Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_mixed_05/test10)

The rewrite relation of the following TRS is considered.

h(X,Z) f(X,s(X),Z) (1)
f(X,Y,g(X,Y)) h(0,g(X,Y)) (2)
g(0,Y) 0 (3)
g(X,s(Y)) g(X,Y) (4)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = h(0,g(0,s(0)))
f(0,s(0),g(0,s(0)))
h(0,g(0,s(0)))
= t2
where t2 = t0