Certification Problem

Input (TPDB TRS_Standard/SK90/4.54)

The rewrite relation of the following TRS is considered.

g(f(x,y))

→

f(f(g(g(x)),g(g(y))),f(g(g(x)),g(g(y))))

(1)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	g(g(f(x8,x9)))
	→	g(f(f(g(g(x8)),g(g(x9))),f(g(g(x8)),g(g(x9)))))
	→	f(f(g(g(f(g(g(x8)),g(g(x9))))),g(g(f(g(g(x8)),g(g(x9)))))),f(g(g(f(g(g(x8)),g(g(x9))))),g(g(f(g(g(x8)),g(g(x9)))))))
	=	t₂

where t₂ = C[t₀σ] and σ = {x9/g(g(x9)), x8/g(g(x8))} and C = f(f(g(g(f(g(g(x8)),g(g(x9))))),g(g(f(g(g(x8)),g(g(x9)))))),f(g(g(f(g(g(x8)),g(g(x9))))),☐))