YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{5, 6 + x1, 8 + x2}
  f#_A(x1,x2) = max{5, 6 + x1, 8 + x2}
  s_A(x1) = max{4, x1}
  s#_A(x1) = max{4, x1}
  a_A(x1) = max{1, x1}
  a#_A(x1) = max{1, x1}
  c_A(x1) = max{3, 3 + x1}
  c#_A(x1) = max{3, 3 + x1}

precedence:

  a > f > c > s