WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {f}
        TcT has computed the following interpretation:
          p(a) = [0] 
          p(c) = [5] 
          p(f) = [13]
          p(s) = [4] 
        
        Following rules are strictly oriented:
        f(X,X) = [13]
               > [5] 
               = c(X)
        
        
        Following rules are (at-least) weakly oriented:
        f(X,c(X)) =  [13]     
                  >= [13]     
                  =  f(s(X),X)
        
        f(s(X),X) =  [13]     
                  >= [13]     
                  =  f(X,a(X))
        
* Step 3: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Weak TRS:
            f(X,X) -> c(X)
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {f}
        TcT has computed the following interpretation:
          p(a) = [0]                  
          p(c) = [1]                  
          p(f) = [1] x1 + [1] x2 + [1]
          p(s) = [0]                  
        
        Following rules are strictly oriented:
        f(X,c(X)) = [1] X + [2]
                  > [1] X + [1]
                  = f(s(X),X)  
        
        
        Following rules are (at-least) weakly oriented:
           f(X,X) =  [2] X + [1]
                  >= [1]        
                  =  c(X)       
        
        f(s(X),X) =  [1] X + [1]
                  >= [1] X + [1]
                  =  f(X,a(X))  
        
* Step 4: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(X),X) -> f(X,a(X))
        - Weak TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {f}
        TcT has computed the following interpretation:
          p(a) = [0]                  
          p(c) = [4]                  
          p(f) = [1] x1 + [1] x2 + [8]
          p(s) = [1]                  
        
        Following rules are strictly oriented:
        f(s(X),X) = [1] X + [9]
                  > [1] X + [8]
                  = f(X,a(X))  
        
        
        Following rules are (at-least) weakly oriented:
           f(X,X) =  [2] X + [8] 
                  >= [4]         
                  =  c(X)        
        
        f(X,c(X)) =  [1] X + [12]
                  >= [1] X + [9] 
                  =  f(s(X),X)   
        
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))