YES(?,O(n^1))

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

Proof:
 RT 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
   interpretation:
    [c](x0) = x0 + 2,
    
    [a](x0) = x0 + 4,
    
    [f](x0, x1) = x0 + x1 + 31,
    
    [s](x0) = x0
   orientation:
    f(s(X),X) = 2X + 31 >= 2X + 35 = f(X,a(X))
    
    f(X,c(X)) = 2X + 33 >= 2X + 31 = f(s(X),X)
    
    f(X,X) = 2X + 31 >= X + 2 = c(X)
   problem:
    strict:
     f(s(X),X) -> f(X,a(X))
    weak:
     f(X,c(X)) -> f(s(X),X)
     f(X,X) -> c(X)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 8,
     
     [a](x0) = x0 + 1,
     
     [f](x0, x1) = x0 + x1 + 8,
     
     [s](x0) = x0 + 8
    orientation:
     f(s(X),X) = 2X + 16 >= 2X + 9 = f(X,a(X))
     
     f(X,c(X)) = 2X + 16 >= 2X + 16 = f(s(X),X)
     
     f(X,X) = 2X + 8 >= X + 8 = c(X)
    problem:
     strict:
      
     weak:
      f(s(X),X) -> f(X,a(X))
      f(X,c(X)) -> f(s(X),X)
      f(X,X) -> c(X)
    Qed