Certification Problem

Input (TPDB TRS_Standard/Rubio_04/gmnp)

The rewrite relation of the following TRS is considered.

f(a) f(c(a)) (1)
f(c(X)) X (2)
f(c(a)) f(d(b)) (3)
f(a) f(d(a)) (4)
f(d(X)) X (5)
f(c(b)) f(d(a)) (6)
e(g(X)) e(X) (7)

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.