Certification Problem

Input (TPDB SRS_Standard/Secret_07_SRS/num-539)

The rewrite relation of the following TRS is considered.

a(a(b(x1)))	→	c(c(a(a(a(x1)))))	(1)
a(c(x1))	→	b(a(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(a(b(b(a(a(a(a(x1)))))))))))
	→	a(a(a(c(c(a(a(a(b(a(a(a(a(x1)))))))))))))
	→	a(a(a(c(c(a(c(c(a(a(a(a(a(a(a(x1)))))))))))))))
	→	a(a(a(c(c(b(a(c(a(a(a(a(a(a(a(x1)))))))))))))))
	→	a(a(a(c(c(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))
	→	a(a(b(a(c(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))
	→	a(a(b(b(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))
	→	c(c(a(a(a(b(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))
	→	c(c(a(c(c(a(a(a(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))))
	→	c(c(b(a(c(a(a(a(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))))
	→	c(c(b(b(a(a(a(a(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))))
	=	t₁₀

where t₁₀ = C[t₀σ] and σ = {x1/a(a(a(a(x1))))} and C = c(c(b(b(☐))))