] x + [2] y + [2]
               > [1] x + [0]        
               = x                  
        
        g(x,y) = [1] x + [2] y + [2]
               > [1] y + [0]        
               = y                  
        
        
        Following rules are (at-least) weakly oriented:
        f(s(x),y,y) =  [5]        
                    >= [5]        
                    =  f(y,x,s(x))
        
* Step 2: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
        - Weak TRS:
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(f) = [2] x_1 + [1] x_2 + [1] x_3 + [12]
          p(g) = [2] x_1 + [2] x_2 + [1]           
          p(s) = [1] x_1 + [8]                     
        
        Following rules are strictly oriented:
        f(s(x),y,y) = [2] x + [2] y + [28]
                    > [2] x + [2] y + [20]
                    = f(y,x,s(x))         
        
        
        Following rules are (at-least) weakly oriented:
        g(x,y) =  [2] x + [2] y + [1]
               >= [1] x + [0]        
               =  x                  
        
        g(x,y) =  [2] x + [2] y + [1]
               >= [1] y + [0]        
               =  y                  
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))