YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = 1
  f#_A(x1) = 4
  c_A(x1,x2) = x2 + 1
  c#_A(x1,x2) = 1
  s_A(x1) = x1 + 1
  s#_A(x1) = 0
  g_A(x1) = x1
  g#_A(x1) = x1 + 1

precedence:

  g > c > s > f