Problem:
 f(s(X),X) -> f(X,a(X))
 f(X,c(X)) -> f(s(X),X)
 f(X,X) -> c(X)

Proof:
 Complexity Transformation Processor:
  strict:
   f(s(X),X) -> f(X,a(X))
   f(X,c(X)) -> f(s(X),X)
   f(X,X) -> c(X)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [c](x0) = x0,
     
     [a](x0) = x0,
     
     [f](x0, x1) = x0 + x1 + 15,
     
     [s](x0) = x0 + 4
    orientation:
     f(s(X),X) = 2X + 19 >= 2X + 15 = f(X,a(X))
     
     f(X,c(X)) = 2X + 15 >= 2X + 19 = f(s(X),X)
     
     f(X,X) = 2X + 15 >= X = c(X)
    problem:
     strict:
      f(X,c(X)) -> f(s(X),X)
     weak:
      f(s(X),X) -> f(X,a(X))
      f(X,X) -> c(X)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [c](x0) = x0 + 8,
       
       [a](x0) = x0,
       
       [f](x0, x1) = x0 + x1 + 8,
       
       [s](x0) = x0
      orientation:
       f(X,c(X)) = 2X + 16 >= 2X + 8 = f(s(X),X)
       
       f(s(X),X) = 2X + 8 >= 2X + 8 = f(X,a(X))
       
       f(X,X) = 2X + 8 >= X + 8 = c(X)
      problem:
       strict:
        
       weak:
        f(X,c(X)) -> f(s(X),X)
        f(s(X),X) -> f(X,a(X))
        f(X,X) -> c(X)
      Qed