Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex6_9_Luc02c_L)

The rewrite relation of the following TRS is considered.

2nd(cons(X)) 2nd(cons1(X,X1)) (1)
2nd(cons1(X,cons(Y))) Y (2)
from(X) cons(X) (3)
The evaluation strategy is outermost

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by AProVE @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = 2nd(cons(X))
2nd(cons1(X,2nd(cons(X))))
= t1
where t1 = C[t0] and C = 2nd(cons1(X,))