YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{12, 9, 11 + x2}
  f#_A(x1,x2) = max{2, 2, x2}
  c_A(x1) = max{3, 6 + x1}
  c#_A(x1) = max{2, 2}
  s_A(x1) = max{1, 1}
  s#_A(x1) = max{2, -7 + x1}

precedence:

  f > c > s