YES
We show the termination of the TRS R:

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


-- SCC decomposition.

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

p1: g#(s(x)) -> f#(g(x))
p2: g#(s(x)) -> g#(x)

and R consists of:

r1: g(|0|()) -> |0|()
r2: g(s(x)) -> f(g(x))
r3: f(|0|()) -> |0|()

The estimated dependency graph contains the following SCCs:

  {p2}


-- Reduction pair.

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

p1: g#(s(x)) -> g#(x)

and R consists of:

r1: g(|0|()) -> |0|()
r2: g(s(x)) -> f(g(x))
r3: f(|0|()) -> |0|()

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            g#_A(x1) = 0
            s_A(x1) = max{0, x1 - 4}
            g#!_A(x1) = 1
            s!_A(x1) = max{1, x1 - 1}
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            g#_A(x1) = x1
            s_A(x1) = x1 + 3
            g#!_A(x1) = max{3, x1 - 12}
            s!_A(x1) = max{3, x1 - 11}
        
  
    partial status:
  
      pi(g#) = [1]
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.