YES

TRS:

  a(b(x)) -> b(a(x))
  a(c(x)) -> x

linear polynomial interpretations on N:

  a_A(x1) = x1 + 2
  a#_A(x1) = x1 + 2
  b_A(x1) = x1 + 1
  b#_A(x1) = x1 + 1
  c_A(x1) = x1
  c#_A(x1) = x1

precedence:

  a = c > b