YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{22, 23, 23}
  f#_A(x1,x2) = max{11, 12, 8 + x2}
  c_A(x1) = max{7, 6 + x1}
  c#_A(x1) = max{12, 10 + x1}
  s_A(x1) = max{2, -7}
  s#_A(x1) = max{0, -9 + x1}

precedence:

  f > s > c