YES

TRS:

  a__f(a(),X,X) -> a__f(X,a__b(),b())
  a__b() -> a()
  mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
  mark(b()) -> a__b()
  mark(a()) -> a()
  a__f(X1,X2,X3) -> f(X1,X2,X3)
  a__b() -> b()

linear polynomial interpretations on N:

  a__f_A(x1,x2,x3) = x1 + x2 + x3
  a__f#_A(x1,x2,x3) = x1 + x3 + 2
  a_A = 1
  a#_A = 1
  a__b_A = 1
  a__b#_A = 2
  b_A = 0
  b#_A = 0
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 3
  f_A(x1,x2,x3) = x1 + x2 + x3
  f#_A(x1,x2,x3) = x3 + 1

precedence:

  f > mark > a__f > a__b > a > b