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()

max/plus interpretations on N:

  a__f_A(x1,x2,x3) = max{15, 12 + x1, 6 + x2, 13 + x3}
  a__f#_A(x1,x2,x3) = max{15, 12 + x1, 6 + x2, 13 + x3}
  a_A = 4
  a#_A = 4
  a__b_A = 5
  a__b#_A = 5
  b_A = 1
  b#_A = 1
  mark_A(x1) = max{9, 7 + x1}
  mark#_A(x1) = max{9, 7 + x1}
  f_A(x1,x2,x3) = max{7, 8 + x1, 6 + x2, 6 + x3}
  f#_A(x1,x2,x3) = max{7, 8 + x1, 6 + x2, 6 + x3}

precedence:

  a > a__b > mark > a__f > b = f