YES

We show the termination of the TRS R:

  f(f(x)) -> f(x)
  g(|0|()) -> g(f(|0|()))

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: g#(|0|()) -> g#(f(|0|()))
p2: g#(|0|()) -> f#(|0|())

and R consists of:

r1: f(f(x)) -> f(x)
r2: g(|0|()) -> g(f(|0|()))

The estimated dependency graph contains the following SCCs:

  (no SCCs)