YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = 1
  f#_A(x1) = x1 + 1
  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 + 3

precedence:

  g > s > f > c