YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = 1
  f#_A(x1,x2) = x2
  c_A(x1) = x1 + 4
  c#_A(x1) = 1
  s_A(x1) = 3
  s#_A(x1) = 2

precedence:

  f > c > s