Certification Problem

Input (TPDB TRS_Standard/CiME_04/dpqs)

The rewrite relation of the following TRS is considered.

f(f(x)) f(c(f(x))) (1)
f(f(x)) f(d(f(x))) (2)
g(c(x)) x (3)
g(d(x)) x (4)
g(c(0)) g(d(1)) (5)
g(c(1)) g(d(0)) (6)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Bounds

The given TRS is match-(raise)-bounded by 2. This is shown by the following automaton.