YES
(VAR x)
(RULES 
f(f(x)) -> f(d(f(x)))
f(f(x)) -> f(c(f(x)))
)

Proving termination of rewriting for dpqs_1:

-> Dependency pairs:
nF_f(f(x)) -> nF_f(d(f(x)))
nF_f(f(x)) -> nF_f(x)
nF_f(f(x)) -> nF_f(c(f(x)))

-> Proof of termination for dpqs_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

(VAR x)
(RULES 
g(c(1)) -> g(d(0))
g(c(0)) -> g(d(1))
g(d(x)) -> x
g(c(x)) -> x
)

Proving termination of rewriting for dpqs_2:

-> Dependency pairs:
nF_g(c(1)) -> nF_g(d(0))
nF_g(c(0)) -> nF_g(d(1))

-> Proof of termination for dpqs_2:
Termination proved: No cycles in dependency graph.

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.