Certification Problem

Input (TPDB SRS_Standard/Secret_06_SRS/1-matchbox)

The rewrite relation of the following TRS is considered.

a(a(b(b(x1))))	→	b(b(b(a(a(a(x1))))))	(1)
a(x1)	→	x1	(2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(a(a(b(b(b(b(b(b(a(b(b(b(x1))))))))))))))
	→	a(a(b(b(b(a(a(a(b(b(b(b(a(b(b(b(x1))))))))))))))))
	→	a(a(b(b(b(a(a(b(b(b(b(a(b(b(b(x1)))))))))))))))
	→	a(a(b(b(b(b(b(b(a(a(a(b(b(a(b(b(b(x1)))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(a(a(a(a(b(b(b(x1)))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(a(b(x1)))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(x1))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(x1)))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(x1))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(a(b(b(x1))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(a(a(a(x1))))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(a(a(x1)))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(a(x1))))))))))))))))))))
	→	a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(x1)))))))))))))))))))
	→	b(b(b(a(a(a(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(x1)))))))))))))))))))))
	→	b(b(b(a(a(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(x1))))))))))))))))))))
	→	b(b(b(b(b(b(a(a(a(b(b(a(b(b(b(b(b(b(a(b(b(b(x1))))))))))))))))))))))
	→	b(b(b(b(b(b(a(a(b(b(a(b(b(b(b(b(b(a(b(b(b(x1)))))))))))))))))))))
	→	b(b(b(b(b(b(b(b(b(a(a(a(a(b(b(b(b(b(b(a(b(b(b(x1)))))))))))))))))))))))
	=	t₁₈

where t₁₈ = C[t₀σ] and σ = {x1/x1} and C = b(b(b(b(b(b(b(b(b(☐)))))))))