YES

TRS:

  a__f(f(a())) -> c(f(g(f(a()))))
  mark(f(X)) -> a__f(mark(X))
  mark(a()) -> a()
  mark(c(X)) -> c(X)
  mark(g(X)) -> g(mark(X))
  a__f(X) -> f(X)

linear polynomial interpretations on N:

  a__f_A(x1) = x1 + 2
  a__f#_A(x1) = x1 + 2
  f_A(x1) = x1 + 2
  f#_A(x1) = x1 + 2
  a_A = 0
  a#_A = 0
  c_A(x1) = x1
  c#_A(x1) = x1
  g_A(x1) = x1
  g#_A(x1) = x1
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 1

precedence:

  a > mark > a__f > f = c = g