* Step 1: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
            b(y,z) -> z
            f(c(a(),z,x)) -> b(a(),z)
        - Signature:
            {b/2,f/1} / {a/0,c/3}
        - Obligation:
             runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity (Just 1))), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity (Just 1))):
        
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = [0]                                    
                 [1]                                    
          p(b) = [2 1] x_1 + [1 1] x_2 + [0]            
                 [3 0]       [2 2]       [5]            
          p(c) = [1 0] x_1 + [1 1] x_2 + [1 0] x_3 + [2]
                 [0 0]       [0 0]       [0 0]       [0]
          p(f) = [1 0] x_1 + [0]                        
                 [2 0]       [1]                        
        
        Following rules are strictly oriented:
          b(x,b(z,y)) = [2 1] x + [3 3] y + [ 5 1] z + [5] 
                        [3 0]     [6 6]     [10 2]     [15]
                      > [1 0] x + [1 0] y + [ 5 1] z + [3] 
                        [2 0]     [2 0]     [10 2]     [7] 
                      = f(b(f(f(z)),c(x,z,y)))             
        
        f(c(a(),z,x)) = [1 0] x + [1 1] z + [2]            
                        [2 0]     [2 2]     [5]            
                      > [1 1] z + [1]                      
                        [2 2]     [5]                      
                      = b(a(),z)                           
        
        
        Following rules are (at-least) weakly oriented:
        b(y,z) =  [2 1] y + [1 1] z + [0]
                  [3 0]     [2 2]     [5]
               >= [1 0] z + [0]          
                  [0 1]     [0]          
               =  z                      
        
* Step 2: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            b(y,z) -> z
        - Weak TRS:
            b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
            f(c(a(),z,x)) -> b(a(),z)
        - Signature:
            {b/2,f/1} / {a/0,c/3}
        - Obligation:
             runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity (Just 1))), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity (Just 1))):
        
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = [0]                                    
                 [1]                                    
          p(b) = [2 1] x_1 + [1 1] x_2 + [1]            
                 [7 0]       [2 1]       [5]            
          p(c) = [1 0] x_1 + [1 1] x_2 + [1 0] x_3 + [3]
                 [0 0]       [0 0]       [0 0]       [0]
          p(f) = [1 0] x_1 + [0]                        
                 [2 0]       [1]                        
        
        Following rules are strictly oriented:
        b(y,z) = [2 1] y + [1 1] z + [1]
                 [7 0]     [2 1]     [5]
               > [1 0] z + [0]          
                 [0 1]     [0]          
               = z                      
        
        
        Following rules are (at-least) weakly oriented:
          b(x,b(z,y)) =  [2 1] x + [3 2] y + [ 9 1] z + [7] 
                         [7 0]     [4 3]     [11 2]     [12]
                      >= [1 0] x + [1 0] y + [ 5 1] z + [5] 
                         [2 0]     [2 0]     [10 2]     [11]
                      =  f(b(f(f(z)),c(x,z,y)))             
        
        f(c(a(),z,x)) =  [1 0] x + [1 1] z + [3]            
                         [2 0]     [2 2]     [7]            
                      >= [1 1] z + [2]                      
                         [2 1]     [5]                      
                      =  b(a(),z)                           
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
            b(y,z) -> z
            f(c(a(),z,x)) -> b(a(),z)
        - Signature:
            {b/2,f/1} / {a/0,c/3}
        - Obligation:
             runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))