Certification Problem

Input (TPDB TRS_Standard/AProVE_10/isList)

The rewrite relation of the following TRS is considered.

f(tt,x) f(isList(x),x) (1)
isList(Cons(x,xs)) isList(xs) (2)
isList(nil) tt (3)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = f(isList(nil),nil)
f(tt,nil)
f(isList(nil),nil)
= t2
where t2 = t0