WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(g) = {1},
          uargs(h) = {1}
        
        Following symbols are considered usable:
          {f,h,k}
        TcT has computed the following interpretation:
          p(a) = [0]                   
          p(f) = [0]                   
          p(g) = [1] x1 + [0]          
          p(h) = [8] x1 + [0]          
          p(k) = [13] x1 + [1] x3 + [8]
        
        Following rules are strictly oriented:
        k(x,h(x),a()) = [13] x + [8]
                      > [8] x + [0] 
                      = h(x)        
        
          k(f(x),y,x) = [1] x + [8] 
                      > [0]         
                      = f(x)        
        
        
        Following rules are (at-least) weakly oriented:
         f(a()) =  [0]        
                >= [0]        
                =  g(h(a()))  
        
        h(g(x)) =  [8] x + [0]
                >= [0]        
                =  g(h(f(x))) 
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
        - Weak TRS:
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(g) = {1},
          uargs(h) = {1}
        
        Following symbols are considered usable:
          {f,h,k}
        TcT has computed the following interpretation:
          p(a) = [0]                                       
                 [4]                                       
                 [2]                                       
          p(f) = [0 2 2]      [0]                          
                 [0 0 0] x1 + [0]                          
                 [0 0 0]      [2]                          
          p(g) = [1 2 2]      [3]                          
                 [0 0 0] x1 + [0]                          
                 [0 0 0]      [2]                          
          p(h) = [4 0 0]      [0]                          
                 [0 0 0] x1 + [1]                          
                 [0 0 1]      [1]                          
          p(k) = [2 3 1]      [3 0 0]      [6 0 4]      [2]
                 [3 0 4] x1 + [0 0 0] x2 + [5 1 4] x3 + [0]
                 [1 1 6]      [0 1 0]      [0 0 1]      [0]
        
        Following rules are strictly oriented:
         f(a()) = [12]            
                  [0]             
                  [2]             
                > [11]            
                  [0]             
                  [2]             
                = g(h(a()))       
        
        h(g(x)) = [4 8 8]     [12]
                  [0 0 0] x + [1] 
                  [0 0 0]     [3] 
                > [0 8 8]     [11]
                  [0 0 0] x + [0] 
                  [0 0 0]     [2] 
                = g(h(f(x)))      
        
        
        Following rules are (at-least) weakly oriented:
        k(x,h(x),a()) =  [14 3 1]     [10]            
                         [ 3 0 4] x + [12]            
                         [ 1 1 6]     [3]             
                      >= [4 0 0]     [0]              
                         [0 0 0] x + [1]              
                         [0 0 1]     [1]              
                      =  h(x)                         
        
          k(f(x),y,x) =  [6 4  8]     [3 0 0]     [4] 
                         [5 7 10] x + [0 0 0] y + [8] 
                         [0 2  3]     [0 1 0]     [12]
                      >= [0 2 2]     [0]              
                         [0 0 0] x + [0]              
                         [0 0 0]     [2]              
                      =  f(x)                         
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a()) -> g(h(a()))
            h(g(x)) -> g(h(f(x)))
            k(x,h(x),a()) -> h(x)
            k(f(x),y,x) -> f(x)
        - Signature:
            {f/1,h/1,k/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))