YES

TRS:

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

max/plus interpretations on N:

  active_A(x1) = max{11, x1}
  active#_A(x1) = max{70, 31 + x1}
  f_A(x1) = max{33, 10 + x1}
  f#_A(x1) = max{93, 33 + x1}
  a_A = 42
  a#_A = 92
  mark_A(x1) = max{1, x1}
  mark#_A(x1) = max{68, 61 + x1}
  c_A(x1) = max{6, 12}
  c#_A(x1) = max{0, 1 + x1}
  g_A(x1) = max{30, 8 + x1}
  g#_A(x1) = max{68, 67}

precedence:

  mark > c > active > g > f > a