YES

TRS:

  f(s(x),y) -> f(x,s(x))
  f(x,s(y)) -> f(y,x)
  f(c(x),y) -> f(x,s(x))

max/plus interpretations on N:

  f_A(x1,x2) = max{0, 2, 1}
  f#_A(x1,x2) = max{4, 5 + x1, 3 + x2}
  s_A(x1) = max{7, 4 + x1}
  s#_A(x1) = max{1, 2}
  c_A(x1) = max{1, 5 + x1}
  c#_A(x1) = max{0, 0}

precedence:

  s > c > f