YES
(VAR X)
(RULES 
f(f(X)) -> f(a(b(f(X))))
f(a(g(X))) -> b(X)
b(X) -> a(X)
)

Proving termination of rewriting for p266:

-> Dependency pairs:
nF_f(f(X)) -> nF_f(a(b(f(X))))
nF_f(f(X)) -> nF_b(f(X))
nF_f(f(X)) -> nF_f(X)
nF_f(a(g(X))) -> nF_b(X)

-> Proof of termination for p266_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.