YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{0, 0}
  f#_A(x1) = max{6, 5}
  c_A(x1,x2) = max{1, -1, -3 + x2}
  c#_A(x1,x2) = max{1, 2, 4}
  s_A(x1) = max{1, 9 + x1}
  s#_A(x1) = max{3, -4}
  g_A(x1) = max{0, 4 + x1}
  g#_A(x1) = max{0, -1 + x1}

precedence:

  f > c > g > s