Certification Problem

Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-4)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	b(a(a(a(b(b(b(x1)))))))
	→	b(a(a(a(a(a(b(b(x1))))))))
	→	b(b(a(a(a(a(b(b(x1))))))))
	→	b(b(b(a(a(a(b(b(x1))))))))
	→	a(a(b(b(a(a(a(b(b(x1)))))))))
	→	a(a(a(a(b(a(a(a(b(b(x1))))))))))
	→	b(a(a(a(b(a(a(a(b(b(x1))))))))))
	→	b(a(a(a(b(a(a(a(a(a(b(x1)))))))))))
	→	b(a(a(a(b(b(a(a(a(a(b(x1)))))))))))
	→	b(a(a(a(b(b(b(a(a(a(b(x1)))))))))))
	=	t₉

where t₉ = t₀σ and σ = {x1/a(a(a(b(x1))))}