Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-530)

The rewrite relation of the following TRS is considered.

a(a(b(x1)))	→	b(c(b(a(a(a(x1))))))	(1)
a(c(x1))	→	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	=	a(a(a(a(b(c(b(a(a(a(x1))))))))))
	→	a(a(b(c(b(a(a(a(c(b(a(a(a(x1)))))))))))))
	→	a(a(b(c(b(a(a(b(b(a(a(a(x1))))))))))))
	→	a(a(b(c(b(b(c(b(a(a(a(b(a(a(a(x1)))))))))))))))
	→	a(a(b(c(b(b(c(b(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))
	→	b(c(b(a(a(a(c(b(b(c(b(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))
	→	b(c(b(a(a(b(b(b(c(b(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))
	→	b(c(b(b(c(b(a(a(a(b(b(c(b(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))
	→	b(c(b(b(c(b(a(b(c(b(a(a(a(b(c(b(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))
	→	b(c(b(b(c(b(a(b(c(b(a(b(c(b(a(a(a(c(b(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))
	→	b(c(b(b(c(b(a(b(c(b(a(b(c(b(a(a(b(b(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))
	→	b(c(b(b(c(b(a(b(c(b(a(b(c(b(b(c(b(a(a(a(b(a(b(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))))
	→	b(c(b(b(c(b(a(b(c(b(a(b(c(b(b(c(b(a(b(c(b(a(a(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))))))))))))))))))))))
	=	t₁₂

where t₁₂ = C[t₀σ] and σ = {x1/a(a(a(x1)))} and C = b(c(b(b(c(b(a(b(c(b(a(b(c(b(b(c(b(a(b(c(b(☐)))))))))))))))))))))