YES

TRS:

  f(c(X,s(Y))) -> f(c(s(X),Y))
  g(c(s(X),Y)) -> f(c(X,s(Y)))

max/plus interpretations on N:

  f_A(x1) = max{1, 5 + x1}
  f#_A(x1) = max{1, 1 + x1}
  c_A(x1,x2) = max{1, -2, -3 + x2}
  c#_A(x1,x2) = max{6, -3, -4}
  s_A(x1) = max{9, 5 + x1}
  s#_A(x1) = max{6, -5}
  g_A(x1) = max{0, 14 + x1}
  g#_A(x1) = max{0, 7 + x1}

precedence:

  g > f > c > s