YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2 + 3
  f#_A(x1,x2) = x1 + x2 + 3
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1
  a_A(x1) = x1 + 1
  a#_A(x1) = x1 + 1
  c_A(x1) = x1 + 2
  c#_A(x1) = x1 + 2

precedence:

  a > s > c > f