YES
(VAR x)
(RULES 
f(f(x)) -> f(x)
g(0) -> g(f(0))
)

Proving termination of rewriting for _4_20:

-> Dependency pairs:
nF_f(f(x)) -> nF_f(x)
nF_g(0) -> nF_g(f(0))
nF_g(0) -> nF_f(0)

-> Dependency pairs narrowed: 
nF_g(0) -> nF_g(f(0))

-> New dependency pairs: 
There are no new dependency pairs.

-> Proof of termination for _4_20_1:
-> -> Dependency pairs in cycle:
nF_f(f(x)) -> nF_f(x)

Termination proved: Cycles verify subterm criterion.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in DG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.