YES

TRS:

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

max/plus interpretations on N:

  active_A(x1) = max{40, x1}
  active#_A(x1) = max{13, -3 + x1}
  f_A(x1,x2,x3) = max{4, 49 + x1, 13 + x2, 68 + x3}
  f#_A(x1,x2,x3) = max{66, 45 + x1, 4 + x2, 49 + x3}
  a_A = 38
  a#_A = 14
  mark_A(x1) = max{40, 1 + x1}
  mark#_A(x1) = max{0, -1 + x1}
  b_A = 15
  b#_A = 64

precedence:

  f = a > b > mark > active