YES

TRS:

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

linear polynomial interpretations on N:

  a_A(x1) = x1 + 3
  a#_A(x1) = x1 + 3
  b_A(x1) = x1 + 2
  b#_A(x1) = x1 + 2

precedence:

  b > a