Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/4.54)

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)

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	=	g(g(f(x',y')))
	→	g(f(f(g(g(x')),g(g(y'))),f(g(g(x')),g(g(y')))))
	→	f(f(g(g(f(g(g(x')),g(g(y'))))),g(g(f(g(g(x')),g(g(y')))))),f(g(g(f(g(g(x')),g(g(y'))))),g(g(f(g(g(x')),g(g(y')))))))
	=	t₂

where t₂ = C[t₀σ] and σ = {x'/g(g(x')), y'/g(g(y'))} and C = f(f(☐,g(g(f(g(g(x')),g(g(y')))))),f(g(g(f(g(g(x')),g(g(y'))))),g(g(f(g(g(x')),g(g(y')))))))