Certification Problem

Input (TPDB TRS_Standard/SK90/2.48)

The rewrite relation of the following TRS is considered.

d(x) e(u(x)) (1)
d(u(x)) c(x) (2)
c(u(x)) b(x) (3)
v(e(x)) x (4)
b(u(x)) a(e(x)) (5)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
d(x) u(e(x)) (6)
u(d(x)) c(x) (7)
u(c(x)) b(x) (8)
e(v(x)) x (9)
u(b(x)) e(a(x)) (10)

1.1 Bounds

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