YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{1, 4 + x1, 2 + x2}
  f#_A(x1,x2) = max{1, 4 + x1, 2 + x2}
  s_A(x1) = max{6, 6 + x1}
  s#_A(x1) = max{6, 6 + x1}
  c_A(x1) = max{3, 5 + x1}
  c#_A(x1) = max{3, 5 + x1}

precedence:

  c > f > s